NNLO electron structure functions (PDFs) from SCET

TL;DR

This paper computes electron structure functions (PDFs) at NNLO in QED using SCET, confirming previous Mellin space results and extending them to include multiple massive fermion flavors, with implications for high-energy scattering processes.

Contribution

It introduces a momentum-space SCET-based calculation of electron PDFs at NNLO, incorporating multiple massive fermion flavors, and discusses factorization and resummation in this context.

Findings

Confirmed earlier Mellin space results with a momentum-space approach.

Extended calculations to include multiple massive fermion flavors.

Discussed the factorization and resummation of large logarithms in electron PDFs.

Abstract

We calculate the electron structure functions, aka parton distribution functions (PDFs), to NNLO in QED. The calculation is based on the definition of the PDFs in terms of operator matrix elements in soft collinear effective theory (SCET) and directly performed in momentum space. The electron PDFs describe the universal effects of collinear initial state radiation (ISR) off the electron (or positron) in DIS or $e^+ e^-$ collision events. The parton collinear to the electron that enters the hard scattering process governed by the energy scale $Q$ can be a photon or a (anti)fermion with mass $m_f \sim m_e \ll Q$. Our SCET momentum-space calculation confirms earlier results obtained from a QED computation in Mellin space and extends them by taking more than one massive fermion flavor into account. The well-known factorization of sufficiently inclusive cross sections into PDFs with massive fermions and hard partonic cross sections with massless fermions at leading order in $m_e/Q$ is discussed from the SCET perspective. Analogies to the nonperturbative PDFs and collinear factorization in QCD are pointed out. Based on this factorization DGLAP-type resummation of large logarithms of the ratio $m_e/Q$ is straightforward.