Modeling the Hadronization of

Quark Matter

G. Toledo Sánchez

Instituto de Fisica UNAM, Mexico

A. Ayala, G. Paic, M. Martinez

ICN-UNAM, México

Strangeness in Quark Matter 07, Levoca Slovakia.

G. Toledo

Outline

MotivationNew states of matter

Hadronization and the proton/pion ratio

The string-flip modelDynamical hadron-quark transition

Variational montecarlo simulation

Results and perspectivesMeson vs. Baryon Hadronization

G. Toledo

Motivation Hadrons - quarks New phases of matter

[Gerlach PR68, Glendenning AAstrophys00, Greiner NPA00]

S.S. Adlernucl-ex/0305030

M. Gyulassynucl-th/0403032

Nuclear modification factor RCP for ( p + p )/2 and π0 at s1/2=200 GeV. PHENIX Coll. S.S. Adler et al, Phys. Rev. Lett. 91, 172301 (2003).

G. Toledo

In the recombination picture 3 quarks or quark/antiquark pairs in a densely populated phase space can form a baryon or a meson, respectively.

In the fragmentation picture, the single parton spectrum is convoluted with a probability Di→h(z) of a parton i to hadronize into a hadron h, which carries a fraction z < 1 of the momentum of the parent parton:

At low PT, for an exponential quark

spectrum, fragmentation is always suppressed with respect recombination.

At large PT, when the spectrum is a power

law, parton fragmentation wins over quark recombination.

We can obtain information about the observed spectrum of particles considering two mechanism: fragmentation and recombination of quarks.

R. F. Fries, B. Müller, C. Nonaka and S. A. Bass,Phys. Rev. Lett. 90, 202303 (2003).

G. Toledo

Recombination Model Provides a quantitative scenario for hadron production in thermal medium. Difficulties:• The hadronization process is instantaneous. • There are not interactions among particles in the medium.

Statistical model with finite hadronization timeIn the hydrodynamic description of the relativistic heavy ion collisions, we can relate the thermodynamical variables of the system to the proper time. The particle spectrum can be set with a degeneracy factor given in the recombination model:

The function P(τ) gives the information about the evolution of the system with proper time and accounts for a hadronization process which is not instantaneous but that occurs over a proper time interval.

To obtain the profile of P()≈ P(τ), we use a Monte Carlo Simulation using the String Flip Model

G. Toledo

QCD phenomenology Low density: Quarks confined into hadrons by gluons.

Color singlets.

No long range forces.

High density: Gas of free quarks.

Equation of state (EoS) at low densities. Degrees of freedom: Hadrons

EoS at high densities. Degrees of freedom: Quarks

Upon the matching the transition information is missing.

G. Toledo

The string flip model Horowitz, Moniz, Negele 80’s

•Quarks as degrees of freedom•Colors: red, blue green•Flavors: Up, Down

Property The model

Confinement Yes

Cluster separability Yes

Gauge invariance, SU(3) No

Exchange symmetry Yes

Lorentz invariance and qq production No

Low density limit (isolated hadrons) Yes

High density limit (free Fermi gas of quarks) Yes

Selects the configuration with minimal energy of the system formed by bound quarks. The quarks interact by a harmonic confining potential and form singlet colour clusters.

The inclusion of interactions between the quarks and provides a picture of the system evolution from low to high quark density.

G. Toledo

Many-body potential Gluon flux tubes producing a

minimal configuration of the system.

Color combinations to built singlets.

Ex. Optimal pairing of red and blue quarks ( Similar for color-anticolor )

Increasing size clustering

Vbaryon=VRB+VRG+VGB

Vmeson=VRR+VGG+VBB

G. Toledo

Variational wave function

Slater determinant

Variational parameterLow density limit:Non relativistic quark model Isgur

High density limit: Gas of quarks

Definite predictions for baryons and mesons

G. Toledo

Monte Carlo Simulation

W=∑ (xn –yn)2/m , Interaction induced termKinetic E. of N-quarks gas. Potential energy

N=Nu+Nd

Using Monte Carlo techniques we can do the integrals

The variational method requieres to minimize the energy

We have used N=64 per color

G. Toledo

Results

Energy per particleEnergy per particleLow density limitLow density limit

Non rel. quark model prediction

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Variational ParameterVariational Parameter

Drop of the clustering efficiency

Proton/pion ratioPHENIX Coll PRL 91 172301(03)

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Baryon fraction evolution Clusters of 3 quarks / All possible

Square radius

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Correlation FunctionCorrelation Function and probabilities

Baryons Mesons

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Transition to strange matterTransition to strange matter

Fermi gas transition continuos. In the model, discontinuous. Interaction effects are important

G. Toledo and J. Piekarewicz, PRC 65 045208(02)

Color screeningColor screening G. Toledo & J. Piekarewicz

PRC 70, 3526(04)

Heavy quark-antiquark potential at zero temperature and finite barion density

G. Toledo

Summary Hadronic matter modeled in terms of quarks

Dynamical interpolation between hadronic and quark matter

We computed the hadron production as a function of the energy density

Transition influenced by the interaction

Radius, baryon fraction, correlation function, correlate with the transition.

Substantial differences are found between the meson and baryon hadronization, which may explain the observation of the proton/pion ratios.

Candidates for the profile of P()≈ P().

Calculation of the hadronic spectra is underway

G. Toledo

Correlation evolution