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Spectrum - Revised.aux
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Spectrum - Revised.aux
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\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces \relax $\chi ^2\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} as a function of \relax $\ensuremath {\alpha '\tmspace +\medmuskip {.2222em}}\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} and \relax $m\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} for the \relax $(J,M^2)\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} trajectory of the \relax $\rho \relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} (left) and \relax $\omega \relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} (right) mesons. The intercept \relax $a\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} is optimized to get a best fit for each point in the \relax $(\ensuremath {\alpha '\tmspace +\medmuskip {.2222em}},m)\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} plane. \relax $\chi ^2\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} in these plots is normalized so that the value of the optimal linear fit \relax $(m=0)\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} is \relax $\chi ^2 = 1\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}.}}{10}{figure.2}}
\newlabel{fig:chi_3d_light}{{2}{10}{\(\chi ^2\) as a function of \(\alp \) and \(m\) for the \((J,M^2)\) trajectory of the \(\rho \) (left) and \(\omega \) (right) mesons. The intercept \(a\) is optimized to get a best fit for each point in the \((\alp ,m)\) plane. \(\chi ^2\) in these plots is normalized so that the value of the optimal linear fit \((m=0)\) is \(\chi ^2 = 1\)}{figure.2}{}}
\@writefile{toc}{\contentsline {section}{\numberline {4}Fit results}{10}{section.4}}
\@writefile{toc}{\contentsline {paragraph}{A note on units and notation:}{10}{section*.2}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.1}Trajectories in the $(J,M^2)$ plane}{10}{subsection.4.1}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {4.1.1}Light quark mesons}{10}{subsubsection.4.1.1}}
\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces Left: \relax $\chi ^2\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} as a function of two masses for the \relax $K^*\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} trajectory. \relax $a\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} and \relax $\ensuremath {\alpha '\tmspace +\medmuskip {.2222em}}\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} are optimized for each point. The red line is the curve \relax $m_1^{3/2}+m_2^{3/2} = 2\times (160)^{3/2}\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} along which the minimum (approximately) resides. The minimum is \relax $\ensuremath {\chi ^2_m/\chi ^2_l = 0.925}\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} and the entire colored area has \relax $\chi ^2_m/\chi ^2_l < 1\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}. On the right is \relax $\chi ^2\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} as a function of \relax $\ensuremath {\alpha '\tmspace +\medmuskip {.2222em}}\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} and \relax $m\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} for the \relax $(J,M^2)\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} trajectory of the \relax $\phi \relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}. The intercept \relax $a\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} is optimized. The minimum is at \relax $\ensuremath {\alpha '\tmspace +\medmuskip {.2222em}}= 1.07, m = 400\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} with \relax $\chi ^2_m/\chi ^2_l < 10^{-4}\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} at the darkest spot. The lightest colored zone still has \relax $\chi ^2_m/\chi ^2_l < 1\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}, and the coloring is based on a logarithmic scale.}}{11}{figure.3}}
\newlabel{fig:chi_j_strange}{{3}{11}{Left: \(\chi ^2\) as a function of two masses for the \(K^*\) trajectory. \(a\) and \(\alp \) are optimized for each point. The red line is the curve \(m_1^{3/2}+m_2^{3/2} = 2\times (160)^{3/2}\) along which the minimum (approximately) resides. The minimum is \(\rchi {0.925}\) and the entire colored area has \(\chi ^2_m/\chi ^2_l < 1\). On the right is \(\chi ^2\) as a function of \(\alp \) and \(m\) for the \((J,M^2)\) trajectory of the \(\phi \). The intercept \(a\) is optimized. The minimum is at \(\alp = 1.07, m = 400\) with \(\chi ^2_m/\chi ^2_l < 10^{-4}\) at the darkest spot. The lightest colored zone still has \(\chi ^2_m/\chi ^2_l < 1\), and the coloring is based on a logarithmic scale}{figure.3}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {4.1.2}Strange and $s\mathaccentV {bar}016{s}$ mesons}{11}{subsubsection.4.1.2}}
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\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces Top: \relax $\chi ^2\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} as a function of two masses for the \relax $D\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} (left) and \relax $D^*_s\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} (right) trajectories. The coloring is based on a logarithmic scale, with the entire colored area having \relax $\chi ^2_m/\chi ^2_l < 1\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}. The minimum is \ensuremath {\chi ^2_m/\chi ^2_l = 5\times 10^{-4}} for the \relax $D\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}, and \ensuremath {\chi ^2_m/\chi ^2_l = 2\times 10^{-6}} for the \relax $D^*_s\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}. On the bottom are \relax $\chi ^2\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} as a function of \relax $m\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} for the \relax $(J,M^2)\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} trajectory of the \relax $\Psi \relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} (left) and the same for the \relax $\Upsilon \relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} (right). In all plots, \relax $a\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} and \relax $\ensuremath {\alpha '\tmspace +\medmuskip {.2222em}}\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} are optimized for each choice of the endpoint masses.}}{13}{figure.4}}
\newlabel{fig:chi_j_heavy}{{4}{13}{Top: \(\chi ^2\) as a function of two masses for the \(D\) (left) and \(D^*_s\) (right) trajectories. The coloring is based on a logarithmic scale, with the entire colored area having \(\chi ^2_m/\chi ^2_l < 1\). The minimum is \rchi {5\ten {-4}} for the \(D\), and \rchi {2\ten {-6}} for the \(D^*_s\). On the bottom are \(\chi ^2\) as a function of \(m\) for the \((J,M^2)\) trajectory of the \(\Psi \) (left) and the same for the \(\Upsilon \) (right). In all plots, \(a\) and \(\alp \) are optimized for each choice of the endpoint masses}{figure.4}{}}
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\@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces Nine \relax $(J,M^2)\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} trajectories fitted using universal quark masses and slope (\relax $m_{u/d}= 60\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}, \relax $m_s = 220\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}, \relax $m_c = 1500\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}, and \relax $\ensuremath {\alpha '\tmspace +\medmuskip {.2222em}}= 0.884\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}). Top left: \relax $\pi \relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} and \relax $\rho \relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}, top right: \relax $\eta \relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} and \relax $\omega \relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}, bottom left: \relax $K^*\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} and \relax $\phi \relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}, bottom right: \relax $D\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}, \relax $D^*_s\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}, and \relax $\Psi \relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}.}}{14}{figure.5}}
\newlabel{fig:multiFit_j}{{5}{14}{Nine \((J,M^2)\) trajectories fitted using universal quark masses and slope (\(\mud = 60\), \(m_s = 220\), \(m_c = 1500\), and \(\alp = 0.884\)). Top left: \(\pi \) and \(\rho \), top right: \(\eta \) and \(\omega \), bottom left: \(K^*\) and \(\phi \), bottom right: \(D\), \(D^*_s\), and \(\Psi \)}{figure.5}{}}
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\@writefile{toc}{\contentsline {subsubsection}{\numberline {4.2.1}Light quark mesons}{15}{subsubsection.4.2.1}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {4.2.2}$s\mathaccentV {bar}016{s}$ mesons}{15}{subsubsection.4.2.2}}
\@writefile{lof}{\contentsline {figure}{\numberline {6}{\ignorespaces \relax $\chi ^2\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} vs. \relax $m_{u/d}\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} and \relax $\ensuremath {\alpha '\tmspace +\medmuskip {.2222em}}\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} for the \relax $h_1\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} (left) and \relax $\omega \relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} (\relax $J=1\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} states alone, right) trajectories. For the \relax $h_1\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} only the darkest area has \relax $\chi ^2_m/\chi ^2_l < 1\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}, while for the \relax $\omega \relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} the entire colored area offers better than linear fits and the minimum has \ensuremath {\chi ^2_m/\chi ^2_l = 0.51}.}}{16}{figure.6}}
\newlabel{fig:chi_n_h1_omg}{{6}{16}{\(\chi ^2\) vs. \(\mud \) and \(\alp \) for the \(h_1\) (left) and \(\omega \) (\(J=1\) states alone, right) trajectories. For the \(h_1\) only the darkest area has \(\chi ^2_m/\chi ^2_l < 1\), while for the \(\omega \) the entire colored area offers better than linear fits and the minimum has \rchi {0.51}}{figure.6}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {7}{\ignorespaces Left: \relax $\chi ^2\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} vs. \relax $m_s\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} for the radial trajectory of the \relax $s\mathaccentV {bar}016{s}\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} \relax $\phi \relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}, with optimum at \relax $m_s = 515\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}. Right: Radial trajectory of the \relax $c\mathaccentV {bar}016{c}\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} \relax $\Psi \relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} meson, \relax $\chi ^2\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} vs. \relax $\ensuremath {\alpha '\tmspace +\medmuskip {.2222em}}\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} and \relax $m_c\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}.}}{16}{figure.7}}
\newlabel{fig:chi_n_sc}{{7}{16}{Left: \(\chi ^2\) vs. \(m_s\) for the radial trajectory of the \(\ssb \) \(\phi \), with optimum at \(m_s = 515\). Right: Radial trajectory of the \(\ccb \) \(\Psi \) meson, \(\chi ^2\) vs. \(\alp \) and \(m_c\)}{figure.7}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {8}{\ignorespaces Left: \relax $\chi ^2\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} as a function of \relax $\ensuremath {\alpha '\tmspace +\medmuskip {.2222em}}\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} and \relax $m_b\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} for the \relax $\Upsilon \relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} radial trajectory. The discontinuity in the plot arises from the condition that the intercept \relax $a \leq 1\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}, otherwise the mass of the ground state is undefined. The two areas in the plot are then where \relax $a\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} is still allowed to change (left) and where \relax $a\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} is blocked from increasing further and is fixed at \relax $a = 1\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} (oval shape on the right). Right: \relax $\chi ^2\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} as a function of \relax $m_b\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} for the \relax $\chi _b\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} trajectory.}}{17}{figure.8}}
\newlabel{fig:chi_n_bb}{{8}{17}{Left: \(\chi ^2\) as a function of \(\alp \) and \(m_b\) for the \(\Upsilon \) radial trajectory. The discontinuity in the plot arises from the condition that the intercept \(a \leq 1\), otherwise the mass of the ground state is undefined. The two areas in the plot are then where \(a\) is still allowed to change (left) and where \(a\) is blocked from increasing further and is fixed at \(a = 1\) (oval shape on the right). Right: \(\chi ^2\) as a function of \(m_b\) for the \(\chi _b\) trajectory}{figure.8}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {4.2.3}$c\mathaccentV {bar}016{c}$ mesons}{17}{subsubsection.4.2.3}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {4.2.4}$b\mathaccentV {bar}016{b}$ mesons}{17}{subsubsection.4.2.4}}
\@writefile{lof}{\contentsline {figure}{\numberline {9}{\ignorespaces \relax $\chi ^2\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} as a function of \relax $m_{u/d}\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} for the \relax $h_1\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} trajectory (left) and for the \relax $\omega \relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} trajectory (right). \relax $\ensuremath {\alpha '\tmspace +\medmuskip {.2222em}}\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} and \relax $a\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} are always optimized.}}{18}{figure.9}}
\newlabel{fig:chi_w_ud}{{9}{18}{\(\chi ^2\) as a function of \(\mud \) for the \(h_1\) trajectory (left) and for the \(\omega \) trajectory (right). \(\alp \) and \(a\) are always optimized}{figure.9}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.3}WKB fits}{18}{subsection.4.3}}
\@writefile{lof}{\contentsline {figure}{\numberline {10}{\ignorespaces \relax $\chi ^2\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} as a function of \relax $m_s\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} for the \relax $\phi \relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} radial trajectory (top left), as a function of \relax $m_c\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} for the \relax $\Psi \relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} trajectory (top right), and as a function of \relax $m_b\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} for the \relax $\Upsilon \relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} (bottom left) and \relax $\chi _b\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} (bottom right) trajectories. The values obtained are \relax $m_s = 515\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} MeV and \relax $m_c = 1500\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} MeV. \relax $m_b = 4735\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} or \relax $4825\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} MeV. \relax $\ensuremath {\alpha '\tmspace +\medmuskip {.2222em}}\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} and \relax $a\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} are always optimized.}}{19}{figure.10}}
\newlabel{fig:chi_w_scb}{{10}{19}{\(\chi ^2\) as a function of \(m_s\) for the \(\phi \) radial trajectory (top left), as a function of \(m_c\) for the \(\Psi \) trajectory (top right), and as a function of \(m_b\) for the \(\Upsilon \) (bottom left) and \(\chi _b\) (bottom right) trajectories. The values obtained are \(m_s = 515\) MeV and \(m_c = 1500\) MeV. \(m_b = 4735\) or \(4825\) MeV. \(\alp \) and \(a\) are always optimized}{figure.10}{}}
\@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces The results of the meson fits in the \relax $(J,M^2)\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} plane. For the uneven \relax $K^*\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} fit the higher values of \relax $m_s\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} require \relax $m_{u/d}\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} to take a correspondingly low value. \relax $m_{u/d}+ m_s\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} never exceeds 480 MeV, and the highest masses quoted for the \relax $s\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} are obtained when \relax $m_{u/d}= 0\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}. The ranges listed are those where \relax $\chi ^2\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} is within 10\% of its optimal value. \relax $N\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} is the number of data points in the trajectory.}}{20}{table.1}}
\newlabel{tab:mes_j}{{1}{20}{The results of the meson fits in the \((J,M^2)\) plane. For the uneven \(K^*\) fit the higher values of \(m_s\) require \(\mud \) to take a correspondingly low value. \(\mud + m_s\) never exceeds 480 MeV, and the highest masses quoted for the \(s\) are obtained when \(\mud = 0\). The ranges listed are those where \(\chi ^2\) is within 10\% of its optimal value. \(N\) is the number of data points in the trajectory}{table.1}{}}
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\@writefile{lot}{\contentsline {table}{\numberline {2}{\ignorespaces The results of the meson fits in the \relax $(n,M^2)\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} plane. The ranges listed are those where \relax $\chi ^2\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} is within 10\% of its optimal value. \relax $N\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} is the number of data points in the trajectory.}}{21}{table.2}}
\newlabel{tab:mes_n}{{2}{21}{The results of the meson fits in the \((n,M^2)\) plane. The ranges listed are those where \(\chi ^2\) is within 10\% of its optimal value. \(N\) is the number of data points in the trajectory}{table.2}{}}
\@writefile{lot}{\contentsline {table}{\numberline {3}{\ignorespaces The results of the meson WKB fits, all in the \relax $(n,M^2)\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} plane. The ranges listed are those where \relax $\chi ^2\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} is within 10\% of its optimal value. \relax $N\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} is the number of data points in the trajectory.}}{21}{table.3}}
\newlabel{tab:mes_w}{{3}{21}{The results of the meson WKB fits, all in the \((n,M^2)\) plane. The ranges listed are those where \(\chi ^2\) is within 10\% of its optimal value. \(N\) is the number of data points in the trajectory}{table.3}{}}
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\@writefile{lot}{\contentsline {table}{\numberline {4}{\ignorespaces The ranges of the intercept from tables (\ref {tab:mes_j})-(\ref {tab:mes_w}) adjusted to fits to \relax $n+L\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}. The right-most column is for the WKB fits and the other two the regular massive fits.}}{22}{table.4}}
\newlabel{tab:l_vs_j}{{4}{22}{The ranges of the intercept from tables (\ref {tab:mes_j})-(\ref {tab:mes_w}) adjusted to fits to \(n+L\). The right-most column is for the WKB fits and the other two the regular massive fits}{table.4}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.5}L vs. J and the values of the intercept}{22}{subsection.4.5}}
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\newlabel{tab:lengths}{{5}{23}{\(l_s/\sqrt {\alp }\) for all the states used in the \((J,M^2)\) trajectories (arranged here by their orbital angular momentum \(L\)). For each trajectory, the length was calculated at the mass in the midpoint of the range given in summary table (\ref {tab:mes_j}), except for the \(K^*\), where we used \(\mud = 60\), \(m_s = 220\)}{table.5}{}}
\@writefile{toc}{\contentsline {section}{\numberline {5}Summary}{23}{section.5}}
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\citation{AHSY}
\citation{Peeters:2005fq}
\citation{oai:arXiv.org:hep-th/0311190}
\citation{PDG:2012}
\citation{Collins:book}
\citation{Eichten:2007qx}
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\@writefile{lot}{\contentsline {table}{\numberline {6}{\ignorespaces The states used in the \relax $(J,M^2)\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} trajectory fits and their PDG status. States marked with a bullet are the established states appearing in the summary tables, while those marked with an `f.' are the less established mesons classified as ``further states''. [a] The \relax $D^J(2740)\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} is a newly observed state, not yet listed by the PDG.}}{28}{table.6}}
\newlabel{tab:states_j}{{6}{28}{The states used in the \((J,M^2)\) trajectory fits and their PDG status. States marked with a bullet are the established states appearing in the summary tables, while those marked with an `f.' are the less established mesons classified as ``further states''. [a] The \(D^J(2740)\) is a newly observed state, not yet listed by the PDG}{table.6}{}}
\@writefile{toc}{\contentsline {section}{\numberline {A}Individual trajectory fits}{28}{appendix.A}}
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\@writefile{toc}{\contentsline {subsection}{\numberline {A.1}The states used in the fits}{28}{subsection.A.1}}
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\citation{Eichten:2007qx}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {A.1.2}The $(n,M^2)$ trajectories}{30}{subsubsection.A.1.2}}
\@writefile{lot}{\contentsline {table}{\numberline {7}{\ignorespaces The states used in the \relax $(n,M^2)\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} trajectory fits. Note that we assign \relax $n = 0\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} to the ground state rather than \relax $n = 1\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}.}}{32}{table.7}}
\newlabel{tab:states_n}{{7}{32}{The states used in the \((n,M^2)\) trajectory fits. Note that we assign \(n = 0\) to the ground state rather than \(n = 1\)}{table.7}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {A.2}Trajectories in the $(J,M^2)$ plane}{32}{subsection.A.2}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {A.2.1}Light quark mesons}{32}{subsubsection.A.2.1}}
\@writefile{toc}{\contentsline {paragraph}{\relax $I = 1\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}. The \relax $\pi /b\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} trajectory:}{33}{section*.4}}
\@writefile{toc}{\contentsline {paragraph}{\relax $I = 1\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}. The \relax $\rho /a\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} trajectory:}{33}{section*.5}}
\@writefile{toc}{\contentsline {paragraph}{\relax $I = 0\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}. The \relax $\eta /h\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} trajectory:}{33}{section*.6}}
\@writefile{lof}{\contentsline {figure}{\numberline {11}{\ignorespaces The \relax $I = 1\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} light quark trajectories. Left: the \relax $\pi /b\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} and optimal massive fit with \relax $m = 170\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}. The red marker represents the pion, not used in the analysis. The plot on the right is the \relax $\rho /a\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} trajectory and fit with \relax $m = 65\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}. The blue lines are the trajectories with massive endpoints, dashed black lines are the linear fits.}}{34}{figure.11}}
\newlabel{fig:pi_rho}{{11}{34}{The \(I = 1\) light quark trajectories. Left: the \(\pi /b\) and optimal massive fit with \(m = 170\). The red marker represents the pion, not used in the analysis. The plot on the right is the \(\rho /a\) trajectory and fit with \(m = 65\). The blue lines are the trajectories with massive endpoints, dashed black lines are the linear fits}{figure.11}{}}
\@writefile{toc}{\contentsline {paragraph}{\relax $I = 0\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}. The \relax $\omega /f\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} trajectory:}{34}{section*.7}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {A.2.2}Strange and $s\mathaccentV {bar}016{s}$ mesons}{34}{subsubsection.A.2.2}}
\@writefile{toc}{\contentsline {paragraph}{Strange. The \relax $K^*\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} trajectory:}{34}{section*.8}}
\citation{Aaij:2013sza}
\citation{Wang:2013tka}
\@writefile{lof}{\contentsline {figure}{\numberline {12}{\ignorespaces The \relax $I = 0\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} light quark trajectories. The \relax $\eta /h\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} are on the left, \relax $\omega /f\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} on the right. For both trajectories the linear fit (dashed black line) is optimal, but we also plot a massive fit with \relax $m = 60\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} for both trajectories (blue line).}}{35}{figure.12}}
\newlabel{fig:eta_omega}{{12}{35}{The \(I = 0\) light quark trajectories. The \(\eta /h\) are on the left, \(\omega /f\) on the right. For both trajectories the linear fit (dashed black line) is optimal, but we also plot a massive fit with \(m = 60\) for both trajectories (blue line)}{figure.12}{}}
\@writefile{toc}{\contentsline {paragraph}{\relax $s\mathaccentV {bar}016{s}\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}. The \relax $\phi /f'\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} trajectory:}{35}{section*.9}}
\@writefile{lof}{\contentsline {figure}{\numberline {13}{\ignorespaces The trajectories involving an \relax $s\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} quark. On the left is \relax $K^*\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}, with the fit where \relax $m_{u/d} = 60\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} and \relax $m_s = 220\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}. On the left is \relax $\phi \relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} with its optimal fit of \relax $m_s = 400\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}. The blue lines are the trajectories with massive endpoints, dashed black lines are the linear fits.}}{36}{figure.13}}
\newlabel{fig:k_phi}{{13}{36}{The trajectories involving an \(s\) quark. On the left is \(K^*\), with the fit where \(m_{u/d} = 60\) and \(m_s = 220\). On the left is \(\phi \) with its optimal fit of \(m_s = 400\). The blue lines are the trajectories with massive endpoints, dashed black lines are the linear fits}{figure.13}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {A.2.3}Charmed, Charmed/Strange, and $c\mathaccentV {bar}016{c}$ mesons}{36}{subsubsection.A.2.3}}
\@writefile{toc}{\contentsline {paragraph}{Charmed. The \relax $D\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} trajectory:}{36}{section*.10}}
\citation{Eichten:2007qx}
\@writefile{lof}{\contentsline {figure}{\numberline {14}{\ignorespaces The charmed meson trajectories. On the left is \relax $D\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} with the massive fit \relax $m_{u/d} = 80\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} and \relax $m_c = 1640\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}, and on the right is the charmed/strange \relax $D^*_s\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}, with its fit of \relax $m_s = 400\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}, \relax $m_c = 1580\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}. The blue lines are the trajectories with massive endpoints, dashed black lines are the linear fits.}}{37}{figure.14}}
\newlabel{fig:d_ds}{{14}{37}{The charmed meson trajectories. On the left is \(D\) with the massive fit \(m_{u/d} = 80\) and \(m_c = 1640\), and on the right is the charmed/strange \(D^*_s\), with its fit of \(m_s = 400\), \(m_c = 1580\). The blue lines are the trajectories with massive endpoints, dashed black lines are the linear fits}{figure.14}{}}
\@writefile{toc}{\contentsline {paragraph}{Charmed/Strange. The \relax $D^*_s\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} trajectory}{37}{section*.11}}
\@writefile{toc}{\contentsline {paragraph}{\relax $c\mathaccentV {bar}016{c}\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}. The \relax $\Psi \relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} trajectory:}{37}{section*.12}}
\@writefile{lof}{\contentsline {figure}{\numberline {15}{\ignorespaces The \relax $c\mathaccentV {bar}016{c}\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} \relax $\Psi \relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} (left) and \relax $b\mathaccentV {bar}016{b}\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} \relax $\Upsilon \relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} (right) trajectories with the massive fits \relax $m_c = 1500\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} and \relax $m_b = 4730\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} respectively. The blue line is the fit with massive endpoints, dashed black line the linear fit.}}{38}{figure.15}}
\newlabel{fig:psi_ups}{{15}{38}{The \(\ccb \) \(\Psi \) (left) and \(\bbb \) \(\Upsilon \) (right) trajectories with the massive fits \(m_c = 1500\) and \(m_b = 4730\) respectively. The blue line is the fit with massive endpoints, dashed black line the linear fit}{figure.15}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {A.2.4}$b\mathaccentV {bar}016{b}$ mesons}{38}{subsubsection.A.2.4}}
\@writefile{toc}{\contentsline {paragraph}{\relax $b\mathaccentV {bar}016{b}\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}. The \relax $\Upsilon \relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} trajectory:}{38}{section*.13}}
\@writefile{lof}{\contentsline {figure}{\numberline {16}{\ignorespaces Left: the \relax $\pi \relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} and \relax $\pi _2\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} with the massive fit \relax $m_{u/d}= 105\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}. Right: the \relax $a_1\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} with its fit for \relax $m_{u/d}= 100\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}.}}{39}{figure.16}}
\newlabel{fig:pi_a1}{{16}{39}{Left: the \(\pi \) and \(\pi _2\) with the massive fit \(\mud = 105\). Right: the \(a_1\) with its fit for \(\mud = 100\)}{figure.16}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {A.3}Trajectories in the $(n,M^2)$ plane}{39}{subsection.A.3}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {A.3.1}Light quark mesons}{39}{subsubsection.A.3.1}}
\@writefile{toc}{\contentsline {paragraph}{\relax $I = 1\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}. The \relax $\pi \relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} trajectory:}{39}{section*.14}}
\@writefile{toc}{\contentsline {paragraph}{\relax $I = 1\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}. The \relax $a_1\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} trajectory:}{40}{section*.15}}
\@writefile{toc}{\contentsline {paragraph}{\relax $I = 0\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}. The \relax $h_1\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} trajectory:}{40}{section*.16}}
\@writefile{lof}{\contentsline {figure}{\numberline {17}{\ignorespaces Left: the \relax $h_1\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} with the massive fit \relax $m_{u/d}= 75\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}. Right: the \relax $\omega \relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} and \relax $\omega _3\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} with their optimal fit of \relax $m_{u/d}= 305\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}.}}{41}{figure.17}}
\newlabel{fig:h1_omega}{{17}{41}{Left: the \(h_1\) with the massive fit \(\mud = 75\). Right: the \(\omega \) and \(\omega _3\) with their optimal fit of \(\mud = 305\)}{figure.17}{}}
\@writefile{toc}{\contentsline {paragraph}{\relax $I = 0\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}. The \relax $\omega \relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} trajectories:}{41}{section*.17}}
\@writefile{lof}{\contentsline {figure}{\numberline {18}{\ignorespaces Left: the \relax $s\mathaccentV {bar}016{s}\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} \relax $\phi \relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} radial trajectory with the massive fit \relax $m_s = 515\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}. The red marker is the state \relax $\omega (1960)\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}, which has the right quantum numbers and mass for the fit but is classified a (primarily) \relax $u/d\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} state, and not \relax $s\mathaccentV {bar}016{s}\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}. Right: the \relax $c\mathaccentV {bar}016{c}\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} \relax $\Psi \relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} trajectory with an optimal massive fit of \relax $m_c = 1425\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}.}}{42}{figure.18}}
\newlabel{fig:phi_psi}{{18}{42}{Left: the \(\ssb \) \(\phi \) radial trajectory with the massive fit \(m_s = 515\). The red marker is the state \(\omega (1960)\), which has the right quantum numbers and mass for the fit but is classified a (primarily) \(u/d\) state, and not \(\ssb \). Right: the \(\ccb \) \(\Psi \) trajectory with an optimal massive fit of \(m_c = 1425\)}{figure.18}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {A.3.2}$s\mathaccentV {bar}016{s}$ mesons}{42}{subsubsection.A.3.2}}
\@writefile{toc}{\contentsline {paragraph}{\relax $s\mathaccentV {bar}016{s}\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}. The \relax $\phi \relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} trajectory:}{42}{section*.18}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {A.3.3}$c\mathaccentV {bar}016{c}$ mesons}{43}{subsubsection.A.3.3}}
\@writefile{toc}{\contentsline {paragraph}{\relax $c\mathaccentV {bar}016{c}\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}. The \relax $\Psi \relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} trajectory:}{43}{section*.19}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {A.3.4}$b\mathaccentV {bar}016{b}$ mesons}{43}{subsubsection.A.3.4}}
\@writefile{toc}{\contentsline {paragraph}{\relax $b\mathaccentV {bar}016{b}\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}. The \relax $\Upsilon \relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} trajectory:}{43}{section*.20}}
\@writefile{lof}{\contentsline {figure}{\numberline {19}{\ignorespaces The \relax $b\mathaccentV {bar}016{b}\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} trajectories and massive fits. Left: \relax $\Upsilon \relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} with its optimal fit of \relax $m_b = 4730\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}. Right: the \relax $\chi _b\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} with \relax $m_b = 4800\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}.}}{44}{figure.19}}
\newlabel{fig:ups_chib}{{19}{44}{The \(\bbb \) trajectories and massive fits. Left: \(\Upsilon \) with its optimal fit of \(m_b = 4730\). Right: the \(\chi _b\) with \(m_b = 4800\)}{figure.19}{}}
\@writefile{toc}{\contentsline {paragraph}{\relax $b\mathaccentV {bar}016{b}\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}. The \relax $\chi _b\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} trajectory:}{44}{section*.21}}
\@writefile{toc}{\contentsline {paragraph}{WKB fit plots:}{44}{section*.22}}
\@writefile{lof}{\contentsline {figure}{\numberline {20}{\ignorespaces The light quark trajectories with their optimal WKB fits. Top left: \relax $\pi \relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} (\relax $0^{-+}\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}) and \relax $\pi _2\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} (\relax $2^{-+}\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}). Top right: \relax $a_1\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} (\relax $1^{++}\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}). Bottom left: \relax $h_1\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} (\relax $1^{+-}\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}). Bottom right: \relax $\omega \relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} (\relax $1^{--}\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}) and \relax $\omega _3\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} (\relax $3^{--}\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}).}}{45}{figure.20}}
\newlabel{fig:wkb_light}{{20}{45}{The light quark trajectories with their optimal WKB fits. Top left: \(\pi \) (\(0^{-+}\)) and \(\pi _2\) (\(2^{-+}\)). Top right: \(a_1\) (\(1^{++}\)). Bottom left: \(h_1\) (\(1^{+-}\)). Bottom right: \(\omega \) (\(1^{--}\)) and \(\omega _3\) (\(3^{--}\))}{figure.20}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {21}{\ignorespaces The heavier quark trajectories with their optimal WKB fits. Top left: \relax $\phi \relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} (\relax $s\mathaccentV {bar}016{s}\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}, \relax $1^{--}\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}). Top right: \relax $\psi \relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} (\relax $c\mathaccentV {bar}016{c}\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}, \relax $1^{--}\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}). Bottom left: \relax $\upsilon \relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} (\relax $b\mathaccentV {bar}016{b}\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} \relax $1^{--}\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}). Bottom right: \relax $\chi _b\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} (\relax $b\mathaccentV {bar}016{b}\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}, \relax $1^{++}\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}).}}{46}{figure.21}}
\newlabel{fig:wkb_heavy}{{21}{46}{The heavier quark trajectories with their optimal WKB fits. Top left: \(\phi \) (\(\ssb \), \(1^{--}\)). Top right: \(\psi \) (\(\ccb \), \(1^{--}\)). Bottom left: \(\upsilon \) (\(\bbb \) \(1^{--}\)). Bottom right: \(\chi _b\) (\(\bbb \), \(1^{++}\))}{figure.21}{}}
\@writefile{lot}{\contentsline {table}{\numberline {8}{\ignorespaces Comparison of calculated and measured masses for all the states used in the universal trajectory fit. There are 38 states in total, and 13 fitting parameters (one slope, 3 quark endpoint masses, and 9 intercepts). We use the values \relax $m_{u/d} = 60\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}, \relax $m_s = 220\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}, and \relax $m_c = 1500\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} MeV for the masses, \relax $\ensuremath {\alpha '\tmspace +\medmuskip {.2222em}}= 0.884\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} GeV\relax $^{-2}\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} for the slope. For the \relax $c\mathaccentV {bar}016{c}\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} \relax $\Psi \relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} we use states with equal \relax $J\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}, but increasing \relax $L\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}.}}{47}{table.8}}
\newlabel{tab:universal_masses}{{8}{47}{Comparison of calculated and measured masses for all the states used in the universal trajectory fit. There are 38 states in total, and 13 fitting parameters (one slope, 3 quark endpoint masses, and 9 intercepts). We use the values \(m_{u/d} = 60\), \(m_s = 220\), and \(m_c = 1500\) MeV for the masses, \(\alp = 0.884\) GeV\(^{-2}\) for the slope. For the \(c\bar {c}\) \(\Psi \) we use states with equal \(J\), but increasing \(L\)}{table.8}{}}
\@writefile{toc}{\contentsline {section}{\numberline {B}Universal fit: Calculated vs. measured masses}{47}{appendix.B}}
\newlabel{app:universal}{{B}{47}{Universal fit: Calculated vs. measured masses}{appendix.B}{}}
\@writefile{toc}{\contentsline {section}{\numberline {C}Predictions for higher states}{47}{appendix.C}}
\@writefile{lot}{\contentsline {table}{\numberline {9}{\ignorespaces Predictions for the next states in the \relax $(J,M^2)\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} plane based on the optimal massive fits, with their \relax $J^{PC}\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} and mass (in MeV) values. The ranges listed correspond to the ranges in table (\ref {tab:mes_j}).}}{48}{table.9}}
\newlabel{tab:predictions}{{9}{48}{Predictions for the next states in the \((J,M^2)\) plane based on the optimal massive fits, with their \(J^{PC}\) and mass (in MeV) values. The ranges listed correspond to the ranges in table (\ref {tab:mes_j})}{table.9}{}}
\@writefile{lot}{\contentsline {table}{\numberline {10}{\ignorespaces Predictions for the next states in the \relax $(n,M^2)\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} plane based on the optimal massive fits. We use an assignment where the ground state has \relax $n = 0\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}, and masses are in MeV. For the \relax $\phi \relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}, where we have assigned the three known states the values \relax $n = 0\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}, \relax $1\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}, and \relax $3\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.}, one of the masses is that of the missing \relax $n = 2\relax \GenericError { }{LaTeX Error: Bad math environment delimiter}{See the LaTeX manual or LaTeX Companion for explanation.}{Your command was ignored.\MessageBreak Type I <command> <return> to replace it with another command,\MessageBreak or <return> to continue without it.} state. The ranges listed correspond to the ranges in table (\ref {tab:mes_n}).}}{48}{table.10}}
\newlabel{tab:predictions_n}{{10}{48}{Predictions for the next states in the \((n,M^2)\) plane based on the optimal massive fits. We use an assignment where the ground state has \(n = 0\), and masses are in MeV. For the \(\phi \), where we have assigned the three known states the values \(n = 0\), \(1\), and \(3\), one of the masses is that of the missing \(n = 2\) state. The ranges listed correspond to the ranges in table (\ref {tab:mes_n})}{table.10}{}}
\bibstyle{JHEP}
\bibdata{Spectrum}