Resummation of Threshold Logarithms in Effective Field Theory For DIS, Drell-Yan and Higgs Production

TL;DR

The paper demonstrates that threshold resummation for DIS, Drell–Yan, and Higgs production can be formulated within soft-collinear effective theory (SCET) and is fully equivalent to traditional factorization-based approaches at all logarithmic orders. By computing anomalous dimensions and matching coefficients up to three loops, it shows how large logarithms exponentiate in an EFT framework through a hierarchy of scales ($Q$, $\mu_I$, $\mu_F$) and exponents $I_1$, $I_2$, and $I_3$. The authors derive explicit expressions for the resummed coefficient functions up to ${\rm N^3LL}$ (with $A^{(4)}$ needed for full completeness), establish universality between quark and gluon channels via the $f_{(q,g)}$ functions, and verify exact equivalence with conventional approaches by recovering known results (Catani–Vogt/Vogt) for all three processes. They also present process-specific finite pieces and show how DY can be related to DIS via DIS PDFs, highlighting the EFT method’s simplicity and physical clarity. The work solidifies SCET-based threshold resummation as a powerful, general tool for precision QCD predictions.

Abstract

We apply the effective field theoretic (EFT) approach to resum the large perturbative logarithms arising when partonic hard scattering cross-sections are taken to the threshold limit. We consider deep inelastic scattering, Drell-Yan lepton pair production and the standard model Higgs production through gluon-gluon fusion via heavy-top loop. We demonstrate the equivalence of the EFT approach with the more conventional, factorization-based methods to all logarithmic accuracies and to all orders in perturbation theory. Specific EFT results are shown for the resummation up to next-to-next-to-next leading logarithmic accuracy for the above mentioned processes. We emphasize the relative simplicity by which we derive most of the results and more importantly their clear physical origin. We find a new relation between the functions $f_{(q,g)}$ in the quark and gluon form factors and the matching coefficients in Drell-Yan and Higgs production, which may explain their universality believed to hold to all orders in perturbation theory.