Quasi-Two-Body $B\to P (K^+K^-, \pi^+\pi^-)$ Decays with $f_0(980)$ Resonance

TL;DR

This paper predicts branching fractions and CP asymmetries for B meson decays involving the f0(980) resonance using perturbative QCD, aligning with some experimental data and guiding future measurements.

Contribution

It introduces a refined model for the f0(980) resonance in B decays and provides detailed predictions for branching ratios and CP asymmetries within the perturbative QCD framework.

Findings

Predicted branching fractions range from 10^-8 to 10^-6.

Results show good agreement with BaBar and Belle data for some decay modes.

Provides theoretical estimates for unmeasured decay channels.

Abstract

In this study, we investigate the $CP$-averaged branching fractions and direct $CP$ asymmetries in the quasi-two-body decays $B\to P (f_0(980) \to )(K^+K^-, \pi^+\pi^-)$ within the framework of perturbative QCD approach, where $P$ denotes light pseudoscalar mesons ($\pi$,$K$). The timelike form factor $F_{S}(\omega)$, characterizing final-state interactions between collinear particles in the resonant region, is modeled through the revised relativistic Breit-Wigner formalism for the $S$-wave $f_0(980)$ resonance. Within the Gegenbauer moments of the $S$-wave two-meson distribution amplitudes constrained by current data, we predict the branching fractions of $B\to P (f_0(980) \to )(K^+K^-, \pi^+\pi^-)$ to lie in the range of $10^{-8}$ to $10^{-6}$. Our calculations reveal that our theoretical results for some decay modes exhibit satisfactory agreement with existing measurements from the BaBar and Belle collaborations. Furthermore, we extract the corresponding branching fractions of $B \to P f_0(980)$ decays from the quasi-two-body counterparts $B\to P (f_0(980) \to )\pi^+\pi^-$ rather than $B\to P (f_0(980) \to )K^+K^-$. All predictions are awaiting experimental verification in current and upcoming collider experiments.