Abstract

We investigate the transverse momentum dependent parton distributions (TMDs) in the quasi-parton-distribution framework. The long standing hurdle of the so-called pinch pole singularity from the space-like gauge links in the TMD definitions can be resolved by the finite length of the gauge link along the hadron moving direction. In addition, with the soft factor subtraction, the quasi-TMD is free of linear divergence. We further demonstrate that the energy evolution equation of the quasi-TMD a.k.a. the Collins-Soper evolution, only depends on the hadron momentum. This leads to a clear matching between the quasi-TMD and the standard TMDs.

Highlights

  • Transverse momentum dependent parton distributions (TMDs) are one of the major focuses in nucleon tomography studies at existing and future facilities [1]

  • large momentum effective theory (LaMET) is based on the observation that parton physics defined in terms of lightcone correlations can be obtained from timeindependent Euclidean correlations, known as quasidistributions, boosted to the infinite momentum frame

  • The major hurdle is that the formulation of the TMDs is different from the integrated PDFs and, in particular, the gauge links associated with the Q-TMDs lead to the so-called pinch pole singularities

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Summary

INTRODUCTION

Transverse momentum dependent parton distributions (TMDs) are one of the major focuses in nucleon tomography studies at existing and future facilities [1]. The major hurdle is that the formulation of the TMDs is different from the integrated PDFs and, in particular, the gauge links associated with the Q-TMDs lead to the so-called pinch pole singularities This is a generic feature of the TMDs defined with a space-like gauge link [2,5]. [41], a soft factor subtraction involving transverse gauge links has been proposed to formulate the Q-TMDs. In Ref. [41], a soft factor subtraction involving transverse gauge links has been proposed to formulate the Q-TMDs This formalism may have practical difficulties for lattice computations at present. With finite length gauge links in the Q-TMDs, there will be no pinch pole singularity This will pave the way to perform the TMD calculations on the lattice.

ABSENCE OF THE PINCH SINGULARITY IN Q-TMDS
MATCHING TO THE STANDARD TMDS
DISCUSSIONS AND SUMMARY
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