Bjorn O. Lange

Factorization and shape-function effects in inclusive B-meson decays

Abstract Using methods of effective field theory, factorized expressions for arbitrary B ¯ → X u l − ν ¯ decay distributions in the shape-function region of large hadronic energy and moderate hadronic invariant mass are derived. Large logarithms are resummed at next-to-leading order in renormalization-group improved perturbation theory. The operator product expansion is employed to relate moments of the renormalized shape function with HQET parameters such as m b , Λ ¯ and λ 1 defined in a new physical subtraction scheme. An analytic expression for the asymptotic behavior of the shape function is obtained, which reveals that it is not positive definite. Explicit expressions are presented for the charged-lepton energy spectrum, the hadronic invariant mass distribution, and the spectrum in the hadronic light-cone momentum P + = E H − | P → H | . A new method for a precision measurement of | V u b | is proposed, which combines good theoretical control with high efficiency and a powerful discrimination against charm background.

Renormalization-group evolution of the B-meson light-cone distribution amplitude.

An integro-differential equation governing the evolution of the leading-order B-meson light-cone distribution amplitude is derived. The anomalous dimension in this equation contains a logarithm of the renormalization scale, whose coefficient is identified with the cusp anomalous dimension of Wilson loops. The exact solution of the evolution equation is obtained, from which the asymptotic behavior of the distribution amplitude is derived. These results can be used to resum Sudakov logarithms entering the hard-scattering kernels in QCD factorization theorems for exclusive B decays.

f(B) and f(B(s)) from QCD sum rules

The decay constants of the pseudoscalar mesons B and B_s are evaluated from QCD sum rules for the pseudoscalar two-point function. Recently calculated perturbative three-loop QCD corrections are incorporated into the sum rule. An analysis in terms of the bottom quark pole mass turns out to be unreliable due to large higher order radiative corrections. On the contrary, in the MS_bar scheme the higher order corrections are under good theoretical control and a reliable determination of f_B and f_{B_s} becomes feasible. Including variations of all input parameters within reasonable ranges, our final results for the pseudoscalar meson decay constants are f_B = 210 +- 19 MeV and f_B_s = 244 +- 21 MeV. Employing additional information on the product sqrt(B_B) f_B from global fits to the unitarity triangle, we are in a position to also extract the B-meson B-parameter B_B = 1.26 +- 0.45. Our results are well compatible with analogous determinations of the above quantities in lattice QCD.

Factorization and the soft overlap contribution to heavy-to-light form factors

Abstract Using the formalism of soft-collinear effective theory, a complete separation of short- and long-distance contributions to heavy-to-light transition form factors at large recoil is performed. The universal functions ζM(E) parameterizing the “soft overlap” contributions to the form factors are defined in terms of matrix elements in the effective theory. Endpoint configurations corresponding to kinematic situations where one of the valence partons in the external mesons carries very small momentum are accounted for in terms of operators involving soft-collinear messenger fields. They contribute at leading order in ΛQCD/E and spoil factorization. An analysis of operator mixing and renormalization-group evolution in the effective theory reveals that the intermediate scale EΛ is without significance to the soft functions ζM(E), and that the soft overlap contribution does not receive a significant perturbative (Sudakov) suppression.

f_B and f_B_s from QCD sum rules

The decay constants of the pseudoscalar mesons B and B_s are evaluated from QCD sum rules for the pseudoscalar two-point function. Recently calculated perturbative three-loop QCD corrections are incorporated into the sum rule. An analysis in terms of the bottom quark pole mass turns out to be unreliable due to large higher order radiative corrections. On the contrary, in the MS_bar scheme the higher order corrections are under good theoretical control and a reliable determination of f_B and f_{B_s} becomes feasible. Including variations of all input parameters within reasonable ranges, our final results for the pseudoscalar meson decay constants are f_B = 210 +- 19 MeV and f_B_s = 244 +- 21 MeV. Employing additional information on the product sqrt(B_B) f_B from global fits to the unitarity triangle, we are in a position to also extract the B-meson B-parameter B_B = 1.26 +- 0.45. Our results are well compatible with analogous determinations of the above quantities in lattice QCD.

Proposal for a precision measurement of |Vub|.

A new method for a precision measurement of the Cabibbo-Kobayashi-Maskawa matrix element |V(ub)| is discussed, which combines good theoretical control with high efficiency and a powerful discrimination against charm background. The resulting combined theoretical uncertainty on |V(ub)| is estimated to be 10%.

The renormalized B-meson light-cone distribution amplitude

I discuss the renormalization-group equation governing the leading order light-cone distribution amplitude of the B-meson φB+(ω,μ) and its exact analytic solution. The solution displays two features concerning the asymptotic behaviour of φB+(ω,μ) for small and large values of ω. I comment on further applications and argue that the loss of normalizability is not a problem in practice.PACS: 12.38.Cy – 12.39.Hg – 12.39.St – 13.25.Hw

QCD-Factorization of inclusive B decays and |Vub|☆

Recent progress in the theoretical description of inclusive B → X u l − ν ¯ decays in the shape-function region is reported. Finite moments of the shape function are related to HQET parameters. Event fractions for several experimental cuts are presented, with a particular emphasis on the hadronic variable P + = E H − | P → H | . The aim of this talk is to introduce the P + spectrum, to compare it to the hadronic invariant mass spectrum and the charged-lepton energy spectrum, and to study the prospect of evaluating | V u b | in the presence of a large background from B → X c decays.

fBandfBsfrom QCD sum rules

The decay constants of the pseudoscalar mesons B and B_s are evaluated from QCD sum rules for the pseudoscalar two-point function. Recently calculated perturbative three-loop QCD corrections are incorporated into the sum rule. An analysis in terms of the bottom quark pole mass turns out to be unreliable due to large higher order radiative corrections. On the contrary, in the MS_bar scheme the higher order corrections are under good theoretical control and a reliable determination of f_B and f_{B_s} becomes feasible. Including variations of all input parameters within reasonable ranges, our final results for the pseudoscalar meson decay constants are f_B = 210 +- 19 MeV and f_B_s = 244 +- 21 MeV. Employing additional information on the product sqrt(B_B) f_B from global fits to the unitarity triangle, we are in a position to also extract the B-meson B-parameter B_B = 1.26 +- 0.45. Our results are well compatible with analogous determinations of the above quantities in lattice QCD.