Renormalization-group improved calculation of the branching ratio

M. Neubert

doi:10.1140/epjc/s2005-02141-1

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2023 Impact factor 4.2

Particles and Fields

Eur. Phys. J. C (2005) 40: 165-186
https://doi.org/10.1140/epjc/s2005-02141-1

theoretical physics

Renormalization-group improved calculation of the $B\to X_s\gamma$ branching ratio

M. Neubert

Institute for High-Energy Phenomenology, Newman Laboratory for Elementary-Particle Physics, Cornell University, NY 14853, Ithaca, USA

Abstract

Using results on soft-collinear factorization for inclusive B-meson decay distributions, a systematic study of the partial $B\to X_s\gamma$ decay rate with a cut $E_\gamma\ge E_0$ on photon energy is performed. For values of E ₀ below about 1.9 GeV, the rate can be calculated without reference to shape functions using a multi-scale operator product expansion (MSOPE). The transition from the shape-function region to the MSOPE region is studied analytically. The resulting prediction for the $B\to X_s\gamma$ branching ratio depends on three large scales: m _b, $\sqrt{m_b\Delta}$ , and $\Delta = m_b-2E_0$ . Logarithms associated with these scales are resummed at next-to-next-to-leading logarithmic order. While power corrections in $\Lambda_{\mathrm {QCD}}/\Delta$ turn out to be small, the sensitivity to the scale $\Delta\approx 1.1$ GeV (for $E_0\approx 1.8$ GeV) introduces significant perturbative uncertainties, which so far have been ignored. The new theoretical prediction for the $B\to X_s\gamma$ branching ratio with $E_\gamma\ge 1.8$ GeV is $\mbox{Br}(B\to X_s\gamma) = \smash{(3.38_{ -0.42}^{ + 0.31}\pm 0.31)}\times 10^{-4}$ , where the first error is an estimate of perturbative uncertainties and the second one reflects uncertainties in input parameters. With this cut $\smash{(89_{ -7}^{ + 6} \pm 1)}\%$ of all events are contained. When this fraction is combined with the previously best prediction for the total decay rate, one obtains $\mbox{Br}(B\to X_s\gamma) = (3.30_{ -0.35}^{ + 0.31}\pm 0.17)\times 10^{-4}$ , with a somewhat less conservative estimate of parametric uncertainties. The implications of larger theory uncertainties for new physics searches are briefly explored with the example of the type-II two-Higgs-doublet model, for which the lower bound on the charged-Higgs mass is reduced compared with previous estimates to approximately 200 GeV at 95% confidence level.