Imprint of SUSY in radiative B-meson decays

We study supersymmetric (SUSY) effects on $C_7(\mu_b)$ and $C'_7(\mu_b)$ which are the Wilson coefficients (WCs) for $b \to s \gamma$ at b-quark mass scale $\mu_b$ and are closely related to radiative $B$-meson decays. The SUSY-loop contributions to $C_7(\mu_b)$ and $C'_7(\mu_b)$ are calculated at leading order (LO) in the Minimal Supersymmetric Standard Model (MSSM) with general quark-flavour violation (QFV). For the first time we perform a systematic MSSM parameter scan for the WCs $C_7(\mu_b)$ and $C'_7(\mu_b)$ respecting all the relevant constraints, i.e. the theoretical constraints from vacuum stability conditions and the experimental constraints, such as those from $K$- and $B$-meson data and electroweak precision data, as well as recent limits on SUSY particle masses and the 125 GeV Higgs boson data from LHC experiments. From the parameter scan we find the following: (1) The MSSM contribution to Re($C_7(\mu_b)$) can be as large as $\sim \pm 0.05$, which could correspond to about 3$\sigma$ significance of New Physics (NP) signal in the future LHCb and Belle II experiments. (2) The MSSM contribution to Re($C'_7(\mu_b)$) can be as large as $\sim -0.08$, which could correspond to about 4$\sigma$ significance of NP signal in the future LHCb and Belle II experiments. (3) These large MSSM contributions to the WCs are mainly due to (i) large scharm-stop mixing and large scharm/stop involved trilinear couplings, (ii) large sstrange-sbottom mixing and large sstrange-sbottom involved trilinear couplings and (iii) large bottom Yukawa coupling $Y_b$ for large $\tan\beta$ and large top Yukawa coupling $Y_t$. In case such large NP contributions to the WCs are really observed in the future experiments at Belle II and LHCb Upgrade, this could be the imprint of QFV SUSY (the MSSM with general QFV).