Resummation with Wilson lines off the light cone

Abstract

I review the resummation formalism for organizing large logarithms in perturbative expansion of collinear subprocesses through the variation of Wilson lines off the light cone. A master equation is derived, which involves the evolution kernel resulting from this variation. It is then demonstrated that all the known single- and double-logarithm summations for a parton distribution function or a transverse-momentum-dependentparton distribution can be reproduced from the master equation by applying appropriate soft-gluon approximations to the evolution kernel. Moreover, jet substructures, information which is crucial for particle identification at the Large Hadron Collider and usually acquired from event generators, can also be calculated in this formalism.

18 pages, 13 figures; invited review article to be published by Physics of Elementary Particles and Atomic Nuclei

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• Non-dipolar Wilson links for transverse-momentum-dependent wave functions
• The next-to-leading order corrections to $B\to \rho$ transition in the $k_T$ factorization
• Next-to-Leading-logarithm threshold resummation for exclusive $B$ meson decays
• Transverse-Distance Dependent Parton Densities in the Large-$x$ Regime