New constraints on R-parity violating couplings through the measurements of the $B^0_{s(d)}$-${\bar{B}^0_{s(d)}}$ and $K^0$-$\bar{K}^0$ mixing

Abstract

We calculate contributions to $B_s-\bar{B}_s$ mixing through tree-level sneutrino exchange in the framework of the minimal supersymmetric standard model with R-parity violation, including the next-to-leading-order QCD corrections. We compare our results with the updated bounds on the $B_s-\bar{B}_s$ mass difference reported by CDF collaborations, and present new constraints on the relevant combinations of parameters of the minimal supersymmetric standard model with R-parity violation. Our results show that upper bound on the relevant combination of couplings of $B_s-\bar{B}_s$ mixing is of the order $10^{-9}$. We also calculate the $B^0_d-\bar{B}^0_d$ and $K^0-\bar{K}^0$ mass differences, and show that the upper bounds on the relevant combinations of couplings are two and four orders of magnitude stronger than ones reported in the literatures, respectively. We also discuss the case of complex couplings and show that how the relevant combinations of couplings are constrained by the updated experiment data of $B_s-\bar{B}_s$, $B_d-\bar{B}_d$ mixing and time-dependent CP asymmetry $S_{J/\psi K_s}$, and future possible observations of $S_{J/\psi\phi}$ at LHCb, respectively.