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.
Highlights
A successful resummation scheme should take care of matching the fixed order hadronic cross section, computed in perturbative QCD at large qT, with the so-called resummed cross section, valid at low qT Q, where large logarithms are properly treated
We study the Semi-Inclusive Deep Inelastic Scattering (SIDIS) cross section as a function of the transverse momentum, qT
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
Summary
For unpolarized SIDIS processes, N → hX, the following CSS expression [6, 7] holds dσtotal dx dy dz dqT2. For SIDIS, we most commonly refer to the transverse momentum P T of the final detected hadron, h, in the γ∗N c.m. frame, rather than to the virtual photon momentum qT , in the N h c.m. frame. They are related by the hadronic momentum fraction z through the expression P T = −z qT , so that dσ dσ 1 dx dy dz dPT2 = dx dy dz dqT2 z2
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