Quasi-two-body decays $B_{(s)}\to P\rho\to P\pi\pi$ in perturbative QCD approach

TL;DR

This paper calculates branching ratios and CP asymmetries for $B_{(s)}$ decays to a pseudoscalar meson and a $ ho$ resonance using perturbative QCD, finding general agreement with data but some discrepancies and novel predictions.

Contribution

It provides a detailed PQCD analysis of quasi-two-body $B_{(s)}$ decays involving $ ho$ resonances, including CP violation, with comparisons to experimental results and new predictions.

Findings

Most predictions agree with experimental data within errors.

The predicted branching ratio for $B o ho^0 o ho^0( o ext{pions})$ is smaller than measured.

A negative CP asymmetry of about -27.5% is predicted for $B^+ o ho^0 o ext{pions}$, matching some theories but differing from BaBar and LHCb.

Abstract

In this work, we calculate the $CP$-averaged branching ratios and the direct $CP$-violating asymmetries of the quasi-two-body decays $B_{(s)} \to P (\rho \to) \pi\pi$ by employing the perturbative QCD (PQCD) approach (here $P$ stands for a light pseudoscalar meson $\pi, K, \eta$ or $\eta^{\prime}$). The vector current time-like form factor $F_{\pi}$, which contains the final state interactions between the pion pair in the resonant region associated with the $P$-wave states $\rho(770)$ along with the two-pion distribution amplitudes, are employed to describe the interactions between the $\rho$ and the pion pair under the hypothesis of the conserved vector current. We found that (a) the PQCD predictions for the branching ratios and the direct $CP$-violating asymmetries for most considered $B_{(s)} \to P (\rho \to) \pi\pi$ decays agree with currently available data within errors; (b) for ${\cal B}(B \to \pi^0 \rho^0 \to \pi^0(\pi^+ \pi^-)$, the PQCD prediction is much smaller than the measured one; and (c) for $B^+ \to \pi^+(\rho^0\to)\pi^+ \pi^-$ decay mode, we found a negative $CP$ asymmetry $(-27.5^{+3.0}_{-3.7})\%$, which agrees with other theoretical predictions but different in sign from those as reported by BaBar and LHCb Collaboration.