Evolution of Light-Like Wilson Loops with a Self-Intersection in Loop Space

Recently, we proposed a general evolution equation for single quadrilateral Wilson loop on the light-cone. In present work, we study the energy evolution of a combination of two such loops that partially overlap or have a self-intersection. We show that, for a class of geometric variations, then evolution is consistent with our previous conjecture, and we are able to handle the intricacies associated with the self-intersections and overlaps. This way, a step forward is made towards the understanding of loop space, with the hope of studying more complicated structures appearing in phenomenological relevant objects, such as parton distributions.Comment: Correction of some small typos and small changes to the figures. To be submitted for publication to Phys Lett

Quantum Chromodynamics at small Bjorken-x

With the advent of very powerful particle accelerators, such as RHIC and the LHC, it becomes possible to study QCD in high energy collisions, in which the gluon content of the proton or nucleus is probed and its density becomes often large enough for nonlinear effects to play a role. This small-x regime of QCD is well described by an effective theory known as the Color Glass Condensate (CGC). In this thesis, we introduce the CGC and apply it to two different problems. First, we use the CGC to study forward heavy-quark production in pA collisions. When the quarks are nearly back-to-back, the CGC result coincides with the one in the TMD factorization approach. This allows us to extract the small-x limit of the Weizs\"acker-Williams gluon distribution, as well as the dipole distribution and one extra gluon TMD. Each of these gluon TMDs is accompanied by a partner, which couples via the quark mass and which describes the linearly polarized gluon content of the unpolarized nucleus. We calculate the six resulting gluon TMDs analytically in the MV model, and evolve them in rapidity using a numerical implementation of JIMWLK. The second problem is situated within heavy-ion physics. Jets, produced in the scattering of two nuclei, travel through the Quark-Gluon Plasma (QGP) before reaching the detector, and are attenuated as a result of their interaction with this medium. This phenomenon, known as jet quenching, is one of the main probes to investigate the QGP. We focus on the transverse momentum broadening of a hard particle traveling through a nuclear medium, and employ small-x techniques to attempt to resum the leading logarithmic corrections due to soft gluon radiation. Although, ultimately, we can only solve the resulting in-medium evolution equation to DLA accuracy, we do present a concise framework for the problem, and draw a detailed comparison with the CGC and with the literature.Comment: PhD thesis, defended at the University of Antwerp, Belgium, on July 3, 201

Forward production of a Drell-Yan pair and a jet at small xx at next-to-leading order

We perform the analytical next-to-leading order calculation of the process $p+A\to \gamma^{*}+\mathrm{jet}+X$, at forward rapidities and low $x$. These kinematics justify a hybrid approach, where a quark from the \textquoteleft projectile' proton scatters off the gluon distribution of the \textquoteleft target', which can be a nucleus or a highly boosted proton. By using the Color Glass Condensate effective theory approach, this gluon distribution is allowed to be so dense that the quark undergoes multiple scattering. Moreover, large high-energy logarithms in the ratio of the hard scale and the center-of-mass energy are resummed by the Balitsky, Kovchegov, Jalilian-Marian, Iancu, McLerran, Weigert, Leonidov, Kovner or BK-JIMWLK evolution equations. We demonstrate that all ultraviolet divergences encountered in the calculation cancel, while the high-energy divergences are absorbed into BK-JIMWLK. The remaining singularities are collinear in nature and can be either absorbed into the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution of the incoming quark, when they stem from initial-state radiation, or else can be treated by introduction of a jet function in case they are caused by final-state emissions. The resulting cross section is completely finite and expressed in function of only a small set of color operators.Comment: 101 plus 17 pages (main text plus appendices and bibliography), 11 figure

Probing the gluon Sivers function in p↑p→J/ψ Xp^\uparrow p\to J/\psi\,X and p↑p→D Xp^\uparrow p \to D\,X

We present a study of transverse single-spin asymmetries (SSAs) in $p^\uparrow p\to J/\psi\,X$ and $p^\uparrow p\to D X$ within the framework of the generalized parton model (GPM), which includes both spin and transverse momentum effects, and show how they can provide useful information on the still almost unknown gluon Sivers function. Moreover, by adopting a modified version of this model, named color gauge invariant (CGI) GPM, we analyze the impact of the initial- and final-state interactions on our predictions. As a consequence, we find that these two processes are sensitive to different gluon Sivers functions, which can be expressed as linear combinations of two distinct, universal gluon distributions. We therefore define proper observables which could allow for a separate extraction of these two independent Sivers functions. At the same time, we show how it would be possible to discriminate between the GPM and the CGI-GPM approaches by comparing the corresponding estimates of SSAs with present and future experimental results at RHIC.Comment: 19 pages, 8 figures, 1 table; v2: minor changes, matches the published versio

Unraveling the Gluon Sivers Function in Hadronic Collisions at RHIC

We study the transverse single-spin asymmetries for $p^\uparrow p\to \pi\, X$ and $p^\uparrow p\to \gamma\, X$ within the so-called color gauge invariant generalized parton model (CGI-GPM) which, in addition to spin and transverse momentum effects, includes initial and final state interactions with the polarized proton remnants. We compute all relevant contributions, focusing in particular on the process dependence of the gluon Sivers function, which, for these processes, can always be expressed as a linear combination of two independent, universal terms. This study extends and completes a previous one, where only quark initiated partonic processes were considered. We then perform a combined phenomenological analysis of RHIC data on transverse single-spin asymmetries in $p^\uparrow p\to \pi\, X$ and $p^\uparrow p\to D\, X$, putting the first preliminary constraints on these two gluon Sivers functions. We show how their size can be estimated by means of these data, and use our results to provide predictions for the process $p^\uparrow p\to J/\psi\,X$, comparing them with data, and $p^\uparrow p\to \gamma\, X$, for which experimental information will soon become available. Corresponding estimates within the simpler GPM approach, without initial and final state interactions and with a single universal gluon Sivers function, are also given, showing that a clear discrimination between these two models is, for the moment, not possible.Comment: 17 pages, 9 figures (19 plots), 4 table

Dijet photoproduction at low xx at next-to-leading order and its back-to-back limit

We compute the cross section for the inclusive photoproduction of a pair of jets at next-to-leading order accuracy in the Color Glass Condensate (CGC) effective theory. The aim is to study the back-to-back limit, to investigate whether transverse momentum dependent (TMD) factorization can be recovered at this order. In particular, we focus on the large Sudakov double logarithms, which are major ingredients of the TMD evolution. Interestingly, the kinematical improvement of the low-$x$ resummation scheme turns out to be a key ingredient in the analysis.Comment: v2, introduction expanded, references added, minor typos correcte

Gluon TMDs and NRQCD matrix elements in J/ψJ/\psi production at an EIC

In this paper we analyze azimuthal asymmetries in the processes of unpolarized and polarized $J/\psi \,(\Upsilon)$ production at an Electron-Ion Collider. Apart from giving access to various unknown gluon transverse momentum distributions, we suggest to use them as a new method to extract specific color-octet NRQCD long-distance matrix elements, i.e.\ $\langle0|{\cal O}_{8}^{J/\psi}(^{1}S_{0})|0\rangle$ and $\langle0|{\cal O}_{8}^{J/\psi}(^{3}P_{0})|0\rangle$, whose values are still quite uncertain and for which lattice calculations are unavailable. The new method is based on combining measurements of analogous asymmetries in open heavy-quark pair production which can be performed at the same energy. To enhance the gluon contribution one can consider smaller values of $x$ and, in order to assess the impact of small-$x$ evolution, we perform a numerical study using the MV model as a starting input and evolve it with the JIMWLK equations.Comment: 22 pages, 10 figures; v2: new section and figure added, references updated, conclusions unchange

Process dependence of the gluon Sivers function in inclusive pppp collisions: theory

Within the color gauge invariant generalized parton model (CGI-GPM), which includes initial and final state interactions in a transverse momentum dependent formalism, we present the complete results, at leading order in perturbative QCD, for transverse single-spin asymmetries in the inclusive hadroproduction of $J/\psi$ and $D$ mesons, pions and direct photons.Comment: 7 pages, 2 figures; to appear in the Proceedings of the 23rd International SPIN Symposium (SPIN 2018), Ferrara (Italy), 10-14 September 201