Matthias Neubert

QCD factorization for B ---> pi pi decays: Strong phases and CP violation in the heavy quark limit

We show that, in the heavy quark limit, the hadronic matrix elements that enter B meson decays into two light mesons can be computed from first principles, including {open_quotes}nonfactorizable{close_quotes} strong interaction corrections, and expressed in terms of form factors and meson light-cone distribution amplitudes. The conventional factorization result follows in the limit when both power corrections in 1/m{sub b} and radiative corrections in {alpha}{sub s} are neglected. We compute the order-{alpha}{sub s} corrections to the decays B{sub d}{r_arrow}{pi}{sup +}{pi}{sup {minus}} , B{sub d}{r_arrow}{pi}{sup 0}{pi}{sup 0} , and B{sup +}{r_arrow}{pi}{sup +}{pi}{sup 0} in the heavy quark limit and briefly discuss the phenomenological implications for the branching ratios, strong phases and {ital CP } violation. {copyright} {ital 1999} {ital The American Physical Society}

Neutrino masses and mixings in non-factorizable geometry

We study bulk fermion fields in the localized gravity model with non-factorizable metric recently proposed by Randall and Sundrum, and Gogberashvili. In addition to a tower of weak-scale Kaluza–Klein states we find a zero mode for any value of the fundamental fermion mass. If the fermion mass is larger than half the curvature of the compact dimension, the zero mode can be localized on the “hidden” 3-brane in the Randall–Sundrum model. Identifying this mode with a right-handed neutrino provides a new way for obtaining small Dirac neutrino masses without invoking a see-saw mechanism. Cancellation of the parity anomaly requires introducing an even number of bulk fermions. This naturally leads to a strong hierarchy of neutrino masses and generically large mixing angles.

QCD factorization for exclusive non-leptonic B-meson decays: General arguments and the case of heavy-light final states

We provide a rigorous basis for factorization for a large class of non-leptonic twobody B-meson decays in the heavy-quark limit. The resulting factorization formula incorporates elements of the naive factorization approach and the hard-scattering approach, but allows us to compute systematically radiative (“non-factorizable”) corrections to naive factorization for decays such as B → Dπ and B → ππ. We first discuss the factorization formula from a general point of view. We then consider factorization for decays into heavy-light final states (such as B → Dπ) in more detail, including a proof of the factorization formula at two-loop order. Explicit results for the leading QCD corrections to factorization are presented and compared to existing measurements of branching fractions and final-state interaction phases.

Heavy-quark symmetry

Abstract We review the current status of heavy-quark symmetry and its applications to weak decays of hadrons containing a single heavy quark. After an introduction to the underlying physical ideas, we discuss in detail the formalism of the heavy-quark effective theory, including a comprehensive treatment of symmetry breaking corrections. We then illustrate some nonperturbative approaches, which aim at a dynamical, QCD-based calculation of the universal form factors of the effective theory. The main focus is on results obtained using QCD sum rules. Finally, we perform an essentially model-independent analysis of semileptonic B meson decays in the context of the heavy-quark effective theory.

QCD factorization in B ---> pi K, pi pi decays and extraction of Wolfenstein parameters

Abstract In the heavy-quark limit, the hadronic matrix elements entering nonleptonic B-meson decays into two light mesons can be calculated from first principles including “nonfactorizable” strong-interaction corrections. The B→πK, ππ decay amplitudes are computed including electroweak penguin contributions, SU(3) violation in the light-cone distribution amplitudes, and an estimate of power corrections from chirally-enhanced terms and annihilation graphs. The results are then used to reduce the theoretical uncertainties in determinations of the weak phases γ and α. In that way, new constraints in the ( ρ , η ) plane are derived. Predictions for the B→πK, ππ branching ratios and CP asymmetries are also presented. A good global fit to the (in part preliminary) experimental data on the branching fractions is obtained without taking recourse to phenomenological models.

On the Structure of Infrared Singularities of Gauge-Theory Amplitudes

A closed formula is obtained for the infrared singularities of dimensionally regularized, massless gauge-theory scattering amplitudes with an arbitrary number of legs and loops. It follows from an all-order conjecture for the anomalous-dimension matrix of n-jet operators in soft-collinear effective theory. We show that the form of this anomalous dimension is severely constrained by soft-collinear factorization, non-abelian exponentiation, and the behavior of amplitudes in collinear limits. Using a diagrammatic analysis, we demonstrate that these constraints imply that to three-loop order the anomalous dimension involves only two-parton correlations, with the possible exception of a single color structure multiplying a function of conformal cross ratios depending on the momenta of four external partons, which would have to vanish in all two-particle collinear limits. We suggest that such a function does not appear at three-loop order, and that the same is true in higher orders. Our formula predicts Casimir scaling of the cusp anomalous dimension to all orders in perturbation theory, and we explicitly check that the constraints exclude the appearance of higher Casimir invariants at four loops. Using known results for the quark and gluon form factors, we derive the three-loop coefficients of the 1/n pole terms (with n = 1,...,6) for an arbitrary n-parton scattering amplitude in massless QCD. This generalizes Catanis two-loop formula proposed in 1998.

Asymptotics of heavy-meson form factors

Using methods developed for hard exclusive QCD processes, we calculate the asymptotic behavior of heavy-meson form factors at large recoil. It is determined by the leading- and subleading-twist meson wave functions. For 1{lt}{vert_bar}v{center_dot}v{sup {prime}}{vert_bar}{lt}m{sub Q}/{Lambda}, the form factors are dominated by the Isgur-Wise function, which is determined by the interference between the wave functions of leading and subleading twist. At {vert_bar}v{center_dot}v{sup {prime}}{vert_bar}{gt}m{sub Q}/{Lambda}, they are dominated by two functions arising at order 1/m{sub Q} in the heavy-quark expansion, which are determined by the leading-twist wave function alone. The sum of these contributions describes the form factors in the whole region {vert_bar}v{center_dot}v{sup {prime}}{vert_bar}{gt}1. As a consequence, there is an exact zero in the form factor for the scattering of longitudinally polarized B{sup {asterisk}} mesons at some value v{center_dot}v{sup {prime}}{approximately}m{sub b}/{Lambda}, and an approximate zero in the form factor of B mesons in the timelike region (v{center_dot}v{sup {prime}}{approximately}{minus}m{sub b}/{Lambda}). We obtain the evolution equations and sum rules for the wave functions of leading and subleading twist as well as for their moments. We briefly discuss applications to heavy-meson pair production in e{sup +}e{sup {minus}} collisions. {copyright} {ital 1997} {ital The American Physical Society}

Infrared singularities of scattering amplitudes in perturbative QCD

An exact formula is derived for the infrared singularities of dimensionally regularized scattering amplitudes in massless QCD with an arbitrary number of loops and legs. It is based on the conjecture that the anomalous-dimension matrix of n-jet operators in soft-collinear effective theory is fully determined by three functions of alpha{s}, which can be extracted from known perturbative results for the quark and gluon form factors. This allows us to predict the three-loop coefficients of all 1/;{k} poles for arbitrary n-parton scattering amplitudes, generalizing existing two-loop results.

QCD anatomy of \(B\to X_s\gamma\) decays

Abstract. We present an updated next-to-leading order analysis of the

Factorization and Momentum-Space Resummation in Deep-Inelastic Scattering

B\to X_s\gamma