B →xc (u)ℓ ν ¯ ℓγ and determination of nonperturbative parameters

This paper explores the calculation of nonperturbative parameters present in the matrix element of semileptonic inclusive B decays. These are important for the inclusive determination of the Cabbibo-Kobayashi-Maskawa parameters in the Standard Model. We focus on calculating the rate for radiative inclusive decay, B→Xcℓν¯ℓγ, where γ is hard. Both the radiative and nonradiative (B→Xcℓν¯ℓ) modes are found to require the same nonperturbative parameters. We propose forming ratios from B→Xcℓν¯ℓγ and B→Xcℓν¯ℓ widths in different lepton energy ranges. Our results provide an efficient way to unambiguously calculate the nonperturbative parameters, especially when combined with total width calculations of B→Xcℓν¯ℓ. This is shown explicitly by working to O(1/mb) and determining λ1 and λ2.