Guido Bell

Analytic regularization in Soft-Collinear Effective Theory

In high-energy processes which are sensitive to small transverse momenta, individual contributions from collinear and soft momentum regions are not separately well-defined in dimensional regularization. A simple possibility to solve this problem is to introduce additional analytic regulators. We point out that in massless theories the unregularized singularities only appear in real-emission diagrams and that the additional regulators can be introduced in such a way that gauge invariance and the factorized eikonal structure of soft and collinear emissions is maintained. This simplifies factorization proofs and implies, at least in the massless case, that the structure of Soft-Collinear Effective Theory remains completely unchanged by the presence of the additional regulators. Our formalism also provides a simple operator definition of transverse parton distribution functions.

The gluon jet function at two-loop order

Abstract The inclusive gluon jet function is evaluated at two-loop accuracy. This function is relevant for resummations of large perturbative logarithms in collider processes involving low-mass gluon jets. The jet function corresponds to the imaginary part of the gluon propagator in light-cone gauge, which is adopted for the calculation. In addition to the leading jet function, the power-suppressed two-gluon jet functions are given and their renormalization is discussed.

NNLL Resummation for Jet Broadening

A bstractThe resummation for the event-shape variable jet broadening is extended to next-to-next-to-leading logarithmic accuracy by computing the relevant jet and soft functions at one-loop order and the collinear anomaly to two-loop accuracy. The anomaly coefficient is extracted from the soft function and expressed in terms of polylogarithmic as well as elliptic functions. With our results, the uncertainty on jet-broadening distributions is reduced significantly, which should allow for a precise determination of the strong coupling constant from the existing experimental data and provide a consistency check on the extraction of αs from higher-log resummations of thrust.

Factorization and Resummation for Jet Broadening

Abstract Jet broadening is an event-shape variable probing the transverse momenta of particles inside jets. It has been measured precisely in e + e − annihilations and is used to extract the strong coupling constant. The factorization of the associated cross section at small values of the broadening is afflicted by a collinear anomaly. Based on an analysis of this anomaly, we present an all-order factorization theorem for jet-broadening distributions, which is free of large perturbative logarithms in the two-jet limit. Our formula reproduces known results at next-to-leading logarithmic order but also extends to higher orders.

Light-Cone Distribution Amplitudes for Heavy-Quark Hadrons

A bstractWe construct parametrizations of light-cone distribution amplitudes (LCDAs) for B-mesons and Λb-baryons that obey various theoretical constraints, and which are simple to use in factorization theorems relevant for phenomenological applications in heavy-flavour physics. In particular, we find the eigenfunctions of the Lange-Neubert renormalization kernel, which allow for a systematic implementation of renormalization-group evolution effects for both B-meson and Λb-baryon decays. We also present a new strategy to construct LCDA models from momentum-space projectors, which can be used to implement Wandzura-Wilczek-like relations, and which allow for a comparison with theoretical approaches that go beyond the collinear limit for the light-quark momenta in energetic heavy-hadron decays.

Master integrals for the two-loop penguin contribution in non-leptonic B-decays

A bstractWe compute the master integrals that arise in the calculation of the leading penguin amplitudes in non-leptonic B-decays at two-loop order. The application of differential equations in a canonical basis enables us to give analytic results for all master integrals in terms of iterated integrals with rational weight functions. It is the first application of this method to the case of two different internal masses.

NNLO soft function for electroweak boson production at large transverse momentum

A bstractThe soft function relevant for the production of an electroweak boson (γ, W, Z or H) with large transverse momentum at a hadron collider is computed at next-to-next-to-leading order. This is the first two-loop computation of a soft function describing emissions from energetic partons in three directions. With the result, the threshold resummation for these processes can now be performed at next-to-next-to-next-to-leading logarithmic accuracy.

Enhanced nonperturbative effects through the collinear anomaly.

We show that nonperturbative effects are logarithmically enhanced for transverse-momentum-dependent observables such as qT spectra of electroweak bosons in hadronic collisions and jet broadening at e+ e- colliders. This enhancement arises from the collinear anomaly, a mechanism characteristic for transverse observables, which induces logarithmic dependence on the hard scale in the product of the soft and collinear matrix elements. Our analysis is based on an operator product expansion and provides, for the first time, a systematic, model-independent way to study nonperturbative effects for this class of observables. For the case of jet broadening, we relate the leading correction to the nonperturbative shift of the thrust distribution.

Transverse-momentum spectra of electroweak bosons near threshold at NNLO

A bstractWe obtain the next-to-next-to-leading order corrections to transverse-momentum spectra of W, Z and Higgs bosons near the partonic threshold. In the threshold limit, the electroweak boson recoils against a low-mass jet and all radiation is either soft, or collinear to the jet or the beam directions. We extract the virtual corrections from known results for the relevant two-loop four-point amplitudes and combine them with the soft and collinear two-loop functions as defined in Soft-Collinear Effective Theory. We have implemented these results in a public code PeTeR and present numerical results for the threshold resummed cross section of W and Z bosons at next-to-next-to-next-to-leading logarithmic accuracy, matched to next-to-leading fixed-order perturbation theory. The two-loop corrections lead to a moderate increase in the cross section and reduce the scale uncertainty by about a factor of two. The corrections are significantly larger for Higgs production.

Heavy-to-light currents at NNLO in SCET and semi-inclusive (B)over-bar -> X(s)l(+)l(-) decay

We perform the two-loop matching calculation for heavy-to-light currents from QCD onto soft-collinear effective theory for the complete set of Dirac structures. The newly obtained matching coefficients enter several phenomenological applications, of which we discuss heavy-to-light form factor ratios and exclusive radiative decays. as well as the semi-inclusive decay (B) over bar -> X(s)l(+)l(-). For this decay, we observe a significant shift of the forward-backward asymmetry zero and find q(0)(2) = (3.34(-0.25)(+0.22)) GeV2 for an invariant mass cut, m(X)(cut) = 2.0 GeV