Randall-Sundrum Corrections to the Width Difference and CP-Violating Phase in $B_s^0$-Meson Decays

Abstract

We study the impact of the Randall-Sundrum setup on the width difference $\Delta {\Gamma }_s$ and the CP-violating phase ${\varphi }_s$ in the ${\bar{B}}_s^0$-$B_s^0$ system. Our calculations are performed in the general framework of an effective theory, based on operator product expansion. The result can thus be used for many new physics models. We find that the correction to the magnitude of the decay amplitude ${\Gamma }_{12}$ is below 4% for a realistic choice of input parameters. The main modification in the $\Delta {\Gamma }_s/{\beta }_s$-plane is caused by a new CP-violating phase in the mixing amplitude, which allows for a better agreement with the experimental results of CDF and DØfrom $B_s^0\to J/\psi \varphi$ decays. The best-fit value of the CP asymmetry $S_{\psi \varphi }$ can be reproduced, while simultaneously the theoretical prediction for the semileptonic CP asymmetry $A_{\mathrm{SL}}^s$ can enter the $1\sigma$ range.

Comments: 12 pages, 1 table, 3 figures, references added, comments added, minor correction in numerics, conclusions unchanged, accepted for publication in Physical Review D