Using methods of effective field theory, factorized expressions for arbitraryB → 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 chargedlepton 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 ub | is proposed, which combines good theoretical control with high efficiency and a powerful discrimination against charm background.

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.

We present "state-of-the-art" theoretical expressions for the triple differentialB → X u l −ν decay rate and for theB → X s γ photon spectrum, which incorporate all known contributions and smoothly interpolate between the "shape-function region" of large hadronic energy and small invariant mass, and the "OPE region" in which all hadronic kinematical variables scale with M B . The differential rates are given in a form which has no explicit reference to the mass of the b quark, avoiding the associated uncertainties. Dependence on m b enters indirectly through the properties of the leading shape function, which can be determined by fitting theB → X s γ photon spectrum. This eliminates the dominant theoretical uncertainties from predictions forB → X u l −ν decay distributions, allowing for a precise determination of |V ub |. In the shape-function region, short-distance and long-distance contributions are factorized at next-to-leading order in renormalization-group improved perturbation theory. Higher-order power corrections include effects from subleading shape functions where they are known. When integrated over sufficiently large portions in phase space, our results reduce to standard OPE expressions up to yet unknown O(α 2 s ) terms. Predictions are presented for partial B → X u l −ν decay rates with various experimental cuts. An elaborate error analysis is performed that contains all significant theoretical uncertainties, including weak annihilation effects. We suggest that the latter can be eliminated by imposing a cut on high lepton invariant mass.

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 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 ϭ210Ϯ19 MeV and f B s ϭ244Ϯ21 MeV. Employing additional information on the product ͱB 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 ϭ1.26 Ϯ0.45. Our results are quite compatible with analogous determinations of the above quantities in lattice QCD.

Soft-collinear effective theory is used to prove factorization of the B → γlν decay amplitude at leading power in Λ/m b , including a demonstration of the absence of non-valence Fock states and of the finiteness of the convolution integral in the factorization formula. Large logarithms entering the hard-scattering kernel are resummed by performing a two-step perturbative matching onto the low-energy effective theory, and by solving evolution equations derived from the renormalization properties of the leading-order B-meson light-cone distribution amplitude. As a byproduct, the evolution equation for heavy-collinear current operators in soft-collinear effective theory is derived.

It has recently been argued that soft-collinear effective theory for processes involving both soft and collinear partons contains a new soft-collinear mode, which can communicate between the soft and collinear sectors of the theory. The formalism incorporating the corresponding fields into the effective Lagrangian is extended to include external current and four-quark operators relevant to weak interactions. An explicit calculation of the anomalous dimensions of these operators reveals that soft-collinear modes are needed for correctly describing the ultraviolet behavior of the effective theory.

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Solving the electronic structure from a generalized or standard eigenproblem is often the bottleneck in large scale calculations based on Kohn-Sham density-functional theory. This problem must be addressed by essentially all current electronic structure codes, based on similar matrix expressions, and by high-performance computation. We here present a unified software interface, ELSI, to access different strategies that address the Kohn-Sham eigenvalue problem. Currently supported algorithms include the dense generalized eigensolver library ELPA, the orbital minimization method implemented in libOMM, and the pole expansion and selected inversion (PEXSI) approach with lower computational complexity for semilocal density functionals. The ELSI interface aims to simplify the implementation and optimal use of the * Corresponding author.