Quark mass effects in B -> Xs gamma

TL;DR

The paper analyzes the decay $\bar{B} \to X_s \gamma$, showing the charm-loop dominates and that QCD logarithms primarily enhance the rate via the top-sector $m_b$ running. By reorganizing the NLO formulae to maintain a charm/top split and renormalizing the top contribution with $m_b(\mu_0)$ at a high scale, the authors achieve better perturbative stability and a clearer handle on NNLO uncertainties. They predict $\mathrm{BR}(\bar B \to X_s \gamma)_{E_\gamma>1.6\,\mathrm{GeV}} = (3.60 \pm 0.30) \times 10^{-4}$, with a notable $\sim$5.5% uncertainty from $m_c/m_b$ in $K_c$, and find the result consistent with current data. The analysis also establishes a strong lower bound on the charged Higgs mass in 2HDM-II ($M_{H^+} > 350$ GeV at 99% CL), illustrating the utility of precise SM predictions for constraining new physics.

Abstract

The charm-loop contribution to B -> Xs gamma is found to be numerically dominant and very stable under logarithmic QCD corrections. The strong enhancement of the branching ratio by QCD logarithms is mainly due to the b-quark mass evolution in the top-quark sector. These observations allow us to achieve better control over residual scale dependence at the next-to-leading order. Furthermore, we observe that the sensitivity of the matrix element < Xs gamma | (sc)_(V-A)(cb)_(V-A) | b > to mc/mb is the source of a sizeable uncertainty that has not been properly taken into account in previous analyses. Replacing mc^pole/mb^pole in this matrix element by the more appropriate mc(mu)/mb^pole with mc < mu < mb causes an 11% enhancement of the SM prediction for BR[B -> Xs gamma]. For E_gamma > 1.6 GeV in the B-meson rest frame, we find BR[ B -> Xs gamma]_{E_gamma > 1.6 GeV} = (3.60 +_ 0.30) * 10^-4. The difference between our result and the current experimental world average is consistent with zero at the level of 1 sigma. We also discuss the implementation of new physics effects in our calculation. The lower bound on the charged Higgs boson mass in 2HDM(II) is found the be higher than 350 GeV.

Figures (6)

• Figure 1: One-loop 1PI diagrams for $b \to s \gamma$ in the SM. There is no $W^{\pm}G^{\mp}\gamma$ coupling in the background-field gauge.
• Figure 2: $X_c$ as a function of $\eta$ (solid line), and its three components in eq. (\ref{['Xc']}) (dashed lines).
• Figure 3: Chirality flows in diagrams contributing to $C_7^{(0)}(\mu_0)$. The photon couples to any of the internal lines.
• Figure 4: Direct and indirect lower bounds on $M_{H^+}$ from different processes in type II 2HDM as a function of $\tan\beta$. The $B\to X_s \gamma$ bound is the one in eq. (\ref{['hbound']}) below.
• Figure 5: The 99% CL bound on the 2HDM-II charged Higgs mass from $B\to X_s \gamma$ as a function of the world average and of its error. The contour lines represent values which lead to the same $M_{H^+}$ bound. The experimental world averages evaluated with use of the preliminary Moriond and published CLEO CLEO results are indicated for reference.