Redundant normalisation factor when Blatt-Weisskopf is used as form factor?

[redeboer]

Currently, BlattWeisskopfSquared is used in two places (see links for the math):

1. as a ratio in EnergyDependentWidth, which implements PDG2021 Equation (50.28).
2. as a form factor in lineshapes that also parametrise production processes, like relativistic_breit_wigner_with_ff(), which originates form Eqs. (50.23), (50.24), and (50.26).

Now, in Equation (50.27), Blatt-Weisskopf factors are not normalised (numerator is always 1), while AmpForm's BlattWeisskopfSquared is normalised (numerator goes as z^L and there is a factor that ensures B_L(1)=1). This is okay in 1., because the momentum ratio q/q₀ that appears in Eq. (50.28) is absorbed into the ratio of the two (normalised) BlattWeisskopfSquared factors and the normalisation constants cancel out. Similarly, for 2., BlattWeisskopfSquared essentially plays the rôle of na of Eq. (50.26) by absorbing (qa/q₀)^L. The only problem, though, is that the normalisation constant for higher L does not cancel out when BlattWeisskopfSquared is used as a form factor. This has an effect in the determination of the couplings through Eq. (50.24).¹

The question is therefore, what to do about the normalisation constants for higher angular momenta when BlattWeisskopfSquared is used as a form factor for production processes?

Footnotes

1. This is also relevant for the K-matrix, see e.g. Eq. (50.29). ↩

[redeboer]

Additional constant is indeed absorbed into 𝛼 of Equation (50.24).