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

  • theoretical physics
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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.

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Received: 18 September 2004, Revised: 18 January 2005, Published online: 21 February 2005

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Neubert, M. Renormalization-group improved calculation of the \(B\to X_s\gamma\) branching ratio. Eur. Phys. J. C 40, 165–186 (2005). https://doi.org/10.1140/epjc/s2005-02141-1

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