# The non-linear regime of quantum chromodynamics in the context of relativistic heavy-ion collisions

- Guerrero Rodríguez, Pablo

- Javier López Albacete Director

Universidade de defensa: Universidad de Granada

Fecha de defensa: 09 de outubro de 2019

- Roberto Pittau Presidente/a
- M. Elvira Gámiz Sánchez Secretario/a
- François Gelis Vogal
- Carlos Alberto Salgado López Vogal
- Jose Guilherme Milhano Vogal

Tipo: Tese

## Resumo

The dynamical regime dominated by large gluon densities and non-linear phenomena -referred to as the gluon saturation regime of Quantum Chromodynamics (QCD)- is relevant in the description of highly energetic heavy ion collisions (HICs). Currently there are two particle accelerators conducting this kind of experiments: the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC). The vast volume of HICs data collected in these facilities has provided striking evidence of collective phenomena at macroscopic scales. These observations hint at the emergence of a highly dense and extremely hot state of matter where quarks and gluons appear to be deconfined. This is known as the Quark Gluon Plasma (QGP). Virtually every stage of the generation, expansion and decay of this substance poses serious qualitative and quantitative challenges to our understanding of QCD. In fact, one of the main obstacles lies in the characterization of the very initial state of HICs, as it requires precise knowledge of the nuclear wave functions prior to the collision and the multiple scattering processes that take place immediately after. A typical approach to this problem relies on the use of a broad variety of phenomenological models that provide initial conditions for Monte Carlo simulations of the expanding QGP. The numerical values of the parameters required as input by these models are constrained by agreement with data, sometimes varying largely from one model to another. Such discrepancy introduces a significant amount of uncertainty in both the precision and physical interpretation of most phenomenological studies of the expansion and cooling of QGP. Nevertheless, the fact that the colliding nuclei are deeply saturated objects provides the opportunity to perform analytical, first-principles calculations based on perturbative QCD methods. Such dense systems allow for a description by means of a semi-classical approximation where gluons are represented by randomly distributed background color fields (MV model). Quantum corrections to the classical fields are introduced by perturbative non-linear evolution equations (the B-JIMWLK equations). This approach is proposed within an effective theory that approximates QCD at high energies and densities: the Color Glass Condensate (CGC). The CGC framework has been extensively applied in the description of the early, non-equilibrium stage of HICs, known as Glasma. Because of the inherently random nature of the positions and partonic content of the colliding nucleons, the Glasma phase is characterized by event-by-event fluctuations of the energy and momentum deposited in the collision area. This feature has been shown to play a key role in the formation and expansion of QGP, and thus it is one of the aspects that the aforementioned phenomenological models seek to reproduce. A main feature of the CGC framework is that it provides analytical tools to describe the early event-by-event fluctuations. These can be quantified through the calculation of correlators, defined as functional averages of observables over the background color fields. This first-principles characterization of the initial state, purely based in QCD interactions, can be used as an analytical input to the hydrodynamical simulations employed in QGP phenomenology. In this thesis we aim to improve and deepen our understanding of the saturation regime of QCD in the light of two fundamental problems of high energy physics: the theoretical characterization of the initial stage of HICs, and the phenomenological analysis of multi-particle production in collider experiments. Our studies are based on the previously explained CGC formalism, which throughout the development of the thesis we extend and modify with the two-fold aim of achieving a more realistic physical picture and expanding the potential applications of our results. On the theoretical side, we start with a first-principles analytical calculation of the one- and two-point correlators of the Glasma energy-momentum tensor (EMT). These objects characterize, respectively, the average and the variance of the distribution of energy density deposited in the plane transverse to the collision axis at an infinitesimal time after the impact. In the course of this work we extend the traditional MV model by introducing an explicit impact parameter dependence in the two-point correlator of color source densities, as well as a generalization of the transverse profile of the interaction. Also, and foremost, throughout our calculations we apply a self-consistent approach where we respect the inherently non-linear character of the Glasma field dynamics, hence departing from the approximations adopted as standard practice in this kind of studies thus far (i.e. the Glasma Graph approximation). In this approach, the expression computed for the two-point correlator of the Glasma EMT displays a remarkably slow vanishing behavior in the limit of long correlation distances, which shows a strong disagreement with the results obtained under the Glasma Graph approximation. These relatively long-range correlations could conflict with the widely-accepted physical picture of Glasma flux tubes, whose main prediction is the emergence of short-range correlations. Then we turn our attention to another fundamental feature of the Glasma phase: the emergence of fluctuations of CP-odd matter. Within the CGC framework these fluctuations are characterized by the two-point correlator of the divergence of the Chern-Simons current, which we compute in the same fashion as the previously obtained correlators of the EMT. Remarkably, the obtained expressions yield an even larger discrepancy with those computed under the Glasma Graph approximate approach. This suggests that the non-linear dynamics followed by the Glasma fields have an even greater effect over the long-range transverse fluctuations of axial charge density than they do over those of the deposited energy. A common conclusion of both studies is that the commonly adopted Glasma Graph approximation yields the exact same result as our approach in the UV limit. This seems to indicate that the non-linear nature of the Glasma fields dynamics can be neglected in this limit, or to a good approximation for correlation distances shorter than the inverse of the saturation momentum. However, the large discrepancies observed in the rest of the spectra provides analytical evidence on the importance of the non-linear dynamics relating color source densities and gauge field correlators. The results of these studies could potentially have a deep impact in both physical interpretations and numerical results for any phenomenological application based on these correlators (e.g. the description of anisotropic flow coefficients, or the analysis of experimental signatures of anomalous transport phenomena in colliders). In the phenomenological part of the thesis we study the influence of saturation physics in the analysis of multi-particle production at the LHC. With this goal, we perform an analysis of data on single inclusive pion production measured by the LHCf collaboration in high-energy proton-proton and proton-nucleus at ultra-forward rapidities. It can be shown that this region of the spectra is sensitive to both dilute and saturated regimes of QCD. Our analysis relies on the use of a Monte Carlo event generator that combines a perturbative description of the partonic-level scattering process on the hybrid formalism of CGC with an implementation of hadronization in the framework of the Lund string fragmentation model. The main dynamical input in this setup is the non-linear evolution equations embedded in the CGC framework, which introduce the energy dependence in our description. With this setup we achieve a good description of the single neutral pion spectrum in the very forward region of the LHC, which adds evidence to the idea that the main dynamical features of a dilute-dense interaction can be reproduced by means of saturation physics. References: [1] J.L.Albacete, Yasushi Nara and P.G.R., “Ultra-forward particle production from CGC+Lund fragmentation”, Phys. Rev. D94 (2016) no.5, 054004. [2] J.L.Albacete, Cyrille Marquet and P.G.R., “Initial correlations of the Glasma energy-momentum tensor”, JHEP 1901 (2019) 073. [3] P.G.R., “Topological charge fluctuations in the Glasma”, JHEP 1908 (2019) 026.