Some novel contributions to radiative $B$ decays in supersymmetry without $R$ parity

We present a systematic analysis at the leading log order of the influence of combination of bilinear and trilinear $R$ parity violating couplings on the decay $b\to s+\gamma$. Such contributions have never been explored in the context of $b\to s+\gamma$ decay. We show that influence of charged-slepton-Higgs mixing mediated loops can dominate the SM and MSSM contributions and hence can provide strong bounds on the combination of bilinear-trilinear $R$ parity violating couplings. Such contributions also are enhanced by large $\tan \beta$. With substantially extended basis of operators (28 operators), we provide illustrative analytical formulas of the major contributions to complement our complete numerical results which demonstrate the importance of QCD running effects.

Figure 1

Various Wilson coefficients versus $|B_3{\lambda }_{323}^{\prime }|$. $+$ sign stands for MSSM chargino contribution, $\times$ for the MSSM charged Higgs contribution, $\star$ for sneutrino contribution, all contributing to $C_7$. Empty square stands for $C_{11}(M_W)$, filled square for $C_7(M_W)$, and empty circle for $C_7(m_b)$.

Figure 2

Various Wilson coefficients versus $|B_3^{*}{\lambda }_{332}^{\prime }|$. $+$ sign stands for charged slepton contribution, $\times$ for sneutrino contribution, $\star$ for MSSM chargino contribution, all contributing to ${\tilde{C}}_7$. Empty square stands for MSSM charged Higgs contribution, filled square for ${\tilde{C}}_{11}(M_W)$, empty circle for $C_7(M_w)$, filled circle for ${\tilde{C}}_7(M_W)$, empty triangle for $C_7(m_b)$, and filled triangle for ${\tilde{C}}_7(m_b)$.