Operator analysis of pT -widths of TMDs

Abstract

Transverse momentum dependent (TMD) parton distribution functions (PDFs), TMDs for short, are defined as the Fourier transform of matrix elements of nonlocal combinations of quark and gluon fields. The nonlocality is bridged by gauge links, which for TMDs have characteristic paths (future or past pointing), giving rise to a process dependence that breaks universality. It is possible, however, to construct sets of universal TMDs of which in a given process particular combinations are needed with calculable, process-dependent, coefficients. This occurs for both T-odd and T-even TMDs, including also the unpolarized quark and gluon TMDs. This extends the by now well-known example of T-odd TMDs that appear with opposite sign in single-spin azimuthal asymmetries in semi-inclusive deep inelastic scattering or in the Drell-Yan process. In this paper we analyze the cases where TMDs enter multiplied by products of two transverse momenta, which includes besides the p T -broadening observable, also instances with rank-2 structures. To experimentally demonstrate the process dependence of the latter cases requires measurements of second harmonic azimuthal asymmetries, while the p T -broadening will require measurements of processes beyond semi-inclusive deep inelastic scattering or the Drell-Yan process. Furthermore, we propose specific quantities that will allow for theoretical studies of the process dependence of TMDs using lattice QCD calculations.

Positivity bounds on gluon TMDs for hadrons of spin ≤ 1

“…Furthermore, since we look at TMDs, one must worry about the process dependence coming from the fact that functions with different types of gauge links may be needed to describe a process at measured transverse momenta [36]. Another complication is that the dependence of the distributions on k 2 T may require additional functions involving gluonic poles [37]. Assumptions on some of the TMDs and using approximations such as taking the large-N c limit, may thus be necessary.…”

Gluon transverse momentum dependent correlators in polarized high energy processes

“…Depending on the rank of the functions, more gluonic pole operators may enter [20]. For two gluonic poles this lead to an interesting link between the Wilson loop correlator and the gluon correlator at x = 0.…”

Probing the Sivers asymmetries through J/ψ photoproduction in p↑p colli

“…To follow up on the understanding of the Sivers effect origin, numerous launched studies have theoretically been achieved in different key processes in the vein of ep ↑ collision, the heavy quark pair and dijet production [33], the inelastic J/ψ photoproduction [47], e + p ↑ → e + J/ψ + X [30,48,49], and also in pp ↑ scattering for instance pp ↑ → h + X [50], D-meson production [34,51] and back to back jet correlations [52], etc. Even so, a great deal of insufficiencies have been pointed out that certain interactions are in failure in quantifying gluon Sivers function attributable to the problem of TMD factorization breaking contributions [53], some features have been somewhat probed.…”