55 research outputs found
NNLO hard functions in massless QCD
We derive the hard functions for all 2 → 2 processes in massless QCD up to next-to-next-to-leading order (NNLO) in the strong coupling constant. By employing the known one- and two-loop helicity amplitudes for these processes, we obtain analytic expressions for the ultraviolet and infrared finite, minimally subtracted hard functions, which are matrices in color space. These hard functions will be useful in carrying out higher-order resummations in processes such as dijet and highly energetic top-quark pair production by means of soft-collinear effective theory methods
Boosted Top Quark Pair Production in Soft Collinear Effective Theory
We review a Soft Collinear Effective Theory approach to the study of
factorization and resummation of QCD effects in top-quark pair production. In
particular, we consider differential cross sections such as the top-quark pair
invariant mass distribution and the top-quark transverse momentum and rapidity
distributions. Furthermore, we focus our attention on the large invariant mass
and large transverse momentum kinematic regions, characteristic of boosted top
quarks. We discuss the factorization of the differential cross section in the
double soft gluon emission and small top-quark mass limit, both in Pair
Invariant Mass (PIM) and One Particle Inclusive (1PI) kinematics. The
factorization formulas can be employed in order to implement the simultaneous
resummation of soft emission and small mass effects up to
next-to-next-to-leading logarithmic accuracy. The results are also used to
construct improved next-to-next-to-leading order approximations for the
differential cross sections.Comment: 6 pages. Proceedings of the Second Annual Conference on Large Hadron
Collider Physics (LHCP 2014), Columbia University, New York, June 2-7, 201
NNLL Resummation for the Associated Production of a Top Pair and a Higgs Boson at the LHC
We study the resummation of soft gluon emission corrections to the production of a top-antitop pair in association with a Higgs boson at the Large Hadron Collider. Starting from a soft-gluon resummation formula derived in previous work, we develop a bespoke parton-level Monte Carlo program which can be used to calculate the total cross section along with differential distributions. We use this tool to study the phenomenological impact of the resummation to next-to-next-to-leading logarithmic (NNLL) accuracy, finding that these corrections increase the total cross section and the differential distributions with respect to NLO calculations of the same observables
Boosted top production: factorization and resummation for single-particle inclusive distributions
We study single-particle inclusive (1PI) distributions in top-quark pair production at hadron colliders, working in the highly boosted regime where the top-quarkpTis much larger than its mass. In particular, we derive a novel factorization formula validin the small-mass and soft limits of the differential partonic cross section. This providesa framework for the simultaneous resummation of soft gluon corrections and small-mass logarithms, and also an efficient means of obtaining higher-order corrections to the differential cross section in this limit. The result involves five distinct one-scale functions, three of which arise through the subfactorization of soft real radiation in the small-mass limit. Welist the NNLO corrections to each of these functions, building on results in the literature by performing a new calculation of a soft function involving four light-like Wilson lines tothis order. We thus obtain a nearly complete description of the small-mass limit of the differential partonic cross section at NNLO near threshold,missing only terms involving closed top-quark loops in the virtual corrections
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Factorization and Momentum-Space Resummation in Deep-Inelastic Scattering
Renormalization-group methods in soft-collinear effective theory are used to perform the resummation of large perturbative logarithms for deep-inelastic scattering in the threshold region x {yields} 1. The factorization theorem for the structure function F{sub 2}(x,Q{sup 2}) for x {yields} 1 is rederived in the effective theory, whereby contributions from the hard scale Q{sup 2} and the jet scale Q{sup 2}(1 - x) are encoded in Wilson coefficients of effective-theory operators. Resummation is achieved by solving the evolution equations for these operators. Simple analytic results for the resummed expressions are obtained directly in momentum space, and are free of the Landau-pole singularities inherent to the traditional moment-space results. We show analytically that the two methods are nonetheless equivalent order by order in the perturbative expansion, and perform a numerical comparison up to next-to-next-to-leading order in renormalization-group improved perturbation theory
Infrared Singularities and Soft Gluon Resummation with Massive Partons
Infrared divergences of QCD scattering amplitudes can be derived from an
anomalous dimension matrix, which is also an essential ingredient for the
resummation of large logarithms due to soft gluon emissions. We report a recent
analytical calculation of the anomalous dimension matrix with both massless and
massive partons at two-loop level, which describes the two-loop infrared
singularities of any scattering amplitudes with an arbitrary number of massless
and massive partons, and also enables soft gluon resummation at
next-to-next-to-leading-logarithmic order. As an application, we calculate the
infrared poles in the q qbar -> t tbar and gg -> t tbar scattering amplitudes
at two-loop order.Comment: Talk presented at Loops and Legs in Quantum Field Theory 2010,
Woerlitz, Germany, April 25-30, 201
Resummation for (boosted) top-quark pair production at NNLO+NNLL\u27 in QCD
We construct predictions for top quark pair differential distributions at hadron colliders that combine state-of-the-art NNLO QCD calculations with double resummation at NNLL′ accuracy of threshold logarithms arising from soft gluon emissions and of small mass logarithms. This is the first time a resummed calculation at full NNLO+NNLL′ accuracy in QCD for a process with non-trivial color structure has been completed at the differential level. Of main interest to us is the stability of the and top-quark distributions in the boosted regime where fixed order calculations may become strongly dependent on the choice of dynamic scales. With the help of numeric and analytic arguments we confirm that the choice for the factorization and renormalization scales advocated recently by some of the authors is indeed optimal. We further derive a set of optimized kinematics-dependent scales for the matching functions which appear in the resummed calculations. Our NNLO+NNLL′ prediction for the top-pair invariant mass is significantly less sensitive to the choice of factorization scale than the fixed order prediction, even at NNLO. Notably, the resummed and fixed order calculations are in nearly perfect agreement with each other in the full range when the optimal dynamic scale is used. For the top-quark distribution the resummation performed here has less of an impact and instead we find that upgrading the matching with fixed-order from NLO+NNLL′ to NNLO+NNLL′ to be an important effect, a point to be kept in mind when using NLO-based Monte Carlo event generators to calculate this distribution
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