Estimate of BR(B -> X_s gamma) at O(alpha_s^2)

Abstract

Combining our results for various O(alpha_s^2) corrections to the weak radiative B-meson decay, we are able to present the first estimate of the branching ratio at the next-to-next-to-leading order in QCD. We find BR(B -> X_s gamma) = (3.15 +_ 0.23) x 10^-4 for E_gamma > 1.6 GeV in the B-meson rest frame. The four types of uncertainties: non-perturbative (5%), parametric (3%), higher-order (3%) and m_c-interpolation ambiguity (3%) have been added in quadrature to obtain the total error.

Figures (4)

• Figure 1: Sample LO diagram for the $b\to s\gamma$ transition.
• Figure 2: Renormalization scale dependence of ${\cal B}(\bar{B} \to X_s \gamma)$ in units $10^{-4}$ at the LO (dotted lines), NLO (dashed lines) and NNLO (solid lines). The plots describe subsequently the dependence on the matching scale $\mu_0$, the low-energy scale $\mu_b$, and the charm mass renormalization scale $\mu_c$.
• Figure 3: ${\cal B}(\bar{B} \to X_s \gamma)$ as a function of the charged Higgs boson mass in the THDM II for $\tan\beta=2$ (solid lines). The dashed and dotted lines show the SM and experimental results, respectively (see the text).
• Figure 4: The 95% CL lower bound on $M_{H^+}$ as a function of the experimental central value (horizontal axis) and error (vertical axis). The experimental result from Eq. (\ref{['hfag']}) is indicated by the black square. The contour lines represent values that lead to the same bound.