NNLO QCD corrections to unpolarized and polarized SIDIS

TL;DR

This work addresses the need for precise SIDIS predictions by computing the complete NNLO QCD corrections to the SIDIS coefficient functions for both polarized and unpolarized beams. The authors perform a full NNLO calculation including all partonic channels (VV, RV, RR), amplitudes, phase-space master integrals via IBP and reverse unitarity, UV renormalization, and mass factorization with spin-dependent kernels, employing Larin's scheme for gamma5 and a subsequent MSbar transformation for polarized observables. The resulting finite coefficient functions are used in extensive phenomenology of $F_1$ and $g_1$ at EIC kinematics, demonstrating that NNLO corrections reduce renormalization and factorization scale uncertainties and improve perturbative stability. This enhances the reliability of SIDIS in constraining PDFs and FFs and paves the way for threshold resummation and small-$x$ analyses, with analytic NNLO expressions provided as ancillary material for use in global fits and evolution studies.

Abstract

The semi-inclusive deep-inelastic scattering (SIDIS) process requires the presence of an identified hadron H$'$ in the final state, which arises from the scattering of a lepton with an initial hadron P. By employing factorization in quantum chromodynamics (QCD), SIDIS provides essential knowledge on the hadron structure, enabling the exploration of parton distribution functions (PDFs) and fragmentation functions (FFs). The coefficient functions for SIDIS can be calculated in perturbative QCD and are currently known to the next-to-next-to-leading order (NNLO) for the cases, where the incoming lepton and the hadron P are either both polarized or unpolarized. We present a detailed description of these NNLO computations, including a thorough discussion of all the partonic channels, the calculation of the amplitudes and master integrals for the phase-space integration as well as the renormalization of ultraviolet divergences and mass factorization of infrared divergences in dimensional regularization through NNLO. We provide an extensive phenomenological analysis of the effects of NNLO corrections on SIDIS cross sections for different PDFs and FFs and various kinematics, including those of the future Electron-Ion Collider (EIC). We find that these corrections are not only significant but also crucial for reducing the dependence on the renormalization and factorization scales $μ_R$ and $μ_F$ to obtain stable predictions.

Figures (20)

• Figure 1: Feynman diagram for the LO process.
• Figure 2: Sub-processes at NLO. The integers denote the numbers of additional diagrams to be considered.
• Figure 3: Schematic representation of two-loop VV Feynman diagrams.
• Figure 4: RV diagrams (one-loop with one real emission) at NNLO.
• Figure 5: RR diagrams: emissions of two gluons. The integer indicates the number of additional diagrams.