Transverse Momentum Dependent Correlators Research Articles

Generalized universality of higher transverse moments of quark transverse momentum dependent correlators

The color gauge-invariant transverse momentum dependent (TMD) quark correlators contain process dependent gauge links in the bilocal matrix elements. In this paper, we split these process dependent correlators into universal TMD correlators, which in turn can be parametrized in universal TMD distribution functions. The process dependence is contained in gluonic pole factors, of which the value is determined by the gauge link. The operator structures of the universal TMD correlators are identified using transverse moments. In this paper, specific results for double transverse weighting of quark TMDs are given. In particular, we show that for a spin 1/2 target one has three universal time-reversal even leading `pretzelocity distributions', two of which involve double gluonic pole matrix elements and come with process dependent gluonic pole factors. We generalize the results for single and double weighting to TMD correlators of any specific rank, illustrating it for unpolarized, spin 1/2 and spin 1 targets.

Gauge links for transverse momentum dependent correlators at tree-level

In this paper we discuss the incorporation of gauge links in hadronic matrix elements that describe the soft hadronic physics in high energy scattering processes. In this description the matrix elements appear in soft correlators and they contain non-local combinations of quark and gluon fields. In our description we go beyond the collinear approach in which case also the dependence on transverse momenta of partons is taken into consideration. The non-locality in the transverse direction leads to a complex gauge link structure for the full process, in which color is entangled, even at tree-level. We show that at tree-level in a 1-parton unintegrated (1PU) situation, in which only the transverse momentum of one of the initial state hadrons is relevant, one can get a factorized expression involving transverse momentum dependent (TMD) distribution functions. We point out problems at the level of two initial state hadrons, even for relatively simple processes such as Drell-Yan scattering.

Non-collinearity in high energy processes

We discuss the treatment of intrinsic transverse momenta in high energy scattering processes. Within the field theoretical framework of QCD, the process is described in terms of correlators containing quark and gluon fields. The correlators, parametrized in terms of distribution and fragmentation functions, contain matrix elements of nonlocal field configurations requiring a careful treatment to assure colour gauge invariance. It leads to nontrivial gauge links connecting the parton fields. For the transverse momentum-dependent correlators the gauge links give rise to time reversal odd phenomena, showing up as single spin and azimuthal asymmetries. The gauge links, arising from multi-gluon initial and final state interactions, depend on the colour flow in the process, challenging universality.

Light-cone divergence in twist-3 correlation functions

It is argued that the definition of the twist-3 transverse momentum dependent correlation functions must be modified if they contain light-like Wilson lines. In the framework of a simple spectator model of the nucleon we show explicitly the presence of a light-cone divergence for a specific twist-3 time-reversal odd parton density. This divergence emerges for all eight twist-3 T-odd correlators and appears also in the case of a quark target in perturbative QCD. The divergence can be removed by using non-light-like Wilson lines. Based on our results we argue that currently there exists no established factorization formula for transverse momentum dependent twist-3 observables in semi-inclusive DIS and related processes.

Parameterization of the quark–quark correlator of a spin-[formula omitted] hadron

The general parameterization of the quark–quark correlation function for a spin-12 hadron is considered. The presence of the Wilson line ensuring color gauge invariance of the correlator induces structures that were not given explicitly in the existing literature. In particular, the general form of the transverse momentum dependent correlator entering various hard scattering processes is derived. In this case two new time-reversal odd parton distributions appear at the twist-3 level.