## Periodic Reporting for period 1 - HPpQCD (Hard Probes of Hot and Dense QCD Matter)

Reporting period: 2015-09-01 to 2017-08-31

The theory of strong interactions (those in charge of keeping atomic nuclei together) is written, in its fundamental form, in terms of quarks and gluons which are particle carrying an additional quantum number known as color. In practice, such particles are never observed in isolation and are always confined into “colorless” hadrons such as the proton or the neutron.This confinement phenomenon implies that the asymptotic states of the theory are not the same as the fundamental degrees of freedom, but at the same time it allows for a phase transition into a deconfined state where quarks and gluons can behave as effectively free particles. Such deconfined state is known as the quark-gluon plasma (QGP) and it can be studied experimentally through heavy ion collisions at both the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory (BNL) and at the Large Hadron Collider (LHC) at CERN.

The QGP is short-lived and cannot be directly measured, therefore its properties have to be inferred from the remnants that hit the detectors. In particular, it is useful to study hard probes -- high-energy particles created in the early stages of the collision whose production rates are not affected by the QGP. These particles then interact with the QGP and, in the case of colored probes, lose energy through gluon radiation.

The most recent experimental programs have greatly improved the quality of the data and opened new possibilities in terms of what can be measured. This has created a large demand for new theoretical tools to properly understand the basic physical processes that characterize such novel states of matter in the presence of large densities and temperatures. This project is aimed at satisfying that demand.

One of the most clear signals of the presence of a medium in heavy ion collisions is the suppression of the high-energy particle spectrum, which is explained by the energy loss particles experience while going through a medium. This effect is called jet quenching.

Jet quenching phenomena has been largely studied by calculating the interactions of one particle going through a strongly interacting medium, and in particular the induced radiation. Such approach is suitable to understand one particle measurements, but suffers from big uncertainties due to our ignorance of the complicated processes involved in turning a quark or gluon into a hadron (hadronization). Since the LHC started taking data on heavy ion collisions, it is possible to measure jets, which by definition are less sensitive to the physics of hadronization. Nevertheless, it involves the complication of describing the jet evolution at the same time as it interacts with the QGP. One of the main objectives of this project is to provide solid theoretical advances in the theory of in-medium jet modification which could help build a platform in which further phenomenological studies can be performed to match the accuracy of the data coming out of the current experiments.

The initial stages of heavy ion collisions also provide another case of strongly interacting matter in extreme conditions. It is well known that, at the energies involved in these violent collisions, there are many quarks and gluons in the wave function of the colliding nuclei, in particular, with higher energies the number of particles carrying a very small fraction of the total energy greatly increases. This is the so called small-x region. Given that this region of phase space is highly populated at the energies involved in collider experiments, it plays an important role in the production of particles and the formation of the QGP. The small-x regime is best described in terms of the Color Glass Condensate (CGC) formalism, which is an effective theory that uses to high occupancy numbers of the small-x degrees of freedom to justify a semi-classical approach to the dynamics of the strong fields. This project also studies this state of matter and aims to improve our understanding of the description of some calculable observables, as well as exploring how to go beyond current limitations. In particular, one of the main limitations of previous calculations is the difficulty to include finite energy corrections and use exact kinematics.

The QGP is short-lived and cannot be directly measured, therefore its properties have to be inferred from the remnants that hit the detectors. In particular, it is useful to study hard probes -- high-energy particles created in the early stages of the collision whose production rates are not affected by the QGP. These particles then interact with the QGP and, in the case of colored probes, lose energy through gluon radiation.

The most recent experimental programs have greatly improved the quality of the data and opened new possibilities in terms of what can be measured. This has created a large demand for new theoretical tools to properly understand the basic physical processes that characterize such novel states of matter in the presence of large densities and temperatures. This project is aimed at satisfying that demand.

One of the most clear signals of the presence of a medium in heavy ion collisions is the suppression of the high-energy particle spectrum, which is explained by the energy loss particles experience while going through a medium. This effect is called jet quenching.

Jet quenching phenomena has been largely studied by calculating the interactions of one particle going through a strongly interacting medium, and in particular the induced radiation. Such approach is suitable to understand one particle measurements, but suffers from big uncertainties due to our ignorance of the complicated processes involved in turning a quark or gluon into a hadron (hadronization). Since the LHC started taking data on heavy ion collisions, it is possible to measure jets, which by definition are less sensitive to the physics of hadronization. Nevertheless, it involves the complication of describing the jet evolution at the same time as it interacts with the QGP. One of the main objectives of this project is to provide solid theoretical advances in the theory of in-medium jet modification which could help build a platform in which further phenomenological studies can be performed to match the accuracy of the data coming out of the current experiments.

The initial stages of heavy ion collisions also provide another case of strongly interacting matter in extreme conditions. It is well known that, at the energies involved in these violent collisions, there are many quarks and gluons in the wave function of the colliding nuclei, in particular, with higher energies the number of particles carrying a very small fraction of the total energy greatly increases. This is the so called small-x region. Given that this region of phase space is highly populated at the energies involved in collider experiments, it plays an important role in the production of particles and the formation of the QGP. The small-x regime is best described in terms of the Color Glass Condensate (CGC) formalism, which is an effective theory that uses to high occupancy numbers of the small-x degrees of freedom to justify a semi-classical approach to the dynamics of the strong fields. This project also studies this state of matter and aims to improve our understanding of the description of some calculable observables, as well as exploring how to go beyond current limitations. In particular, one of the main limitations of previous calculations is the difficulty to include finite energy corrections and use exact kinematics.

The work performed in the jet quenching part of the project has been mainly directed towards providing quantitative foundations to how coherence among quarks and gluons in a single jet affects jet formation and modification inside a medium. In order to have a correct description of jet quenching it is necessary to show how the limiting cases arise from a common formalism which can accommodate both modification of the branching structure as well as medium-induced radiation into regions of phase space not available through normal vacuum mechanisms. The main results in this direction of research are: the successful isolation of the vacuum contribution to the radiation spectrum of gluons inside a medium, the explicit demonstration that the emission of hard collinear gluons does not increase the medium-induced radiation from a quark, and reconciling the calculations for radiative corrections to momentum broadening in the multiple scattering formalism with results from opacity expansion approaches.

For the CGC part of the project, work was performed in exploring ways of consistently extending the formalism to go beyond the high-energy approximations used in multiple scattering and including corrections that are usually suppressed by powers of the high energy scale. In particular, the focus of the efforts in this project was in understanding the effects of beyond-eikonal corrections, particularly how they affect the small-x evolution and how the new operators needed for such description behave as a function of energy. The main results of this work are: the finite energy corrections do not modify the evolution to leading logarithmic accuracy, and the current formalism is not well poised to calculate the evolution of the new operators, therefore new degrees of freedom must be taken into account when non-eikonal interactions are included.

For the CGC part of the project, work was performed in exploring ways of consistently extending the formalism to go beyond the high-energy approximations used in multiple scattering and including corrections that are usually suppressed by powers of the high energy scale. In particular, the focus of the efforts in this project was in understanding the effects of beyond-eikonal corrections, particularly how they affect the small-x evolution and how the new operators needed for such description behave as a function of energy. The main results of this work are: the finite energy corrections do not modify the evolution to leading logarithmic accuracy, and the current formalism is not well poised to calculate the evolution of the new operators, therefore new degrees of freedom must be taken into account when non-eikonal interactions are included.

The step in going from physical picture to quantitative calculation for the color coherence effects in jet quenching that has been done in the calculations of collinear systems of particles, as well as the differentiation of the vacuum components of the radiated spectrum, are beyond the state of the art and will have a big impact in further developments aimed at setting the theoretical basis for phenomenological studies of jet suppression and modification of jet substructure. Showing that this effects, which had been predicted in a qualitative way, actually arise from the multiple scattering formalism in a consistent way is a fundamental step towards establishing a broad theoretical framework in which the different effects playing a role in jet quenching can be included in calculations of observables.

The inclusion of beyond-eikonal effects in the CGC formalism is a novel tool that has been developed in the last few years. Finding its effects on the small-x degrees of freedom of the nuclear wave function is beyond the state of the art in the field. Finding the appropriate extensions to the evolution equations in order to properly account for the evolution of the new operators will be a mayor advance in improving the current theoretical framework for precision measurements as well as computing spin observables in the small-x regime.

The inclusion of beyond-eikonal effects in the CGC formalism is a novel tool that has been developed in the last few years. Finding its effects on the small-x degrees of freedom of the nuclear wave function is beyond the state of the art in the field. Finding the appropriate extensions to the evolution equations in order to properly account for the evolution of the new operators will be a mayor advance in improving the current theoretical framework for precision measurements as well as computing spin observables in the small-x regime.