SCET, Light-Cone Gauge and the T-Wilson Lines

TL;DR

This paper extends Soft-Collinear Effective Theory (SCET) to be applicable in both covariant and singular gauges by deriving a modified Lagrangian, enabling gauge-invariant factorization in semi-inclusive processes with non-integrated transverse momenta.

Contribution

The work introduces a new SCET Lagrangian valid in both regular and singular gauges, broadening the theory's applicability to more complex scattering processes.

Findings

Derived a gauge-invariant SCET Lagrangian for singular gauges.

Enabled factorization theorems for semi-inclusive processes.

Ensured non-perturbative matrix elements are gauge invariant.

Abstract

Soft-Collinear Effective Theory (SCET) has been formulated since a decade now in covariant gauges. In this work we derive a modified SCET Lagrangian applicable in both classes of gauges: regular and singular ones. This extends the range of applicability of SCET. The new Lagrangian must be used to obtain factorization theorems in cases where the transverse momenta of the particles in the final states are not integrated over, such as semi-inclusive deep inelastic scattering, Drell-Yan and the Higgs production cross-section at low transverse momentum. By doing so all non-perturbative matrix elements appearing in the factorized cross-sections are gauge invariant.