Positivity bounds on gluon TMDs for hadrons of spin ≤\le 1

We consider the transverse momentum dependent gluon distribution functions (called gluon TMDs) by studying the light-front gluon-gluon correlator, extending the results for unpolarized and vector polarized targets to also include tensor polarized targets -- the latter type of polarization is relevant for targets of spin $\ge1$. The light-front correlator includes process-dependent gauge links to guarantee color gauge invariance. As from the experimental side the gluon TMDs are largely unknown, we present positivity bounds for combinations of leading-twist gluon distributions that may be used to estimate their maximal contribution to observables. Since the gluonic content of hadrons is particularly relevant in the small-$x$ kinematic region, we also study these bounds in the small-$x$ limit for the dipole-type gauge link structure using matrix elements of a single Wilson loop.Comment: 10 page

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

Directed flow from C-odd gluon correlations at small xx

It is shown that odd harmonic azimuthal correlations, including the directed flow $v_1$, in forward two-particle production in peripheral proton-nucleus ($pA$) collisions can arise simply from the radial nuclear profile of a large nucleus. This requires consideration of the C-odd part of the gluonic generalized transverse momentum dependent (GTMD) correlator of nucleons in the nucleus. The gluonic GTMD correlator is the Fourier transform of an off-forward hadronic matrix element containing gluonic field strength tensors that are connected by gauge links. It is parametrized in terms of various gluon GTMD distribution functions (GTMDs). We show (in a gauge invariant way) that for the relevant dipole-type gauge link structure in the small-$x$ limit the GTMD correlator reduces to a generalized Wilson loop correlator. The Wilson loop correlator is parametrized in terms of a single function, implying that in the region of small $x$ there is only one independent dipole-type GTMD, which can have a C-odd part. We show that the odderon Wigner distribution, which is related to this C-odd dipole GTMD by a Fourier transform, generates odd harmonics in the two-particle azimuthal correlations in peripheral $pA$ collisions. We calculate the first odd harmonic $v_1$ for forward production within the color glass condensate framework in the limit of a large number of colors. We find that nonzero odd harmonics are present without breaking the rotational symmetry of the nucleus, arising just from its inhomogeneity in the radial direction. Using a CGC model with a cubic action, we illustrate that percent level $v_1$ can arise from this C-odd mechanism. In contrast, we show that only even harmonics arise in diffractive dijet production in ultra-peripheral $pA$ collisions where this gluon dipole GTMD also appears.Comment: 23 pages, 3 figures. v2: References added; Added plot for A=63 in Fig.3 and a discussion on the A dependence. Version accepted for publication in JHE

Suppression of maximal linear gluon polarization in angular asymmetries

We perform a phenomenological analysis of the $\cos 2 \phi$ azimuthal asymmetry in virtual photon plus jet production induced by the linear polarization of gluons in unpolarized $pA$ collisions. Although the linearly polarized gluon distribution becomes maximal at small $x$, TMD evolutionleads to a Sudakov suppression of the asymmetry with increasing invariant mass of the $\gamma^*$-jet pair. Employing a small-$x$ model input distribution, the asymmetry is found to be strongly suppressed under TMD evolution, but still remains sufficiently large to be measurable in the typical kinematical region accessible at RHIC or LHC at moderate photon virtuality, whereas it is expected to be negligible in $Z/W$-jet pair production at LHC. We point out the optimal kinematics for RHIC and LHC studies, in order to expedite the first experimental studies of the linearly polarized gluon distribution through this process. We further argue that this is a particularly clean process to test the $k_t$-resummation formalism in the small-$x$ regime.Comment: 11 pages, 6 figure

No Generalized TMD-Factorization in the Hadro-Production of High Transverse Momentum Hadrons

It has by now been established that standard QCD factorization using transverse momentum dependent parton distribution functions fails in hadro-production of nearly back-to-back hadrons with high transverse momentum. The essential problem is that gauge invariant transverse momentum dependent parton distribution functions cannot be defined with process-independent Wilson line operators, thus implying a breakdown of universality. This has led naturally to proposals that a correct approach is to instead use a type of "generalized" transverse momentum dependent factorization in which the basic factorized structure is assumed to remain valid, but with transverse momentum dependent parton distribution functions that contain non-standard, process dependent Wilson line structures. In other words, to recover a factorization formula, it has become common to assume that it is sufficient to simply modify the Wilson lines in the parton correlation functions for each separate hadron. In this paper, we will illustrate by direct counter-example that this is not possible in a non-Abelian gauge theory. Since a proof of generalized transverse momentum dependent factorization should apply generally to any hard hadro-production process, a single counter-example suffices to show that a general proof does not exist. Therefore, to make the counter-argument clear and explicit, we illustrate with a specific calculation for a double spin asymmetry in a spectator model with a non-Abelian gauge field. The observed breakdown of generalized transverse momentum dependent factorization challenges the notion that the role of parton transverse momentum in such processes can be described using separate correlation functions for each external hadron.Comment: 19 pages, 11 figures, typos fixed and minor explanations added, version to appear in Physical Review

Dijet imbalance in hadronic collisions

The imbalance of dijets produced in hadronic collisions has been used to extract the average transverse momentum of partons inside the hadrons. In this paper we discuss new contributions to the dijet imbalance that could complicate or even hamper this extraction. They are due to polarization of initial state partons inside unpolarized hadrons that can arise in the presence of nonzero parton transverse momentum. Transversely polarized quarks and linearly polarized gluons produce specific azimuthal dependences of the two jets that in principle are not suppressed. Their effects cannot be isolated just by looking at the angular deviation from the back-to-back situation, rather they enter jet broadening observables. In this way they directly affect the extraction of the average transverse momentum of unpolarized partons that is thought to be extracted. We discuss appropriately weighted cross sections to isolate the additional contributions.Comment: 15 pages, 2 figures; revised version, published in Phys. Rev.

Colour unwound - disentangling colours for azimuthal asymmetries in Drell-Yan scattering

It has been suggested that a colour-entanglement effect exists in the Drell-Yan cross section for the 'double T-odd' contributions at low transverse momentum $Q_T$, rendering the colour structure different from that predicted by the usual factorisation formula [1]. These T-odd contributions can come from the Boer-Mulders or Sivers transverse momentum dependent distribution functions. The different colour structure should be visible already at the lowest possible order that gives a contribution to the double Boer-Mulders (dBM) or double Sivers (dS) effect, that is at the level of two gluon exchanges. To discriminate between the different predictions, we compute the leading-power contribution to the low-$Q_T$ dBM cross section at the two-gluon exchange order in the context of a spectator model. The computation is performed using a method of regions analysis with Collins subtraction terms implemented. The results conform with the predictions of the factorisation formula. In the cancellation of the colour entanglement, diagrams containing the three-gluon vertex are essential. Furthermore, the Glauber region turns out to play an important role - in fact, it is possible to assign the full contribution to the dBM cross section at the given order to the region in which the two gluons have Glauber scaling. A similar disentanglement of colour is found for the dS effect.Comment: 36 pages, 11 figures; v2: typos corrected/ reference added, v3: minor corrections/ small explanations added/ references added, v4: very minor correction/ small explanations added/ references added (this version has been accepted for publication in SciPost

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