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Note on the Extraction of |V_{ub}| using Radiative B Decays

Matthias Neubert

Abstract

The element |V_{ub}| of the quark mixing matrix can be extracted with small theoretical uncertainties by combining weighted integrals over the endpoint regions of the lepton spectrum in B -> X_u l nu decays and the photon spectrum in B -> X_s gamma decays. The perturbative corrections to this determination are computed at next-to-leading order including operator mixing, which has an important impact. The effect of Sudakov resummation is shown to be numerically insignificant.

Note on the Extraction of |V_{ub}| using Radiative B Decays

Abstract

The element |V_{ub}| of the quark mixing matrix can be extracted with small theoretical uncertainties by combining weighted integrals over the endpoint regions of the lepton spectrum in B -> X_u l nu decays and the photon spectrum in B -> X_s gamma decays. The perturbative corrections to this determination are computed at next-to-leading order including operator mixing, which has an important impact. The effect of Sudakov resummation is shown to be numerically insignificant.

Paper Structure

This paper contains 9 equations, 2 figures.

Figures (2)

  • Figure 1: Scale dependence of the coefficient $K_{\rm pert}$ for $m_c/m_b=0.29$ (lower curve) and 0.22 (upper curve). The dashed line shows the result without operator mixing.
  • Figure 2: Comparison of the resummed weight function in (\ref{['wIra']}) (dashed lines) with the one-loop function in (\ref{['wfun']}) (solid line) for $E_0=2.3$ GeV. The singularity of the integrand is avoided by replacing the upper limit of integration by $0.98\,E_\gamma$ (long dashed), $0.99\,E_\gamma$ (dashed), and $0.995\,E_\gamma$ (short dashed).