Color entanglement for azimuthal asymmetries in the Drell-Yan process

In the resummation of collinear gluons emitted together with active partons from the hadrons in the Drell-Yan process (DY) effects of color entanglement become important when the transverse directions are taken into account. It is then no longer possible to write the cross section as the convolution of two soft correlators and a hard part. We show that the color entanglement introduces additional color factors that must be taken into account in the extraction of transverse momentum dependent parton distribution functions (TMD PDFs) from azimuthal asymmetries. Examples where such effects matter are the extraction of the double Sivers and double Boer-Mulders asymmetries. Furthermore, we will argue why this color entanglement is a basic ingredient already in the tree-level description of azimuthal asymmetries.Comment: 5 pages, minor corrections and updated reference

Modelling distribution functions and fragmentation functions

We present examples for the calculation of the distribution and fragmentation functions using the representation in terms of non-local matrix elements of quark field operators. As specific examples, we use a simple spectator model to estimate the leading twist quark distribution functions and the fragmentation functions for a quark into a nucleon or a pion.Comment: 5 pages RevTeX, talk presented at the First ELFE School on Confinement Physics, 22-28 July 1995, Cambridge, Englan

Universality of TMD distribution functions of definite rank

Transverse momentum dependent (TMD) distribution and fragmentation functions are described as Fourier transforms of matrix elementscontaining nonlocal combinations of quark and gluon fields. These matrix elements also contain a gauge link operator with a process dependent path, of which the process dependence that can be traced back to the color flow in the process. Expanding into irreducible tensors built from the transverse momenta p_\st, we can define a universal set of TMD correlators of definite rank with a well-defined operator structure.Comment: 6 pages, to be published in proceedings of the Third Worshop on the QCD Structure of the Nucleon (QCD N'12), Bilbao, Spain, 22-26 October 201

Estimate of the Collins function in a chiral invariant approach

We estimate the Collins function at a low energy scale by calculating the fragmentation of a quark into a pion at the one-loop level in the chiral invariant model of Manohar and Georgi. We give a useful parametrization of our results and we briefly discuss different spin and/or azimuthal asymmetries containing the Collins function and measurable in semi-inclusive DIS and e+ e- annihilationComment: 5 pages, 4 figures, to appear in Proceedings of 10th International Workshop on Deep Inelastic Scattering (DIS 2002), Cracow, Poland, 30 Apr-4 May 200

Universality of TMD correlators

In a high-energy scattering process with hadrons in the initial state, color is involved. Transverse momentum dependent distribution functions (TMDs) describe the quark and gluon distributions in these hadrons in momentum space with the inclusion of transverse directions. Apart from the (anti)-quarks and gluons that are involved in the hard scattering process, additional gluon emissions by the hadrons have to be taken into account as well, giving rise to Wilson lines or gauge links. The TMDs involved are sensitive to the process under consideration and hence potentially nonuniversal due to these Wilson line interactions with the hard process; different hard processes give rise to different Wilson line structures. We will show that in practice only a finite number of universal TMDs have to be considered, which come in different linear combinations depending on the hard process under consideration, ensuring a generalized universality. For quarks this gives rise to three Pretzelocity functions, whereas for gluons a richer structure of functions arises.Comment: 6 pages, presented by the first author at the 4th International Workshop on Transverse Polarization Phenomena in Hard Processes (Transversity 2014), June 9-13, 2014, Chia, Italy. To appear in EPJ Web of Conference

Operator analysis of pTp_T-widths of TMDs

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 {\it 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 two 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.Comment: 10 pages, no figures; expanded discussions, matches version accepted by JHE

Spectral analysis of gluonic pole matrix elements for fragmentation

The non-vanishing of gluonic pole matrix elements can explain the appearance of single spin asymmetries in high-energy scattering processes. We use a spectator framework approach to investigate the spectral properties of quark-quark-gluon correlators and use this to study gluonic pole matrix elements. Such matrix elements appear in principle both for distribution functions such as the Sivers function and fragmentation functions such as the Collins function. We find that for a large class of spectator models, the contribution of the gluonic pole matrix element in fragmentation functions vanishes. This outcome is important in the study of universality for fragmentation functions and confirms findings using a different approach.Comment: 9 pages, 4 figures, added reference

Positivity bounds on spin-one distribution and fragmentation functions

We establish a connection between the distribution functions of quarks in spin-one hadrons and the helicity matrix for forward scattering of antiquarks off spin-one hadrons. From positivity of this matrix we obtain inequality relations among the distribution functions. Analogous relations hold also for fragmentation functions. The bounds we obtained can be used to constrain estimates of unknown functions, occurring in particular in semi-inclusive deep inelastic scattering or e+ e- annihilation with vector mesons in the final state.Comment: 7 page