Singular and Regular Gauges in Soft Collinear Effective Theory: The Introduction of the New Wilson Line T

Abstract

Gauge invariance in soft-collinear effective theory (SCET) is discussed in regular (covariant) and singular (light-cone) gauges. It is argued that SCET, as it stands, is not capable to define in a gauge invariant way certain non-perturbative matrix elements that are an integral part of many factorization theorems. Those matrix elements involve two quark or gluon fields separated not only in light-cone direction but also in the transverse one. This observation limits the range of applicability of SCET. To remedy this we argue that one needs to introduce a new Wilson line as part of SCET formalism, that we call T. This Wilson line depends only on the transverse component of the gluon field. As such it is a new feature to the SCET formalism and it guarantees gauge invariance of the non-perturbative matrix elements in both classes of gauges.

Version to appear in Phys. Lett. B. The discussion of the zero-bin subtraction is modified. Some typos corrected

References in corpus (4)

• The Zero-Bin and Mode Factorization in Quantum Field Theory
• Wilson lines and transverse-momentum dependent parton distribution functions: A renormalization-group analysis
• Renormalization, Wilson lines, and transverse-momentum dependent parton distribution functions
• Endpoint singularities in unintegrated parton distributions

Cited by in corpus (14)

• Forward-Central Jet Correlations at the Large Hadron Collider
• SCET, Light-Cone Gauge and the T-Wilson Lines
• Transverse momentum dependent operator expansion at next-to-leading power
• Collinear matching for Sivers function at next-to-leading order
• Factorization for Azimuthal Asymmetries in SIDIS at Next-to-Leading Power
• Transverse Momentum Distributions in the Non-Perturbative Region
• One-loop Matching for Spin-Dependent Quasi-TMDs
• Cusped light-like Wilson loops in gauge theories
• Definition and evolution of transverse momentum dependent distribution of twist-three
• Evolution of cusped light-like Wilson loops and geometry of the loop space
• Matching generalised transverse-momentum-dependent distributions onto generalised parton distributions at one loop
• On Geometric Scaling of Light-Like Wilson Polygons: Higher Orders in ${\alpha }_s$
• Nucleon tomography. What can we do better today than Rutherford 100 years ago?
• Evolution of unpolarized transverse momentum dependent parton distributions of twist-3