Large-x resummation of off-diagonal deep-inelastic parton scattering from d-dimensional refactorization

Building on the recent derivation of a bare factorization theorem for the b-quark induced contribution to the h → γγ decay amplitude based on soft-collinear effective theory, we derive the first renormalized factorization theorem for a process described at subleading power in scale ratios, where λ = mb/Mh « 1 in our case. We prove two refactorization conditions for a matching coefficient and an operator matrix element in the endpoint region, where they exhibit singularities giving rise to divergent convolution integrals. The refactorization conditions ensure that the dependence of the decay amplitude on the rapidity regulator, which regularizes the endpoint singularities, cancels out to all orders of perturbation theory. We establish the renormalized form of the factorization formula, proving that extra contributions arising from the fact that “endpoint regularization” does not commute with renormalization can be absorbed, to all orders, by a redefinition of one of the matching coefficients. We derive the renormalization-group evolution equation satisfied by all quantities in the factorization formula and use them to predict the large logarithms of order $$ {\alpha \alpha}_s^2{L}^k $$ αα s 2 L k in the three-loop decay amplitude, where $$ L=\ln \left(-{M}_h^2/{m}_b^2\right) $$ L = ln − M h 2 / m b 2 and k = 6, 5, 4, 3. We find perfect agreement with existing numerical results for the amplitude and analytical results for the three-loop contributions involving a massless quark loop. On the other hand, we disagree with the results of previous attempts to predict the series of subleading logarithms $$ \sim {\alpha \alpha}_s^n{L}^{2n+1} $$ ∼ αα s n L 2 n + 1 .

Section: Jhep01(2021)077mentioning

confidence: 99%

Factorization at subleading power and endpoint divergences in h → γγ decay. Part II. Renormalization and scale evolution

Liu

Mecaj

Neubert

et al. 2021

“…We comment on the comparison with our work in section 4.4.3 Although important progress has been made, see e.g [16,37,39]…”

mentioning

confidence: 88%

“…A general resummation framework for soft-quark emissions is still under development (see e.g. [37][38][39] for recent process in the SCET framework).…”

Section: Introductionmentioning

confidence: 99%

Next-to-leading power threshold corrections for finite order and resummed colour-singlet cross sections

Beekveld

Laenen

Damsté

et al. 2021

Self Cite

We study next-to-leading-power (NLP) threshold corrections in colour-singlet production processes, with particular emphasis on Drell-Yan (DY) and single-Higgs production. We assess the quality of the partonic and hadronic threshold expansions for each process up to NNLO. We determine numerically the NLP leading-logarithmic (LL) resummed contribution in addition to the leading-power next-to-next-to-leading logarithmic (LP NNLL) resummed DY and Higgs cross sections, matched to NNLO. We find that the inclusion of NLP logarithms is numerically more relevant than increasing the precision to N3LL at LP for these processes. We also perform an analytical and numerical comparison of LP NNLL + NLP LL resummation in soft-collinear effective theory and direct QCD, where we achieve excellent analytical and numerical agreement once the NLP LL terms are included in both formalisms. Our results underline the phenomenological importance of understanding the NLP structure of QCD cross sections.

“…Examples using direct QCD arguments include developing factorisation theorems for NLP contributions that extend their LP counterparts [43][44][45][46][47][48][49]; carrying out fixed-order studies that aim to motivate such formulae [50][51][52][53][54][55][56]; resumming NLP contributions by combining factorisation and renormalisation group arguments [26,[57][58][59][60][61]; and resumming specific contributions [62]. There is also an ever-growing body of work examining NLP effects in SCET, including identifying relevant operators contributing at NLP order and/or their mixing under renormalisation [63][64][65][66][67][68][69][70]; development of factorisation formulae [71][72][73][74]; and explicit studies for particular observables, either at fixed-order or resummed [75][76][77][78][79][80][81][82][83][84][85][86]. This has pr...…”

Section: Introductionmentioning

confidence: 99%

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

Beekveld¹,

Vernazza

White

2021

Self Cite

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.