Analytic Calculations of the Branching Ratio and CP Violation in \(B_s^0 \to {K^{*0}}{\overline K ^{*0}}\) Decay

Abstract

We present an analytic calculation of Branching Ratio (BR) and Charge—Parity (CP) violating asymmetries of the \(B_s^0\) meson decays to light vector mesons \(\left( {{K^{*0}}{{\overline K }^{*0}}} \right)\) within the framework of Naive Factorization (NF) and QCD Factorization (QCDF). We find the \({\rm{BR}}\left( {B_s^0 \to {K^{*0}}{{\overline K }^{*0}}} \right) = 1.87 \times {10^{ - 5}}\) and 1.40 × 10⁻⁵ for NF and QCDF, respectively. We also find that within QCDF the direct CP violation \(\left( {{\cal A}_{CP}^{{\rm{dir}}}} \right) = - 0.01\), CP violation in mixing \(\left( {{\cal A}_{CP}^{{\rm{mix}}}} \right) = 0.31\) and CP violation due to interference \(\left( {{\cal A}_{CP}^{{\rm{\Delta \Gamma }}}} \right) = 0.95\).