Will the subprocesses ρ(770,1450)0→K+K− contribute large branching fractions for B±→π±K+K− decays?

Wen-Fei Wang

doi:10.1103/physrevd.101.111901

Abstract

We analyze the quasi-two-body decays $B^+\to\pi^+\rho(770,1450)^0 \to\pi^+ K^+K^-$ in the perturbative QCD approach. The results in this work do not support that large branching fractions contributed by the resonances $\rho(770,1450)^0$ in the $B^\pm \to \pi^\pm K^+K^-$ decays. The virtual contribution for $K^+K^-$ from the tail of the resonance $\rho(770)^0$ which has been ignored in the experimental studies is about $1.5$ times of the $\rho(1450)^0 \to K^+K^-$ contribution, with the predicted branching fractions ${\mathcal B}_v=(1.31\pm0.27)\times10^{-7}$ and ${\mathcal B}=(8.96\pm2.61)\times10^{-8}$, respectively, for these two subprocesses in the $B^\pm \to \pi^\pm K^+K^-$ decays. The absence of $\rho(770)^0\to K^+K^-$ for the decay amplitude of a three-body hadronic $B$ decay involving charged kaon pair could probably result in a larger proportion for the contribution from the resonance $\rho(1450)^0$ in the experimental analysis.

Highlights

Strong dynamics in the charmless three-body hadronic B meson decays is related to the short-distance processes like in the two-body cases, and it involves the hadronhadron interactions, the three-body effects [1,2], and the rescattering processes [3,4] in the final states
The virtual contribution for KþK− from the tail of the resonance ρð770Þ0, which has not been taken into the decay amplitudes of BÆ → πÆKþK− and other charmless threebody B meson decays involving kaon pair in the experimental studies, is about 1.5 times of the contribution from ρð1450Þ0 for the charged kaon pair as shown in Eq (13) for the branching fractions
The large virtual contribution of ρð770Þ0 for the charged kaon pair is mainly due to its large decay width which result in a relative dispersive distribution of the differential branching fraction as shown in Fig. 2, where the red short dash line is for the decay BÆ → πÆρð1450Þ0 → πÆKþK−, the blue dash-dot line is for the process BÆ → πÆρð770Þ0 → πÆKþK− and the black solid line is for BÆ → πÆðρð770Þ0 þ ρð1450Þ0Þ → πÆKþK−

Summary

INTRODUCTION

Strong dynamics in the charmless three-body hadronic B meson decays is related to the short-distance processes like in the two-body cases, and it involves the hadronhadron interactions, the three-body effects [1,2], and the rescattering processes [3,4] in the final states. LHCb Collaboration presented a surprising large fit fraction ð30.7 Æ 1.2 Æ 0.9Þ% of the total threebody result in [9] for the subprocess ρð1450Þ0 → KþK− in the amplitude analysis of the BÆ → πÆKþK− decays. We shall analyze the ρð770; 1450Þ0 → KþK− contributions for the three-body decays BÆ → πÆKþK− with the quasi-two-body framework based on the perturbative QCD (PQCD) approach [32,33,34,35]. This paper is organized as follows: In Sec. II, we briefly review the electromagnetic timelike form factor for the charged kaon, we introduce the P-wave KþK− system distribution amplitudes and give the expression of differential branching fractions for the quasi-two-body decays BÆ → πÆρ0 → πÆKþK−.

FRAMEWORK

RESULTS

SUMMARY