Width effects in resonant three-body decays: $B$ decay as an example

TL;DR

This paper addresses how to accurately extract quasi-two-body decay rates in three-body hadron decays involving broad resonances, highlighting the significance of finite width effects and providing correction factors for theoretical and experimental comparisons.

Contribution

It introduces a method to properly account for finite width effects in three-body decays, improving the accuracy of decay rate extractions and comparisons with theoretical models.

Findings

Finite width effects can cause up to 40% deviation in scalar resonance decays.

Correction factors are computed within the QCD factorization framework.

Differences are generally below 10% for tensor and vector resonances.

Abstract

For three-body hadron decays mediated by intermediate resonances with large widths, we show how to properly extract the quasi-two-body decay rates for a meaningful comparison with the corresponding theoretical estimates, using several $B$ decays as explicit examples. We compute the correction factor from finite width effects in the QCD factorization approach, and make a comparison with that using the experimental parameterization in which the momentum dependence in the weak dynamics is absent. Although the difference is generally less than $10\%$ for tensor and vector resonances, it can be as large as $(25-40)\%$ for scalar resonances. Our finding can in fact be applied to general quasi-two-body decays.