fix: compute |ɑ| correctly

[redeboer]

$\left|\overline{\alpha}\right|$ is now computed from the average $\overline{\alpha_j}$. Statistical uncertainties are added in quadrature and the systematic uncertainties are computed by evaluating $\left|\overline{\alpha}\right|$ for the extrema of $\overline{\alpha_j}$.

$$ \begin{split} \begin{array}{ccr} \overline{\alpha_x} & = & \left(-62.6 \pm 6.4_{-14.8}^{+8.4} \right) \times 10^{-3} \\ \overline{\alpha_y} & = & \left(+8.9 \pm 8.5_{-12.7}^{+9.1} \right) \times 10^{-3} \\ \overline{\alpha_z} & = & \left(-278.0 \pm 21.3_{-40.4}^{+12.6} \right) \times 10^{-3} \\ \color{red}\left|\overline{\alpha}\right| & \color{red}= & \color{red}\left(285.1 \pm 23.8_{-42.6}^{+13.6} \right) \times 10^{-3} \\ \color{gray}\overline{\left|\alpha\right|} & \color{gray}= & \color{gray}\left(629.3 \pm 7.0_{-12.4}^{+13.2} \right) \times 10^{-3} \\ \end{array} \end{split} $$

See also #136 (comment)

[redeboer]

@mmikhasenko is this the correct way?

[mmikhasenko]

The value of $\overline{|\vec{\alpha}|}$ looks silghtly smaller than in the LHCb paper.
0.63 here, and 0.66 for LHCb. Let's check the code together.

[redeboer]

The new value, using the equation for $\overline{\left|\alpha\right|}^2 = S_0^2$ from #138 (comment):

$$ \overline{\left|\alpha\right|} = \left(669.4 \pm 6.9_{-10.4}^{+15.3} \right) \times 10^{-3} $$