A study on the interplay between perturbative QCD and CSS/TMD formalism in SIDIS processes

TL;DR

This paper investigates the application of CSS and TMD formalisms to SIDIS processes, highlighting challenges in matching fixed order QCD with soft gluon resummation and emphasizing the importance of non-perturbative effects.

Contribution

It provides a detailed analysis of the matching procedure in SIDIS, revealing limitations of the Y-factor method and emphasizing the role of non-perturbative contributions.

Findings

Y-factor matching is ineffective in SIDIS kinematics.

Non-perturbative effects are significant even at high energies.

Perturbative expansion in the matching region is less reliable than previously thought.

Abstract

We study the Semi-Inclusive Deep Inelastic Scattering (SIDIS) cross section as a function of the transverse momentum, $q_T$. In order to describe it over a wide region of $q_T$, soft gluon resummation has to be performed. Here we will use the original Collins-Soper-Sterman (CSS) formalism; however, the same procedure would hold within the improved Transverse Momentum Dependent (TMD) framework. We study the matching between the region where fixed order perturbative QCD can successfully be applied and the region where soft gluon resummation is necessary. We find that the commonly used prescription of matching through the so-called Y-factor cannot be applied in the SIDIS kinematical configurations we examine. In particular, the non-perturbative component of the resummed cross section turns out to play a crucial role and should not be overlooked even at relatively high energies. Moreover, the perturbative expansion of the resummed cross section in the matching region is not as reliable as it is usually believed and its treatment requires special attention.