University of Catania INFN-LNS

“Chemical” composition of the Quark-Gluon Plasma in relativistic heavy-ion collisions

F. Scardina, V. Greco, S. Plumari, M. Colonna Outline

 Our model: Transport theory with Quasiparticle

 Box calculation

 Results for RHIC and LHC

 Conclusion and future developments Transport theory

  p   f ( x, p )  M X   M X  p f X , p  C22

Free Mean Field Collisions streaming

We consider both elastic and inelastic collisions Transport theory

  p   f ( x, p )  M X   M X  p f X , p  C22

Free Mean Field Collisions streaming

We consider both elastic and inelastic collisions

For the numerical solutions of the Boltzmann equation we use a three dimensional lattice that discretizes the space and the standard test particle methods that samples the distributions t  0 Exact solution 3 x  0

[ Z. Xhu, et al. PRC71(04)] Test of the model in a box Massless case Equilibrium value quark  eq vquark 2* 2* 3* Nfl p   f ( x, p )  C22 gluon    2.25 eq  gluon 2* 8 (Nfl=3) Test of the model in a box Massless case Equilibrium value quark  eq vquark 2* 2* 3* Nfl p   f ( x, p )  C22 gluon    2.25 eq  gluon 2* 8 Simulations in which a (Nfl=3) particle ensemble in a box evolves dynamically Test of the model in a box Massless case Equilibrium value quark  eq vquark 2* 2* 3* Nfl p   f ( x, p )  C22 gluon    2.25 eq  gluon 2* 8 Simulations in which a (Nfl=3) particle ensemble in a box evolves dynamically

 quark gg  qq qq  gg  quark Init  0,33 Inelastic collisions eq gluon lead the system to chemical equilibrium gluon  2.25  Init eq Quasiparticle model (QP)

From lQCD we know that QGP is significantly different from a massless gas showing deviation of both  and p and exihibiting a large trace anomaly

The lattice results can be described in terms of a massive quasiparticle model in which both gluons and quarks acquire thermal masses

Effective masses are generated through the interaction Quasiparticle model (QP)

From lQCD we know that QGP is significantly different from a massless gas showing deviation of both  and p and exihibiting a large trace anomaly

The lattice results can be described in terms of a massive quasiparticle model in which both gluons and quarks acquire thermal masses

Effective masses are generated through the interaction

In order to apply quasiparticle model it is necessary evaluate masses

They can be perturbatively evaluated

We are interested in the non perturbative region, hence we use these two only to fix the mq/mg ratio and g is determined through a fit to lQCD data Quasiparticle model (QP) Usually it is carried out as follow 3  2 It is evaluated P d p p QP P  d f p  B T summing the contribution of QP  i  i     iu,d ,s,g 2  3E all particle Bag pressure B i + f(p)=equilibrium  E  p2  m2(T ) distribution functions i i i

3 From the pressure PQP the energy d p QP  di 3 Ei fi Ei  Bmi T density QP can be evaluated   i 2 Quasiparticle model (QP) Usually it is carried out as follow 3  2 It is evaluated P d p p QP P  d f p  B T summing the contribution of QP  i  i     iu,d ,s,g 2  3E all particle Bag pressure B i + f(p)=equilibrium  E  p2  m2(T ) distribution functions i i i

3 From the pressure PQP the energy d p QP  di 3 Ei fi Ei  Bmi T density QP can be evaluated   i 2

To have thermodynamic B d 3 p m consistency this relation  P   d i f E   0    0 i  3 i has to be satisfied m mi 2  Ei  i T , This equation link B(T) to g(T), the only function that has to be determinated g(T) is determinated imposing  QP   Lattice _ QCD Quasiparticle model (QP)

Once g is known it is possible to evaluate masses and also B Hot QCD W-B

Knowing masses and B the other thermodynamic quantities can be evaluated

[Plumari et. al PRD 84 094004 (2011] Quasiparticle model (QP) While lattice QCD cannot be used to study the dynamical evolution of a system the quasi particle model can be used

In order to do that it is necessary to couple the Boltzamnn equation with the equation for the quasi-particle masses.

Quasiparticle model and Kinetic theory

  p   f ( x, p ) mi x  mi x p f x, p  C22

B d 3 p m (x)  d i f x, p  0 i  3   mi 2  Ei (x) In order to solve the collision The two equations have to be integral it is necessary to solved autoconsistently know the cross section between massive particles s2->2 inelastic for quasiparticle We have evaluated s in a pQCD leading order scheme

The processes we are interested in are gg  q q and q q  gg

The 3 diagrams contributing to the processes correspond to the u,t,s channels, for which we have evaluated the squared matrix elements M

2 2 2 2 2 2 2 2 m  m  t m  m  u  3m s  2m m M   2 2 12 q g q g g q g s s 2 2 s  m g 

2 2 2 2 2 2 2 2 2 2 2 2 8 mq  mg  tmq  mg  u 2mq mq  t mg s  4mq mg M t   s  2 3 t  m2 

2 2 2 2 2 2 2 2 2 2 2 2 8 mq  mg tmq  mg  u 2mq mq  u mg s  4mq mg M u   s  2 3 u  m2 

+ Interference terms s2->2 inelastiche for quasiparticle Process gg  qq

t Tot 1  2 2 2  ggqq s  dtM s  M t  M u  Interferenceterms 2 t  16ss  4mg 

s Integration limits 2 2 2 2 2 2 2 t  mq  mg  1 1 4mq s 1 4mg s 16mq mg s  2

[T. S. Biro et. al PRD 42 (1990)] Comparison with Combridge cross sections (mg=0)

[B. L. Combridge Nucl. Phys. B 151 (1979) 429]

s [ GeV ] Chemical equilibrium

Massless case quark T 3 eq vquark 2* 2* 3* Nfl    2.25 (Nfl=3) eq  2 V gluon  eq  gluon 2* 8

Massive case

quark 2 eq vquark mq T  K2 mq T  gluon  2 eq vgluon mg T  K2 mg T 

Bessel function

1 n=2 ,   m2  p2 T

The equilibrium value depends on the ratio between the degrees of freedom but also on mq/mg and on m/T Chemical equilibrium

However the ratio between the masses is fixed in the quasiparticle model so

Nq/Ng depends only on temperature

quark 2 T=0,17 GeV (only15% of gluons) eq vquark mq T  K2 mq T  gluon  2 eq vgluon mg T  K2 mg T 

In the massive case we have a larger quark abundances especially at low temperature.

Near Tc only the 15% of the particle should be gluons Test of the model in a box

T=0.6 GeV

T=0.17 GeV

The relaxations times are different because ρ it is different (ρ≈T3) and the collision rate depends on ρ

Our code is able to reproduces the expected equilibria value Plasma created in the heavy ion collisions during its evolution does reach chemical equilibrium ? Why studying chemical equilibration of QGP ?

A closer look into the theoretical approaches describing the QGP probes reveals that the different models assume different chemical composition of the QGP

 In some cases the QGP is described as a gluon plasma. This is for example is assumed in the most popular jet quenching models.

 In hydrodynamics instead a chemical quark to gluon equilibration is implicit in the employment of a lattice QCD equation of state

 The coalescence model assumes a quark dominance in the plasma Tc Simulations at RHIC and LHC

Initial conditions: Coordinates-space Glauber model Momenta -space Boltzmann-Jutter plus minijet

Nq/Ng 75% gluons 25 % quarks Temperature T=340 Mev (RHIC); T=600 MeV (LHC) Initial time =0.6 fm (RHIC); =0.3 fm (RHIC)

We consider the running coupling and we use the standard one-loop perturbative formula for the s Results at RHIC and LHC (massless case)

 Nq quickly increases during the first Nq/Ng strongly decreases with pT part of the fireball evolution because the collision rate R(σ,ρ)  Open system -> it does not reach  At LHC the ratio keep an higher the expected equilibrium value value in a wider region of pT because partons have more time to equilibrate Results at RHIC and LHC (massless case)

 Nq quickly increases during the first Nq/Ng strongly decreases with pT part of the fireball evolution because the collision rate R(σ,ρ)  Open system -> it does not reach  At LHC the ratio keep an higher the expected equilibrium value value in a wider region of pT because partons have more time to equilibrate Results at RHIC (massive case)

 Nq/Ng in the massive case is two times greater than in the massless case  The ratio keeps to increase and does not show the saturation behavior observed for m=0 Results at RHIC (massive case)

 N /N in the massive case is two q g N /N (p ) shows a large difference times greater than in the massless case q g T between massless and massive case  The ratio keeps to increase and (strong momentum-dependence does not show the saturation below pt equal to 2 GeV) behavior observed for m=0 Results at RHIC (massive case)

 Nq/Ng in the massive case is two  The pT dependence can be times greater than in the massless case evaluated at equilibrium and our result scales with the expectations  The ratio keeps to increase and q 2 quark q  mT 0 pT  T dN d p   qq mT e does not show the saturation T  gluoni  mg  p T behavior observed for m=0 2 g  T 0 T  dN d pT   g mT e Results ad LHC (massive case)

QGP has longest lifetime at LHC but Nq/Ng reaches a lower value The difference between RHIC and RHICINIT LHCINIT LHC is due to the different temperatures experienced by the plasma during its evolution Effects of inelastic collisions on high pT hadrons dN dN We have evaluated the hadrons spectra h  dz f D ( z ) using the AKK fragmentation functions 2  2 f h d ph f d p f Conclusions and Perspective

 Inelastic collision lead the initial Glasma towards a quark dominated plasma

 A realistic description of the lQCD thermodynamic using the quasi-

particle model implies a ratio Nq/Ng almost two times greater than that expected in the massless case

 The inelastic collisions affect the high pT hadrons abundances

 Our results provide a support to the quark coalescence , capable to explains two main observations at RHIC: The barion/meson anomaly and the quark number scaling of the elliptic flow

s2->2 inelastic for quasiparticle

• Process qq  gg

  The cross section q q  gg differs from gg  q q only for the different average over the initial color and spin states

1 t 2 2  ggqq s  dtM t  M u  2 t  16ss  4mg 

64 1 t 2 2  qq gg s  dtM t  M u  2 t  9 16ss  4mq 

Funzioni di distribuzioni partoniche La coalescenza modifica il flusso ellittico

Coalescence scaling 1  p  V  T  n 2  n 

Innalzamento del v2

v2,M (pT )  2v2,q (pT /2)

v2,B (pT )  3v2,q (pT /3)