b→sγconstraints on the minimal supergravity model with largetanβ

In the minimal supergravity model (MSUGRA), as the parameter $\tan \beta$ increases, the charged Higgs boson and light bottom squark masses decrease, which can potentially increase contributions from ${\mathrm{tH}}^{\pm }$, $\tilde{g}{b}_j$ and $Z_i{b}_j$ loops in the decay $\overrightarrow{b}s\gamma$. We update a previous QCD improved $\overrightarrow{b}s\gamma$ decay calculation to include in addition the effects of gluino and neutralino loops. We find that, in the MSUGRA model, loops involving charginos also increase, and dominate over $\mathrm{tW}$, ${\mathrm{tH}}^{\pm }$, $\tilde{g}\tilde{q}$ and $Z_i\tilde{q}$ contributions for $\tan \beta \gtrsim 5-10$. We find for large values of $\tan \beta \sim 35$ that most of the parameter space of the MSUGRA model for $\mu <0\mathrm{}$ is ruled out due to too large a value of branching ratio $B\left(\overrightarrow{b}s\gamma \right)$. For $\mu >0\mathrm{}$ and large $\tan \beta$, most of parameter space is allowed, although the regions with the least fine-tuning (low $m_0$ and $m_{1/2})$ are ruled out due to too low a value of $B\left(\overrightarrow{b}s\gamma \right)$. We compare the constraints from $\overrightarrow{b}s\gamma$ to constraints from the neutralino relic density, and to expectations for sparticle discovery at CERN LEP2 and the Fermilab Tevatron $p\overline{p}$ colliders. Finally, we show that non-universal GUT scale soft breaking squark mass terms can enhance gluino loop contributions to $\overrightarrow{b}s\gamma$ decay rate even if these are diagonal.