QCD anatomy of $B\to X_s\gamma$ decays

Abstract

We present an updated next-to-leading order analysis of the B → X s γ 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 γ) = (2.57 ± 0.26 +0.31 −0.36 ) × 10 −4 for the integral over the high-energy part of the photon spectrum with E lab γ > 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 γ) = (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 study 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.

Lower limit on the neutralino mass in the general MSSM

“…Our calculation of the b → sγ closely follows the approach of Kagan and Neubert [59] (see also [60]) with NLO, bremstrahlung and some non-perturbative effects taken into account. This approach makes it easier to include the effects of New Physics.…”

A two-loop relation between inclusive radiative and semileptonicB-decay spectra

“…The remaining power corrections fall into two distinct classes: kinematical corrections that start at order α s and come with the leading shape function [12,21], and hadronic power corrections that start at tree level and involve new, subleading shape functions [23,24,25,26,27,28,29,30]. Because different combinations of these hadronic functions enter inB → X u l −ν andB → X s γ decays, it is impossible to eliminate their contributions in relations such as (1).…”

“…Secondly, relation (1) is independent of the CKM factor |V tb V * ts |. Thirdly, unlike the totalB → X s γ decay rate, the shape of the photon spectrum is rather insensitive to possible New Physics contributions [12], which could distort the outcome of a |V ub | measurement via relation (2). Lastly, as we will see below, the weight function W (∆, P + ) possesses a much better perturbative expansion than the function W (∆, P + ) = |V tb V * ts | 2 W (∆, P + )/Γ s (E * ).…”

B→Xulbar nul decay distributions to order αs

“…The first three moments satisfy A 0 = 1, A 1 = 0 and A 2 = 1 3 µ 2 π , where µ 2 π is the average momentum squared of the b quark inside the B meson [29]. For our purposes, it is sufficient to adopt the simple form [30] …”

“…The spread of the results provides a realistic estimate of the theoretical uncertainty associated with the treatment of Fermi motion. This uncertainty could be removed if the shape function were extracted, e.g., from a precise measurement of the photon energy spectrum in B → X s γ decays [30]. Figure 5 shows the results for the charged-lepton energy spectrum and for the hadronic energy spectrum, including Fermi motion effects.…”