Transverse Momentum Distribution Through Soft-Gluon Resummation in Effective Field Theory

TL;DR

The paper develops a soft-collinear effective theory (SCET) approach to resumming large transverse-momentum–related logarithms in hadronic processes, focusing on Drell-Yan and Higgs production. By performing two-step matching (QCD to SCET_I, then SCET_I to SCET_II) and computing the SCET current anomalous dimension γ1 to two loops, it derives a factorized W(b) in impact-parameter space with explicit hard, soft, and collinear pieces, and shows that the resulting Sudakov exponent reproduces standard CSS results at NLL. The work also provides explicit one- and two-loop matching coefficients and demonstrates how the SCET formalism maps onto CSS, enabling NNLL progress with additional calculations. Overall, the study clarifies the field-theoretic underpinnings of transverse-momentum resummation and lays groundwork for high-precision predictions at colliders.

Abstract

We study resummation of transverse-momentum-related large logarithms generated from soft-gluon radiations in soft-collinear effective field theory. The anomalous dimensions of the effective quark and gluon currents, an important ingredient for the resummation, are calculated to two-loop order. the result at next-to-leading-log reproduces that obtained using the standard method for deep-inelastic scattering, Drell-Yan process, and Higgs production through gluon-gluon fusion. We comment on the extension of the calculation to next-to-next-to-leading logarithms.

Figures (1)

• Figure 1: Non-vanishing Feynman diagrams contributing to Drell-Yan production in the soft-collinear-effective theory: (a) for the soft gluon radiation; (b)-(e) for $n$ and $\bar{n}$ collinear gluon radiations. The mirror diagrams of (a-c) are not shown here but are included in the results.