Chiral Dynamics and S-wave Contributions in Semileptonic B decays

TL;DR

This paper investigates the S-wave contributions in semileptonic B decays involving Kπ and KK final states, revealing their significant impact on decay widths and proposing a new method to measure S-wave phase variations.

Contribution

It introduces a novel approach to estimate S-wave effects in B decays using dispersion relations and Chiral Perturbation Theory, highlighting their importance in decay analysis.

Findings

S-wave modifies decay widths by about 10% in B→Kπl+l− decays.

S-wave contributes around 5% to decay widths in B_s→KKl+l− decays.

Forward-backward asymmetry from S-P wave interference offers a new phase measurement method.

Abstract

The flavor-changing neutral current process $b\to s l^+l^-$ is beneficial to testing the standard model and hunting for new physics scenarios. In exclusive decay modes like $B\to K^*(892)l^+l^-$, the S-wave effects may not be negligible and thus have to be reliably estimated. Using the scalar form factors derived from dispersion relations in two channels and matched to Chiral Perturbation Theory, we investigate the S-wave contributions in $\bar B^0\to K^- \pi^+ l^+l^-$, with the $K\pi$ invariant mass lying in the vicinity of the mass of $K^*(892)$, and the $B_s\to K^- K^+ l^+l^-$ with $m_{KK}\sim m_{\phi}$. We find that the S-wave will modify differential decay widths by about 10% in the process of $\bar B^0\to K^- \pi^+ l^+l^-$ and about 5% in $B_s\to K^- K^+ l^+l^-$. A forward-backward asymmetry for the charged kaon in the final state arises from the interference between the S-wave and P-wave contributions. The measurement of this asymmetry offers a new way to determine the variation of the $K\pi$ S-wave phase versus the invariant mass.