Theoretical Uncertainties and Phenomenological Aspects of $B \rightarrow X_s \gamma$ Decay

We analyze uncertainties in the theoretical prediction for the inclusive branching ratio $BR[B \rightarrow X_s \gamma]$. We find that the dominant uncertainty in the leading order expression comes from its $\mu$-dependence. We discuss a next-to-leading order calculation of $B \rightarrow X_s \gamma$ in general terms and check to what extent the $\mu$-dependence can be reduced in such a calculation. We present constraints on the Standard and Two-Higgs-Doublet Model parameters coming from the measurement of $b \rightarrow s \gamma$ decay. The current theoretical uncertainties do not allow one to definitively restrict the Standard Model parameters much beyond the limits coming from other experiments. The bounds on the Two-Higgs-Doublet Model remain very strong, though significantly weaker than the ones present in the recent literature. In the Two-Higgs-Doublet Model case, the $b \rightarrow s \gamma$, $Z \rightarrow b \bar{b}$ and $b \rightarrow c \tau \bar{\nu}_{\tau}$ processes are enough to give the most restrictive bounds in the $M_{H^{\pm}}-tan \beta$ plane