Dynamical threshold enhancement and resummation in Drell-Yan production

Abstract

Partonic cross sections for the production of massive objects in hadronic collisions receive large corrections when the invariant mass of the initial-state partons is just above the production threshold. Since typically the center-of-mass energy of the hadronic collision is much higher than the mass of the heavy objects, it is not obvious that these contributions translate into large corrections to the hadronic cross section. Using a recent approach to threshold resummation based on effective field theory, we quantify to which extent the fall-off of the parton densities at high x leads to a dynamical enhancement of the partonic threshold region. With the example of Drell-Yan production, we study the emergence of an effective physical scale characterizing the soft emissions in the process. We derive compact analytical expressions for the resummed Drell-Yan cross section and rapidity distribution directly in momentum space. They are free of Landau-pole singularities and are trivially matched onto fixed-order perturbative calculations. Evaluating the resummed cross sections at NNNLL order and matching onto NNLO fixed-order calculations, we perform a detailed numerical analysis of the cross section and rapidity distribution in pp collisions.

Precision direct photon andW-boson spectra at highpTand comparison to LHC data

“…To analytically continue the result to negative η values, or to improve convergence, it is useful to perform subtractions [30,32]. A single subtraction would use…”

“…For electroweak boson production at large transverse momentum, they amount to 70-80% of the NLO correction [19]. For inclusive Drell-Yan and Higgs production, also the NNLO correction is known, and it is found that a similarly large fraction of the perturbative corrections arises from the partonic threshold region [30,40].…”

“…In hadronic collisions, one needs a somewhat more sophisticated procedure since the scales can depend on the functional form of the non-perturbative PDFs. A method for determining these scales without any arbitrary input of what is natural and what is not was proposed in [30] and applied to direct photon and W production in [18,19]. The idea is very simple: one supplements the leading order calculation with just one part of the SCET calculation at a time, for example, the hard, jet or soft function evaluated at NLO in fixed-order perturbation theory.…”

“…To what extent this dynamical enhancement of the threshold is effective was analyzed in detail in [30]. There is a simple phenomenological argument why it should hold: in events with a 300 GeV gauge boson, there is almost always a jet with p T ∼ 300 GeV recoiling against it.…”

One-loop matching and next-to-next-to-leading log resummation for all partonic2→2processes in QCD

“…Since observables at the LHC generally involve many scales, it is likely that resummation will lead to a quantitatively significant improvement of our theoretical predictions. Recent advances in Soft-Collinear Effective Theory have shown resummation to be achievable at the next-to-leading (NLL) [1,2], next-to-nextto-leading (NNLL) [3,4,5,6] and next-to-next-to-next-to-leading (N 3 LL) logarithmic order [7,8,9,10,11,12,13]. Practical results have included a precise measurement of α s from event shapes [10,11], better agreement with Tevatron data and reduced theoretical uncertainty for the the direct photon p T spectrum [5], and a bound on possible new colored states [14].…”