Threshold resummation of new partonic channels at next-to-leading power

Abstract

Collider observables involving heavy particles are subject to large logarithmic terms near threshold, which must be summed to all orders in perturbation theory to obtain sensible results. Relatively recently, this resummation has been extended to next-to-leading power in the threshold variable, using a variety of approaches. In this paper, we consider partonic channels that turn on only at next-to-leading power, and show that it is possible to resum leading logarithms using well-established diagrammatic techniques in Quantum Chromodynamics. We first consider deep inelastic scattering, where we reproduce the results of a recent study using an effective theory approach. Next, we consider the quark-gluon channel in both Drell-Yan and Higgs boson production, showing that an explicit all-order form for the leading logarithmic partonic cross section can be obtained. Our results agree with previous conjectures based on fixed-order results.

Snowmass 2021 White Paper: Resummation for future colliders

“…The resummation of logarithms with c NLP nm coefficients, contributing at next-to-leading power (NLP), has been considered only more recently and it is still subject of intense study. Progress has been made by employing diagrammatic [50,65,66], effective field theory [44,47,52,67,68] and renormalization group methods [69,70]. In this section, we provide a brief overview of the diagrammatic approach, while the application of SCET to the resummation of large logarithms at NLP will be discussed in the following section.…”

“…(2.4) is not possible for off-diagonal channels. Despite this complication, it has been possible to derive an all-order resummation formula for NLP LLs in off diagonal channels of processes such as DIS, Drell-Yan and Higgs production [66,68,84]. To this end, a fundamental input is provided by deriving so-called consistency conditions, obtained by requiring the cancellation of leading poles in the total cross section.…”

“…Requiring pole cancellation in the bare total cross section provides a set of equations, whose solution determines the minimal number of parameters needed to fix all the poles -and thus the related large logarithms. The derivation is rather technical, and we refer to [66,68] for further details. The relevant observation is that a minimal set of parameters is given entirely by those associated to a single scale in the problem -one parameter for each perturbative order.…”

“…2 [66]. These can be calculated to all orders, and subsequently the consistency condition allow one to fix the entire cross section.…”

“…(2.7) completes the resummation of LLs at NLP in all the production channels contributing to Drell-Yan. Analogous equations can be obtained for Higgs boson production in gluon fusion and DIS, and we refer to [66,68] for a detailed derivation.…”