Factorized approach to radiative corrections for inelastic lepton-hadron collisions

Tianbo Liu,N. Sato,Jian-Wei Qiu,W. Melnitchouk

doi:10.1103/physrevd.104.094033

Abstract

We propose a factorized approach to QED radiative corrections for inclusive and semi-inclusive deep-inelastic scattering to systematically account for QED and QCD radiation contributions to both processes on equal footing. This is achieved by utilizing factorization to resum logarithmically enhanced QED radiation into universal lepton distribution and fragmentation (or jet) functions. Numerical simulations suggest that the QED effects induced by the rotational distortion of the hadron transverse momentum, arising from the mismatch between the experimental Breit frame and the true photon-hadron frame, can be as large as 50\% for moderate $Q$, and become increasingly important for large transverse momenta. Our framework provides a uniform treatment of radiative effects for extracting three-dimensional hadron structure from high-energy lepton-hadron scattering at current and future facilities, such as the Electron-Ion Collider.

Highlights

Lepton-hadron deep-inelastic scattering (DIS) has played a critical role in the development of our understanding of the internal structure of nucleons and nuclei, since the first such experiments were performed at SLAC over 50 years ago [1]
With the leptonic plane defined by l and l0 and the hadronic plane defined by P and Ph, angular modulations between these planes in semi-inclusive DIS (SIDIS) allow the extraction of various transverse momentum dependent distributions (TMDs), which encode rich information about the hadron’s three-dimensional structure in momentum space [3,4,5,6,7,8]
After a careful study of the QED transverse momentum broadening in terms of transverse momentum dependent lepton distribution functions (LDFs) and Sudakov resummation of QED logarithms, we found that the broadening from QED radiation is much smaller than the corresponding broadening from QCD radiation, mainly due to the fact that α ≪ αs [54]

Summary

INTRODUCTION

Lepton-hadron deep-inelastic scattering (DIS) has played a critical role in the development of our understanding of the internal structure of nucleons and nuclei, since the first such experiments were performed at SLAC over 50 years ago [1]. By detecting a hadron (or jet) of momentum Ph in the final state, the semi-inclusive DIS (SIDIS) process has two naturally ordered momentum scales: Q, and the transverse momentum PhT ≡ jPhTj ≪ Q, defined in the “photon-hadron” frame, where the virtual photon collides with the hadron moving along the z axis. The collision with a large momentum transfer triggers radiation of photons from the colliding and scattered leptons and quarks (Fig. 1). This radiation changes the momentum transfer q, making it problematic to define PhT in the true photon-hadron frame and alters the angular modulation between the leptonic and hadronic planes. We will show that this approach especially impacts the extraction of TMDs from lepton-hadron scattering

INCLUSIVE LEPTON-NUCLEON DIS

SEMI-INCLUSIVE DIS

OUTLOOK