Average transverse momentum quantities approaching the lightfront

TL;DR

This paper discusses alternative, well-defined definitions of average transverse momentum quantities in hadrons, using Bessel-weighting and rapidity cut-offs, which are more suitable for theoretical and lattice evaluations.

Contribution

It introduces regularized definitions of transverse momentum quantities that improve upon conventional integrals by reducing sensitivity to large transverse momenta.

Findings

Regularized quantities are well-defined and suitable for lattice calculations.

Alternative definitions reduce sensitivity to high transverse momentum regions.

Conventional definitions are recovered as limiting cases.

Abstract

In this contribution to Light Cone 2014, three average transverse momentum quantities are discussed: the Sivers shift, the dijet imbalance, and the $p_T$ broadening. The definitions of these quantities involve integrals over all transverse momenta that are overly sensitive to the region of large transverse momenta, which conveys little information about the transverse momentum distributions of quarks and gluons inside hadrons. TMD factorization naturally suggests alternative definitions of such integrated quantities, using Bessel-weighting and rapidity cut-offs, with the conventional definitions as limiting cases. The regularized quantities are given in terms of integrals over the TMDs of interest that are well-defined and moreover have the advantage of being amenable to lattice evaluations.