Chiral Dynamics and S-wave contributions in Semileptonic $D_s/B_s$ decays into $\pi^+\pi^-$

TL;DR

This paper investigates the S-wave contributions in semileptonic $D_s$ and $B_s$ decays into $^+^-$ pairs, using chiral dynamics and sum rules to predict decay widths and compare with experimental data.

Contribution

It introduces a combined approach using unitarized chiral perturbation theory and light-cone sum rules to analyze $^+^-$ contributions in $D_s$ and $B_s$ decays, providing new theoretical predictions.

Findings

Good agreement with experimental decay data

Predicted differential decay widths consistent with observations

Validated the use of scalar form factors from chiral theories

Abstract

In this work, we study the semileptonic decay modes $B_s^0\to \pi^+\pi^-\ell^+\ell^-$ and $D_s^+\to \pi^+\pi^-\ell^+ \nu$ in the kinematics region where the $\pi^+\pi^-$ system has a invariant mass in the range $0.5$-$1.3$ GeV. These processes are valuable towards the determination of S-wave $\pi^+\pi^-$ light-cone distribution amplitudes whose normalizations are scalar form factors. We compare the results for scalar form factors predicted in unitarized chiral perturbation theory and extracted from the data on the $B_s\to J/\psi \pi^+\pi^-$. Then the $B_s\to \pi^+\pi^-$ and $D_s\to \pi^+\pi^-$ form factors are calculated in light-cone sum rules, based on which predictions for differential decay widths are made. The results are in good agreement with the experimental data on the $B_s$ and $D_s$ decays into $\pi^+\pi^-$. More accurate measurements at BEPC, LHC and KEKB in future will be helpful to examine our formalism and constrain the input parameters more precisely.