On next to soft threshold corrections to DIS and SIA processes

Abstract

We study the perturbative structure of threshold enhanced logarithms in the coefficient functions of deep inelastic scattering (DIS) and semi-inclusive e+e− annihilation (SIA) processes and setup a framework to sum them up to all orders in perturbation theory. Threshold logarithms show up as the distributions ((1−z)−1 logi(1−z))+ from the soft plus virtual (SV) and as logarithms logi(1−z) from next to SV (NSV) contributions. We use the Sudakov differential and the renormalisation group equations along with the factorisation properties of parton level cross sections to obtain the resummed result which predicts SV as well as next to SV contributions to all orders in strong coupling constant. In Mellin N space, we resum the large logarithms of the form logi(N) keeping 1/N corrections. In particular, the towers of logarithms, each of the form $$ {a}_s^n/{N}^{\alpha }{\log}^{2n-\alpha }(N),{a}_s^n/{N}^{\alpha }{\log}^{2n-1-\alpha }(N)\cdots $$ a s n / N α log 2 n − α N , a s n / N α log 2 n − 1 − α N ⋯ etc for α = 0, 1, are summed to all orders in as.

Next-to SV resummed Drell-Yan cross section beyond leading-logarithm

“…Recently, in [48], we investigated the structure of NSV terms present in the quark anti-quark initiated channels in the inclusive production of pair of leptons in Drell-Yan process and gluon/bottom anti-bottom initiated ones for Higgs boson production. We also analyzed the all-order perturbative structure of the NSV logarithms in the coefficient functions of deep inelastic scattering (DIS) and semi-inclusive e + e − annihilation (SIA) processes in [85]. The formalism is even extended in the context of rapidity distributions to study the all-order behaviour of the NSV terms in addition to the SV distributions in the aforementioned threshold processes, namely Drell-Yan and Higgs production through gluon fusion and bottom quark annihilation in [86].…”

Resummed Higgs boson cross section at next-to SV to $ \rm NNLO + \rm \overline {NNLL}$

“…Recently, in [60], we investigated the structure of NSV terms present in the quark anti quark initiated channels in the inclusive production of a pair of leptons in Drell-Yan process and gluon/bottom anti bottom initiated ones for production of Higgs boson exploiting the factorisation properties and renormalisation group invariance along with the certain universal structure of real and virtual contributions obtained through Sudakov K+G equation. We also studied the allorder perturbative structure of the NSV logarithms in the CFs of deep inelastic scattering (DIS) and semi-inclusive e + e − annihilation (SIA) processes in [88]. The formalism was later extended for studying the all-order behaviour of NSV terms in rapidity distributions of Drell-Yan and Higgs production through gluon fusion and bottom quark annihilation in [89].…”

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

“…[41,42]), there has been more widespread interest in exploring the properties of NLP terms, which could not be more timely given the numerical motivation mentioned above. 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]<...>…”