Direct CP violation for B¯s0→ϕπ+π− in perturbative QCD

Sheng-Tao Li,Gang Lü

doi:10.1103/physrevd.99.116009

Abstract

In perturbative QCD approach, we study the direct $CP$ violation in the decay of $\bar{B}_s^0\to\rho(\omega )\phi\to {\pi^+}{\pi^-}\phi$ via isospin symmetry breaking. An interesting mechanism involving the charge symmetry violating between $\rho$ and $\omega$ is applied to enlarge the $CP$ violating asymmetry. We find that the $CP$ violation can be enhanced by the $\rho-\omega$ mixing mechanism when the invariant masses of the $\pi^+\pi^-$ pairs are in the vicinity of the $\omega$ resonance. For the decay process of $\bar{B}^0_{s}\to\rho(\omega )\phi\to{\pi^+}{\pi^-}\phi$, the maximum $CP$ violation can reach $5.98\%$. The possibility of detecting the $CP$ violation is also presented.

Highlights

CP violation has obtained extensive attention even since its first discovery in the neutral kaon systems [1]
In the perturbative QCD approach, we study the direct CP violation in the decay of B 0s → ρðωÞφ → πþπ−φ via isospin symmetry breaking
We have investigated the CP violating asymmetry, ACP, for the B 0s → ρ0ðωÞφ → πþπ−φ decay process

Summary

INTRODUCTION

CP violation has obtained extensive attention even since its first discovery in the neutral kaon systems [1]. The nonleptonic weak decay amplitudes of the B meson involve the hadronic matrix elements of hM1M2jOijBi, which can be calculated from the different factorization methods. Based on the power expansion in 1=mb (mb is the b-quark mass), all of the theories of factorization are shown to deal with the hadronic matrix elements in the leading power of 1=mb These methods pertain to whether one takes into account the collinear degrees of freedom or the transverse momenta. We will focus on the CP violation of the decay process B 0s → ρðωÞφ → πþπ−φ via ρ-ω mixing in the pQCD approach. One can find that ρ-ω mixing produces the large CP violation from the effect of isospin symmetry breaking in the three- and four-body decay processes. The related function defined in the text are given in the Appendix

THE FRAMEWORK

Formalism

Calculation details

INPUT PARAMETERS

SUMMARY AND CONCLUSION