Next-to-Leading QCD Corrections to B -> X_s gamma: Standard Model and Two-Higgs Doublet Model

TL;DR

The paper computes next-to-leading order QCD corrections to the matching conditions for the flavor-changing magnetic and chromo-magnetic operators in the SM and two-Higgs doublet models using an off-shell matching approach, enabling Taylor-series evaluations without asymptotic expansions. It confirms SM predictions for BR(B -> X_s gamma) and provides explicit NLO Wilson coefficients for 2HDM scenarios, leading to tighter bounds on the charged-Higgs mass in Model II (about 370–380 GeV for large tanβ) while Model I yields only modest reductions. The authors also carefully treat theoretical uncertainties, including different error definitions, which strongly affect the robustness of the bounds. Overall, the method reduces perturbative uncertainties and strengthens the use of radiative B decays as probes of new physics.

Abstract

We present the QCD corrections to the matching conditions of the Delta B =1 magnetic and chromo-magnetic operators in the Standard Model and in two-Higgs doublet models. We use an off-shell matching procedure which allows us to perform the computation using Taylor series in the external momenta, instead of asymptotic expansions. In the Standard Model case, we confirm previous results derived on-shell and we obtain BR(B -> X_s gamma)=(3.62\pm 0.33) 10^{-4}. In the case of the usual two-Higgs doublet model, we show that going from the leading to the next-to-leading order result improves the CLEO bound on the charged-Higgs mass from 260 GeV to 380 GeV. This limit is very sensitive to the definition of errors and we carefully discuss the theoretical uncertainties. Finally, in the case of the two-Higgs doublet model in which both up- and down-type quarks couple to the same Higgs field, the theoretical prediction for BR(B -> X_s gamma) can be reduced by at most 20% with respect to the Standard Model value.

Figures (6)

• Figure 1: Examples of the correspondence between diagrams in the "full" theory and in the off-shell effective theory.
• Figure 2: The $\mu_b$ scale dependence of $BR_\gamma(\delta=0.99)$ at LO (lower curves) and NLO (upper curves). The solid line represents the case in which all input parameters are fixed to their central values. The dashed lines represent the errors coming from all input parameters, other than $\mu_b$, added in quadratures.
• Figure 3: Predicted $BR_\gamma(\delta=0.99)$ in Model II as a function of the charged-Higgs mass $M_H$, for $\tan \beta =2$ at LO (solid line). The dashed lines represent the uncertainty obtained by adding in quadratures the errors coming from the different input parameters. The dot-dashed lines define the uncertainty range with the "scanning" method (see text).
• Figure 4: Predicted $BR_\gamma(\delta=0.99)$ in Model II as a function of the charged-Higgs mass $M_H$, for $\tan \beta =2$ at NLO (solid line). The dashed lines represent the uncertainty obtained by adding in quadratures the errors coming from the different input parameters. The dot-dashed lines define the uncertainty range with the "scanning" method (see text).
• Figure 5: Exclusion regions in the plane $BR_\gamma /BR_{SL}$ versus $M_H$ for $\tan \beta =$ 1 (dashed lines), 2 (solid lines), 5 (dot-dashed lines) obtained by our NLO calculation with $\delta=0.90$. The upper lines correspond to a theoretical uncertainty defined by one "Gaussian" standard deviation, and the lower lines to the "scanning" method (see text).