The T-Wilson Line

We argue that soft-collinear effective theory, as is currently formulated, lacks an ingredient which is essential for obtaining a gauge invariant definitions of certain non-perturbative matrix elements relevant for semi-inclusive high-energy processes. Those processes and the companion cross-sections are to be analyzed and measured at the Large Hadron Collider. The missing feature is a gauge link constructed only from the transverse component of the gluon field denoted by the "$T$-Wilson line"'. It is neither soft nor collinear. As such it is a new feature of the theory.