QCD Anatomy of B -> X_s gamma Decays

TL;DR

This work delivers an updated, fully consistent next-to-leading order analysis of B → X_s γ, incorporating Fermi motion through a universal shape function within the heavy-quark expansion and refining renormalization-scale and QED corrections. It shows that bound-state effects, particularly the b-quark mass, dominate uncertainties in partially integrated branching ratios, and provides a robust method to connect the photon spectrum to the hadronic mass distribution and to extract a short-distance mb. The results yield Standard Model predictions for high-energy photon cuts in good agreement with CLEO and establish a framework to constrain New Physics via modified Wilson coefficients and right-handed operators, while the photon spectrum remains largely insensitive to NP. Overall, the paper reduces model dependence in photon-spectrum analyses and informs future precision tests and mb extractions, strengthening inclusive radiative B decay as a probe of the flavor sector.

Abstract

We present an updated next-to-leading order analysis of the B -> X_s gamma branching ratio and photon spectrum, including consistently the effects of Fermi motion in the heavy-quark expansion. For the Standard Model, we obtain B(B -> X_s gamma) = (2.57+-0.26^{+0.31}_{-0.36}) * 10^{-4} for the integral over the high-energy part of the photon spectrum with E_gamma^{lab} > 2.2 GeV, where the first error reflects the uncertainty in the input parameters, and the second one the uncertainty in the calculation of Fermi motion. This prediction agrees with the CLEO measurement of the same quantity within one standard deviation. From a reanalysis of the CLEO data, we obtain for the total branching ratio B(B -> X_s gamma) = (2.62+-0.60_{exp}^{+0.37}^{-0.30{th}}) * 10^{-4} using the measured rate above 2.2 GeV, and (2.66+-0.56_{exp}^{+0.43}_{-0.48{th}}) * 10^{-4} using a fit to the photon energy spectrum. Both values are consistent with the Standard Model prediction of (3.29+-0.33) * 10^{-4}. Our analysis contains an improved discussion of renormalization scale dependence and QED corrections. We also discuss the sensitivity of the branching ratio and photon spectrum to hadronic parameters such as the b-quark mass, and to possible contributions from New Physics beyond the Standard Model.

Figures (10)

• Figure 1: Dependence of the $B\to X_s\gamma$ branching ratio on the cutoff parameter $\delta$. The dashed lines indicate the extrapolation to the "total" branching ratio.
• Figure 2: Scale dependence of the $B\to X_s\gamma$ branching ratio (left) and of its three most important components (right) in the Standard Model. For comparison, the lower plots show the results obtained at leading order.
• Figure 3: Theoretical predictions for the integrated $B\to X_s\gamma$ branching ratio (upper plots) and the corresponding photon spectra (lower plots) for various choices of the shape-function parameters ($m_b$, $\mu_\pi^2$) and functional form, as explained in the text. The calculation of the photon spectra will be discussed in Section \ref{['sec:spectrum']}.
• Figure 4: Different components of the photon spectrum in $B\to X_s\gamma$ decays
• Figure 5: Theoretical predictions for the photon energy spectrum in the laboratory frame for different parameters of the shape function. The gray line in the left-hand plot shows the result obtained using a Gaussian form of the shape function with central values of $m_b$ and $\mu_\pi^2$. The data points show the CLEO results. In the left-hand plot, no fit to the data is performed, whereas the right-hand plot shows the results of the best fits reported in Table \ref{['tab:fits']}.