b→ sγ Constraints on the Minimal Supergravity Model with Large β

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In the minimal supergravity model (mSUGRA), as the parameter β increases, the charged Higgs boson and light bottom squark masses decrease, which can potentially increase contributions from tH±, ⱼ and ᵢⱼ loops in the decay b→ sγ. We update a previous QCD improved b→ sγ 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 tW, tH±, and ᵢ contributions for β 5-10. We find for large values of β 35 that most of the parameter space of the mSUGRA model for μ<0 is ruled out due to too large a value of branching ratio B(b→ sγ). For μ>0 and large β, most of parameter space is allowed, although the regions with the least fine-tuning (low m₀ and m₁/₂) are ruled out due to too low a value of B(b→ sγ). We compare the constraints from b→ sγ to constraints from the neutralino relic density, and to expectations for sparticle discovery at LEP2 and the Fermilab Tevatron p p colliders. Finally, we show that non-universal GUT scale soft breaking squark mass terms can enhance gluino loop contributions to b→ sγ decay rate even if these are diagonal.