# Evolution of collisions and QGP

Extreme density and temperature allow the transition for the ordinary matter to the deconfined phase, in which quarks and gluons are free from their parent hadrons and they can interact with each other.
Such conditions can be reached by ultrarelativistic heavy ion collisions.

Different phases of evolution of the matter are predicted according to theoretical models and on the basis of data collected so far.
Nuclei that are accelerated to ultrarelativistic energies become Lorentz-contracted and they are supposed to be in a glass colour condensate state.
Protons and neutrons of colliding nuclei at such energies can be considered transparent for each other and thus only their inner components are involved in the interaction.
In heavy-ion collisions, a large number of nucleons is involved in the processes while the collision takes place in a very tight region.

The impact parameter of a collision $b=|\vec{b}|$ indicate the projection of the vector $\vec{b}$ defined as the distance between the centres of the two colliding nuclei in a plane transverse to the beam axis.

Central collisions, i.e. characterized by an impact parameter $b\sim0$, involve all the protons and neutrons of the nuclei.
Otherwise, in non-central collisions, the involved nucleons are called participants while the others spectators.

A schematic of the evolution of a central heavy-ion collision is provided in the Figure below.

The formation of QGP matter occurs if critical temperature and critical energy density are reached.
If the matter produced in the impact does not meet such conditions, the system will run into a hydrodynamical evolution (the left side of the Figure).
Soon after the impact there is a pre-hadronic phase in which, despite an enhancement of pressure and temperature, a real parton deconfiment does not occur.
Nucleons, however, can recombine into new hadrons that can be detected after the hadron gas phase freeze-out.

In the right side of the Figure it is shown the evolution of the heavy-ion collision in the case of QGP formation is shown. The following distinction is thus allowed.

• Pre-equilibrium ($t\lesssim 1\ fm/c$): partons scatter among each other and give rise to an abundant production of deconfined quarks and gluons.
High transverse momentum particles ($p_T \gg 1\ GeV/c$) are produced at this stage.
At energies higher than those reached by $\textsf{SPS}$, such particles can also be produced in subsequent stages. A large quantity of photons is also produced, \textit{direct photons}, real or virtual.
Virtual photons decay in lepton-antilepton pairs.
• Thermalization ($t\sim1\div 10\ fm/c$): elastic and inelastic interactions between partons in QGP lead to the thermalization phase.
Inhelastic interactions can modify the flavour composition of particles.
Due to its internal pressure, the system at thermal equilibrium rapidly expands.
While expanding, the system begins to convert into hadron gas. This is the mixed phase.
• Hadronization ($t\sim20\ fm/c$): during its expansion, the system cools down.
When it reaches again the critical energy density, the hadronization begins and quarks and gluons of the QGP matter condensate in new hadrons.
There are two possible reaction mechanisms for hadronization: fragmentation i.e. when a high $p_T$ parton fragments in lower $p_T$ hadrons and coalescence that involves partons with lower momenta which combines to form larger $p_T$ hadrons.
Fragmentation dominates at higher energies, while coalescence at lower ones.
The energy density of the system strongly decreases and the interaction region physically expands while the temperature remains stable at $T_C$.
Hadrons continue to interact among themselves until the interaction rate can no more substain the QGP expansion. At this point the flavour composition of the QGP matter is fixed. This is called chemical freeze-out.
• Thermal freeze-out: when the mean distance between the hadrons becomes greater than the radius of strong interaction (at $T\sim120\ MeV$), elastic scatterings between hadrons cease and kinematical spectra of the resulting matter also become fixed.

Some theoretical models predict for the pre-equilibrium and the thermalization phases the incoherent production of mini-jets that compose the plasma in a global equilibrium state.
Coherent approaches, instead, predict the formation of strings of colour that decay in hadrons.
At the end of the thermalization phase, the evolution of the system is ruled by relativistic hydrodynamics. Different models can be used mainly depending by the assumption of viscosity in the system.

Relative abundances are almost fixed at $T\approx T_C$.
This is because hadronic cross section is strongly dominated by resonant processes, like $\pi+N\rightarrow\Delta\rightarrow\pi+N$, in which the bound state often decays in the same parent hadrons.
The measure of relative abundances of quark flavours in resulting hadrons provides an evaluation of the critical temperature of the system.

Some of the characteristic parameters of the system created after ion collisions are listed in the following Table.