Power Counting and Modes in SCET

TL;DR

This paper reformulates soft-collinear effective theory (SCET) for two-jet processes, making it boost-invariant, avoiding ultrasoft modes at the hard scale, and clarifying power counting and infrared divergence issues.

Contribution

It introduces a new formulation of SCET that is boost-invariant, does not require ultrasoft modes at the hard scale, and clarifies the treatment of infrared divergences.

Findings

Infrared divergences are resolved with correct sector overlap subtraction.

The formulation is manifestly boost-invariant and power-counting consistent.

Application to deep inelastic scattering demonstrates the approach.

Abstract

We present a formulation of soft-collinear effective theory (SCET) in the two-jet sector as a theory of decoupled sectors of QCD coupled to Wilson lines. The formulation is manifestly boost-invariant, does not require the introduction of ultrasoft modes at the hard matching scale Q, and has manifest power counting in inverse powers of Q. The spurious infrared divergences which arise in SCET when ultrasoft modes are not included in loops disappear when the overlap between the sectors is correctly subtracted, in a manner similar to the familiar zero-bin subtraction of SCET. We illustrate this approach by analyzing deep inelastic scattering in the endpoint region in SCET and comment on other applications.