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

Abstract

We analyze uncertainties in the theoretical prediction for the inclusive branching ratio $BR[B \rightarrow X_s γ]$. We find that the dominant uncertainty in the leading order expression comes from its $μ$-dependence. We discuss a next-to-leading order calculation of $B \rightarrow X_s γ$ in general terms and check to what extent the $μ$-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 $b \rightarrow s γ$ 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 $b \rightarrow s γ$, $Z \rightarrow b \bar{b}$ and $b \rightarrow c τ\barν_τ$ processes are enough to give the most restrictive bounds in the $M_{H^{\pm}}-tan β$ plane.

Figures (8)

• Figure 1: Leading order one loop diagrams generating the $b \rightarrow s \gamma$ transition in the SM.
• Figure 2: $\mu$-dependence of the theoretical prediction for the ratio R, for $m_t$=150 GeV and $\alpha_s(M_Z)=0.12$. The solid line corresponds to the leading order prediction. The dashed lines describe possible next-to-leading results (see section 4).
• Figure 3: Predictions for $B\rightarrow X_s\gamma$ in the SM, as a function of the top quark-mass, with the theoretical uncertainties taken into account (see the text).
• Figure 4: Lower limits for $m_t$ in the SM as a function of $\alpha_s(M_Z)$ (see the text).
• Figure 5: Charged scalar exchanges contributing to $b \rightarrow s \gamma$ in the 2HDM.