Factorization of Lepton Radiation in SIDIS

The factorization theorem plays an important role in the analysis of high energy QCD processes, separating the nonperturbative hadronic interaction into the universal parton distribution functions (PDFs) and fragmentation functions (FFs). However, the lepton-hadron collision induced QED radiation can change the momentum of the exchanged unobserved virtual photon, making the photon-hadron frame, where the factorization formalism for lepton-hadron semi-inclusive deep inelastic scattering (SIDIS) was derived, ill defined. An new analogous factorization approach has been introduced to separate the leading power process independent QED radiative contributions to the single photon exchange by introducing lepton distribution functions (LDFs) and fragmentation functions (LFFs), while process dependent effects are calculated with large logarithms removed [J. High Energ. Phys. 2021, 157 (2021)]. These LDFs and LFFs are considered global, as they appear in many different interactions, such as e⁺ e^- and SIDIS, so data from experiments can be used to describe these functions across a wide range of lepton scattering. In this talk, I will apply this hybrid approach to lepton-hadron SIDIS to study the transition between the two-scale region, where the transverse momentum dependent (TMD) factorization is relevant, and the single scale region, where collinear factorization approach is more relevant, treating both QCD and QED factorization equally. I also derive the NLO perturbative coefficients for SIDIS in both regions, and investigate the matching between these two regions.