Large beyond-leading-order effects inb→sγ in supersymmetry with general flavor mixing

Abstract

We examine squark--gluino loop effects on the process $b \to s \gamma$ in minimal supersymmetry with general flavor mixing in the squark sector. In the regime of heavy squarks and gluino, we derive analytic expressions for the beyond--LO corrections to the Wilson coefficients and find them to be often large, especially at large $\tan\beta$ and $\mu>0$. The ensuing ranges of values of the Wilson coefficients are typically smaller than in the LO approximation, and sometimes even change sign. This has the effect of often reducing, relative to the LO, the magnitude of supersymmetric contributions to $BR(B \to X_s \gamma)$. This ``focusing effect'' is caused by contributions from: (i) an RG evolution of the Wilson coefficients; (ii) a correction to the LO chargino contribution to the Wilson coefficients, which can considerably reduce the LO gluino contribution. This partial cancellation of the two contributions takes place only in the case of general flavor mixing. As a result, stringent lower bounds on the mass scale of superpartners, which apply in the case of minimal flavor violation, can be substantially reduced for even small departures from the scenario. The often disfavored case of $\mu<0$ can also become allowed for $M_{SUSY}$ as small as $\sim$ 200 GeV, compared to > $\sim$ 500 GeV at LO and over 2 TeV in the case of minimal flavor violation. Limits on the allowed amount of flavor mixing among the 2nd and 3rd generation down--type squarks are also typically considerably weakened. The input CKM matrix element $K^{(0)}_{cb}$ can be larger than the experimental value by a factor of ten, or can be as small as zero.