# Quantum Chromodynamics (QCD)

**Color glass condensate**

The quark and gluon content of a hadron, and more generally of a nucleus, depends on its energy. When the hadron moves close to the speed of light, virtual quarks and gluons, collectively called partons, are emitted for a short period of time. Furthermore, the special theory of relativity predicts that the size of a particle is contracted along the direction of its motion. Therefore the high-energy snapshot of the hadron looks like a thin disk and partons are confined to living in a thin surface, making the hadron a very dense object. This is the phenomenon of parton saturation and it has been customary to call this hadron state a Color Glass Condensate (CGC). Color because of the charge of the nuclear force. Glass because the slower moving partons live a shorter time than their parent ones and the presence of two times scales is a feature of normal glass. Condensate because the hadron is dense.

The CGC reflects very non-trivial dynamics of QCD and at ECT* we are involved in the improvement of this effective theory and study its qualitative and quantitative predictions. All this can be tested, for example, in proton-lead collisions at the Large Hadron Collider at CERN and more importantly in Deep Inelastic Scattering experiments in the forthcoming Electron-Ion Collider at BNL in the United States. Furthermore, we are interested in seeing to what extent the CGC can describe the initial stages of ultra-relativistic lead-lead collisions, where thousands of quarks and gluons are liberated and are expected to form a Quark Gluon Plasma.

**Schwinger-Dyson equations**

When quantum corrections are taken into account, the equations for the field correlators of QCD are described by an infinite set of coupled non-linear integral equations: the so-called Schwinger-Dyson equations (SDEs). These equations are fully nonperturbative, and, if solved, would give access to the physics content of the theory in all kinematic regimes. However, solving the full hierarchy of equations for specific correlators is currently beyond our computation capabilities, and one need to resort to judicious truncation schemes which preserves the symmetries of the theory.

At ECT* we have developed a novel truncation scheme allowing us to solve the SDE of the gluon two-point correlator. The solutions obtained reproduce correctly the infrared properties predicted by lattice simulations, in particular the infrared saturation to a non-zero finite value. This latter property would seem to indicate that the gluon acquires dynamically a (momentum dependent) mass, and the plethora of phenomena related to this discovery is currently investigated.

#### Emergent Hadronic Mass

The Standard Model has two mechanisms for mass generation. One is connected with the Higgs boson, discovered at the large hadron collider in 2012, which produces the Lagrangian current-mass for each of the quarks. Yet, regarding the kernels of all known nuclei, these current masses account for less than 2% of the mass of a neutron or proton. More than 98% of visible mass emerges as a consequence of strong interactions within QCD: this is emergent hadronic mass (EHM). However complex this might seem, Nature is even more subtle. Contrasting to the massiveness of the proton, the pion appears as unnaturally light, although both are of composite nature. This dichotomy forms a key part of the conundrum of EHM.

The mechanism responsible for the generation of mass is the dynamical breaking of the scale invariance in QCD; and measurements of Parton Distribution Functions (PDFs) are sensitive to this effect and its corollaries. At ECT* we study symmetry preserving schemes that provide access to hadrons’ PDFs. The resulting predictions require confrontation with both lattice QCD calculations as well as accurate experimental data, like those that would become available at current and planned facilities around the world.