Quasi-two-body B(s)→Vππ decays with resonance f0(980) in the PQCD approach

Lei Yang,Xin Liu,Cui-Hua Li,Ying Li,Zhi-Tian Zou

doi:10.1103/physrevd.103.113005

Abstract

Motivated by the measurements of branching fractions of the quasi-two-body decays $B^0\to K^{*0}(f_0(980)\to )\pi^+\pi^-$ and $B^0\to \rho^0(f_0(980)\to )\pi^+\pi^-$, we study the charmless $B\to V (f_0(980)\to ) \pi^+\pi^-$ decays in the perturbative QCD approach. Supposing that $f_0(980)$ is a two-quark state and mixture of $n\bar n=(u\bar u+d\bar d)/\sqrt 2$ and $s\bar s$ with the mixing angle $\theta$, we calculate the branching fractions of these decays with the new introduced $s$-wave $\pi^+\pi^-$-pair wave function. When the mixing angle $\theta$ lies in the range $[135^{\circ}, 155^{\circ}]$, the calculated branching fractions of the $B^0\to K^{*0}f_0(980)\to K^{*0}\pi^+\pi^-$ and $B^0\to \rho^0f_0(980)\to \rho^0\pi^+\pi^-$ decays are in agreement with the experimental data. The branching fractions of other decays could be measured in the current LHCb and Belle II experiments. Considering the isospin symmetry, we also estimate the branching fractions of the quasi-two-body decays $B\to Vf_0(980)\to V\pi^0\pi^0$, which are half of those the corresponding decays $B\to Vf_0(980)\to V\pi^+\pi^-$. Moreover, the direct $CP$ asymmetries of these decays are also calculated, and some of them can be tested in the current experiments.

Highlights

In recent years, scholars have paid more attention to the nonleptonic three-body decays of B mesons on both the experimental and theoretical sides, as these decays can be used to test the standard model, to extract the angles of the Cabibbo-Kobayashi-Maskawa (CKM) unitarity triangle, and to search for the sources of the CP violation
On the factorization hypothesis, a few of theoretical methods have been proposed to study these decays, such as approaches based on the symmetry principle [11], the QCD factorization approach (QCDF) [12,13,14,15,16], the perturbative QCD approach (PQCD) [17,18,19,20,21,22], and other theoretical methods [23]
One can find that adopting the appropriate wave functions of initial and final states, our predictions are in good agreement with the current experimental data, there are only upper limits for the B0 → ωðf0 →Þπþπ− and Bþ → ρþðf0 →Þπþπ− decays

Summary

INTRODUCTION

Scholars have paid more attention to the nonleptonic three-body decays of B mesons on both the experimental and theoretical sides, as these decays can be used to test the standard model, to extract the angles of the Cabibbo-Kobayashi-Maskawa (CKM) unitarity triangle, and to search for the sources of the CP violation. The central region so-called Mercedes Star configuration corresponds to the case where all the invariant masses are roughly the same and of order of mB. In this region all three light mesons have a large energy in the B meson rest frame and fly apart at about 120° angles. Compared with two other regions, the physics picture at the edges of the Dalitz plot is very similar to a two-body decay by viewing the two-meson pair as a whole, and we call it quasi-two-body decay. In the past 20 years, the PQCD approach based on the kT factorization has been used to study the B meson two-body decays. For the sake of convenience f0ð980Þ is abbreviated to f0 in the following context unless otherwise indicated

FRAMEWORK

NUMERICAL RESULTS

SUMMARY