Randall-Sundrum corrections to the width difference and $CP$-violating phase in $B_s^0$-meson decays

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 ${\overline{B}}_s^0$-$B_s^0$ system. Our calculations are performed in the general framework of an effective theory, based on operator product expansion. The results can thus be used for many new-physics models. We find that the correction to the magnitude of the decay amplitude ${\Gamma }_{12}^s$ 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 the CDF and D0 Collaborations from $B_s^0\to J/\psi \varphi$ 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.

Figure 1

RS corrections to the magnitude and $CP$-violating phase of the ${\overline{B}}_s^0$-$B_s^0$ decay amplitude, $R_{\Gamma }$ and ${\varphi }_{\Gamma }$, as well as for the mixing amplitude, $R_M$ and ${\varphi }_M$. Blue (dark gray) points correspond to the minimal, orange (light gray) to the custodial RS model. The dashed lines mark the 95% confidence region with respect to the measurement of $\Delta m_{B_s}$. See text for details.

Figure 2

Upper panel: Corrections within the $\Delta {\Gamma }_s^{\mathrm{SM}}/{\beta }_s$-plane for the minimal (blue/dark gray) and custodial (orange/light gray) RS model. Bounds from $Z^{0}b\overline{b}$, $\Delta m_{B_s}$, and ${ϵ}_K$ are satisfied. See text for details. Lower panel: Experimental constraints from flavor-tagged $B_s^0\to J/\psi \varphi$ decays. Figure taken from 5.

Figure 3

Corrections within the $A_{\mathrm{SL}}^s/S_{\psi \varphi }$-plane for the minimal (blue/dark gray) and custodial (orange/light gray) RS model. Bounds from $Z^{0}b\overline{b}$, $\Delta m_{B_s}$, and ${ϵ}_K$ are satisfied. See text for details.