Supersymmetric contributions to $\bar{B}_s \to \phi \pi^0$ and $\bar{B}_s \to \phi \rho^0$ decays in SCET

Abstract

We study the decay modes $\bar{B}_s\to \phi \pi^0$ and $\bar{B}_s\to \phi \rho^0$ using Soft Collinear Effective Theory. Within Standard Model and including the error due to the SU(3) breaking effect in the SCET parameters we find that BR $\bar{B}_s\to \phi \pi^0 =7_{-1-2}^{+1+2}\times 10^{-8} $ and BR $\bar{B}_s\to \phi \pi^0=9_{-1-4}^{+1+3}\times 10^{-8}$ corresponding to solution 1 and solution 2 of the SCET parameters respectively.For the decay mode $\bar{B}_s\to \phi \rho^0$, we find that BR $\bar{B}_s\to \phi \rho^0 = 20.2^{+1+9}_{-1-12}\times 10^{-8} $ and BR $ \bar{B}_s\to \phi \rho^0 = 34.0^{+1.5 + 15}_{-1.5-22}\times 10^{-8} $ corresponding to solution 1 and solution 2 of the SCET parameters respectively. We extend our study to include supersymmetric models with non-universal A-terms where the dominant contributions arise from diagrams mediated by gluino and chargino exchanges. We show that gluino contributions can not lead to an enhancement of the branching ratios of $\bar{B}_s\to \phi \pi^0$ and $\bar{B}_s\to \phi \rho^0$. In addition, we show that SUSY contributions mediated by chargino exchange can enhance the branching ratio of $\bar{B}_s\to \phi \pi^0$ by about 14% with respect to the SM prediction. For the branching ratio of $\bar{B}_s\to \phi \rho^0$, we find that SUSY contributions can enhance its value by about 1% with respect to the SM prediction.