Alexander R. Williamson

Subleading shape function contributions to the hadronic invariant mass spectrum in anti-B ---> X(u) l anti-nu(l) decay

We study the O(Lambda/mb) corrections to the singly and doubly differential hadronic invariant mass spectra d\Gamma/dsH and d\Gamma/dsH dq^2 in b -> u decays, and discuss the implications for the extraction of the CKM matrix element |Vub|. Using simple models for the subleading shape functions, the effects of subleading operators are estimated to be at thefew percent level for experimentally relevant cuts. The subleading corrections proportional to the leading shape function are larger, but largely cancel in the relation between the hadronic invariant mass spectrum and the photon spectrum in B -> X_s \gamma. We also discuss the applicability of the usual prescription of convoluting the partonic level rate with the leading light-cone wavefunction of the b quark to subleading order.

Renormalon analysis of heavy-light exclusive B decays

We study two-body exclusive decays of the form

Towards the anomalous dimension toO(ΛQCD/mb)for phase space restrictedB¯→Xuℓν¯andB¯→Xsγ

\overline{B}\ensuremath{\rightarrow}{D}^{(*)}L (L=\ensuremath{\pi},\ensuremath{\rho},\dots{})

Phenomenology ofB→ππ,πKdecays atO(αs2β0)in QCD factorization

in the heavy-quark limit. We perform a renormalon analysis of such processes to determine the order at which nonperturbative factorization-breaking power corrections enter the amplitude. We find that a class of leading power corrections to the color octet matrix element, of

Towards the anomalous dimension to O({lambda}{sub QCD}/m{sub b}) for phase space restricted B{yields}X{sub u}l{nu} and B{yields}X{sub s}{gamma}

\mathcal{O}({\ensuremath{\Lambda}}_{\mathrm{QCD}}{/m}_{b}),

Phenomenology of B?pp, pK decays at O(as20) in QCD factorization

vanishes in the limit of a symmetric light meson parton distribution function. We discuss the phenomenological significance of this result.

Phenomenology of B-->pipi, piK decays at O(alphas2beta0) in QCD factorization

We examine the anomalous dimension matrix appropriate for the phase space restricted B --> X(u) ell anti-nu and B --> X(s) gamma decay spectra to subleading nonperturbative order. The effects of the time ordered products of the HQET Lagrangian with the leading order shape function operator are calculated, as are the anomalous dimensions of subleading operators. We establish the renormalizability and closure of a subset of the non-local operator basis, a requirement for the establishment of factorization theorems at this order. Operator mixing is found between the operators which occur to subleading order, requiring the subleading operator basis be extended. We comment on the requirement for new shape functions to be introduced to characterize the matrix elements of these new operators, and the phenomenological consequences for extractions of

Towards the anomalous dimension to O(ΛQCD/mb) for phase space restricted B→Xułv and B→Xsγ

|V_{ub}|

Publisher's Note: Two body B decays with isosinglet final states in soft collinear effective theory [Phys. Rev. D 74, 014003 (2006)]

.

Towards the anomalous dimension to O(LambdaQCD/mb) for phase space restricted B¯-->Xulnu¯ and B¯-->Xsgamma

We study O(alpha^2 beta_0) perturbative corrections to matrix elements entering two-body exclusive decays of the form B -> pi pi, pi K in the QCD factorization formalism, including chirally enhanced power corrections, and discuss the effect of these corrections on direct CP asymmetries, which receive their first contribution at O(alpha). We find that the O(alpha^2 beta_0) corrections are often as large as the O(alpha) corrections. We find large uncertainties due to renormalization scale dependence as well as poor knowledge of the non-perturbative parameters. We assess the effect of the perturbative corrections on the direct CP violation parameters of B -> pi^+ pi^-.