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

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

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

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

Single spin asymmetries from a single Wilson loop

We study the leading-power gluon transverse momentum dependent distributions (TMDs) of relevance to the study of asymmetries in the scattering off transversely polarized hadrons. Next-to-leading-order perturbative calculations of these TMDs show that at large transverse momentum they have common dynamical origins, but that in the limit of small longitudinal momentum fraction $x$ only one origin remains. We find that in this limit only the dipole-type gluon TMDs survive and become identical to each other. At small $x$ they are all given by the expectation value of a single Wilson loop inside the transversely polarized hadron, the so-called spin-dependent odderon. This universal origin of transverse spin asymmetries at small $x$ is of importance to current and future experimental studies, paving the way to a better understanding of the role of gluons in the three-dimensional structure of spin-polarized protons.Comment: 5 pages, 1 figure. Various changes to the text, additional references, conclusions unchanged, version accepted for publication in Physical Review Letter

Polarization effects in double open-charm production at LHCb

Double open-charm production is one of the most promising channels to disentangle single from double parton scattering (DPS) and study different properties of DPS. Several studies of the DPS contributions have been made. A missing ingredient so far has been the study of polarization effects, arising from spin correlations between the two partons inside an unpolarized proton. We investigate the impact polarization has on the double open-charm cross section. We show that the longitudinally polarized gluons can give significant contributions to the cross section, but for most of the considered kinematic region only have a moderate effect on the shape. We compare our findings to the LHCb data in the D0D0 final state, identify observables where polarization does have an impact on the distribution of the final state particles, and suggest measurements which could lead to first experimental indications of, or limits on, polarization in DPS.Comment: 16 pages, 13 figure

Effects of TMD evolution and partonic flavor on e+e−e^+e^- annihilation into hadrons

We calculate the transverse momentum dependence in the production of two back-to-back hadrons in electron-positron annihilations at the medium/large energy scales of BES-III and BELLE experiments. We use the parameters of the transverse-momentum-dependent (TMD) fragmentation functions that were recently extracted from the semi-inclusive deep-inelastic-scattering multiplicities at low energy from HERMES. TMD evolution is applied according to different approaches and using different parameters for the nonperturbative part of the evolution kernel, thus exploring the sensitivity of our results to these different choices and to the flavor dependence of parton fragmentation functions. We discuss how experimental measurements could discriminate among the various scenarios.Comment: 33 pages, 10 composite figures, JHEP style fil

Scattered light mapping of protoplanetary disks

High-contrast scattered light observations have revealed the surface morphology of several dozens of protoplanetary disks at optical and near-infrared wavelengths. Inclined disks offer the opportunity to measure part of the phase function of the dust grains that reside in the disk surface which is essential for our understanding of protoplanetary dust properties and the early stages of planet formation. We aim to construct a method which takes into account how the flaring shape of the scattering surface of an (optically thick) protoplanetary disk projects onto the image plane of the observer. This allows us to map physical quantities (scattering radius and scattering angle) onto scattered light images and retrieve stellar irradiation corrected (r^2-scaled) images and dust phase functions. We apply the method on archival polarized intensity images of the protoplanetary disk around HD 100546 that were obtained with VLT/SPHERE in R'-band and VLT/NACO in H- and Ks-band. The brightest side of the r^2-scaled R'-band polarized intensity image of HD 100546 changes from the far to the near side of the disk when a flaring instead of a geometrically flat disk surface is used for the r^2-scaling. The decrease in polarized surface brightness in the scattering angle range of ~40-70 deg is likely a result of the dust phase function and degree of polarization which peak in different scattering angle regimes. The derived phase functions show part of a forward scattering peak which indicates that large, aggregate dust grains dominate the scattering opacity in the disk surface. Projection effects of a protoplanetary disk surface need to be taken into account to correctly interpret scattered light images. Applying the correct scaling for the correction of stellar irradiation is crucial for the interpretation of the images and the derivation of the dust properties in the disk surface layer.Comment: Accepted for publication in A&A, 6 pages, 3 figure