On next to soft threshold corrections to DIS and SIA processes

A H Ajjath,V Ravindran,Pooja Mukherjee,Aparna Sankar,Surabhi Tiwari

doi:10.1007/jhep04(2021)131

A H Ajjath, V Ravindran + Show 3 more

Open Access

https://doi.org/10.1007/jhep04(2021)131

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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 etc for α = 0, 1, are summed to all orders in as.

Highlights

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
We study these observables in the large Q2 region, we drop the power suppressed contributions denoted by O(1/Q2) in the above formula and consider only the first term for rest of our study. σI(0) is the born level cross section and μR is the ultraviolet renormalisation scale, fa denotes PDF for I = DIS and parton fragmentation functions (PFF) for I = SIA
From eqs. (2.30), (2.31), we find that the explicit results on φf,c extracted for different structure functions do not coincide, implying that they are sensitive to hard scattering of quarks/anti-quarks with the photon

Summary

Next to SV in z space

We begin with the unpolarised inclusive deep-inelastic lepton-nucleon scattering: l(k) + H(P ) → l(k ) + X(PX ) ,. In [28, 45], using the K+G structure of FF and the finiteness of inclusive cross sections, it was shown that the soft distribution functions SJc equivalently, ΦcJ in Drell-Yan production of lepton pairs and production of Higgs boson in gluon fusion in hadron colliders and soft plus jet function in DIS processes were shown to satisfy K+G type differential equations. We can determine soft and collinear divergences present in ΦcJ at every order in perturbation theory using FF, AP kernel but the finite part requires the explicit computation of real emission subprocesses around z = 1. Note that the SV part of the diagonal splitting function in the logarithms of diagonal AP kernel in eq (2.9) cancels the one from GcJ,SV and the remaining divergence coming from NSV part cancels against φs,c making ∆c finite to all orders in as.

Resummation in N space

Physical evolution kernel

Conclusions