Modeling the Hadronization of Quark Matter G Toledo

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Modeling the Hadronization of Quark Matter G. Toledo Sánchez Instituto de Fisica UNAM, Mexico

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.

Outline n Motivation New states of matter Hadronization and the proton/pion ratio n The

Outline n Motivation New states of matter Hadronization and the proton/pion ratio n The string-flip model Dynamical hadron-quark transition Variational montecarlo simulation n Results and perspectives Meson vs. Baryon Hadronization G. Toledo

Motivation n n Hadrons - quarks New phases of matter [Gerlach PR 68, Glendenning

Motivation n n Hadrons - quarks New phases of matter [Gerlach PR 68, Glendenning AAstrophys 00, Greiner NPA 00] Nuclear modification factor R CP for ( p + p )/2 and π0 at s 1/2=200 Ge. V. PHENIX Coll. S. S. Adler et al, Phys. Rev. Lett. 91, 172301 (2003). G. Toledo S. S. Adler nucl-ex/0305030 M. Gyulassy nucl-th/0403032

We can obtain information about the observed spectrum of particles considering two mechanism: fragmentation

We can obtain information about the observed spectrum of particles considering two mechanism: fragmentation and recombination of quarks. n n 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. G. Toledo R. F. Fries, B. Müller, C. Nonaka and S. A. Bass, Phys. Rev. Lett. 90, 202303 (2003).

Recombination Model Provides a quantitative scenario for hadron production in thermal medium. Difficulties: •

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 time In the hydrodynamic description of the relativistic heavy ion collisions, we can relate 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(e)≈ P(τ), we use a Monte Carlo Simulation using the String Flip Model G. Toledo

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

QCD phenomenology n Low density: Quarks confined into hadrons by gluons. n Color singlets. n No long range forces. n High density: Gas of free quarks. n Equation of state (Eo. S) at low densities. Degrees of freedom: Hadrons n Eo. S at high densities. Degrees of freedom: Quarks n Upon the matching the transition information is missing. G. Toledo

The string flip model Horowitz, Moniz, Negele 80’s • Quarks as degrees of freedom

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

Many-body potential n n Gluon flux tubes producing a minimal configuration of the system.

Many-body potential n n 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 ) Vbaryon=VRB+VRG+VGB Vmeson=VRR+VGG+VBB G. Toledo Increasing size clustering

Variational wave function Slater determinant Low density limit: Non relativistic quark model Isgur Definite

Variational wave function Slater determinant Low density limit: Non relativistic quark model Isgur Definite predictions for baryons and mesons High density limit: Gas of quarks G. Toledo Variational parameter

Monte Carlo Simulation Kinetic E. of N-quarks gas. W=∑ (xn –yn)2/m , Interaction induced

Monte Carlo Simulation Kinetic E. of N-quarks gas. W=∑ (xn –yn)2/m , Interaction induced term N=Nu+Nd We have used N=64 per color Using Monte Carlo techniques we can do the integrals The variational method requieres to minimize the energy G. Toledo Potential energy

Results Low density limit Non rel. quark model prediction G. Toledo Energy per particle

Results Low density limit Non rel. quark model prediction G. Toledo Energy per particle

Variational Parameter Drop of the clustering efficiency Proton/pion ratio PHENIX Coll PRL 91 172301(03)

Variational Parameter Drop of the clustering efficiency Proton/pion ratio PHENIX Coll PRL 91 172301(03) G. Toledo

G. Toledo

G. Toledo

Baryon fraction evolution Clusters of 3 quarks / All possible G. Toledo Square radius

Baryon fraction evolution Clusters of 3 quarks / All possible G. Toledo Square radius

Correlation Function and probabilities Baryons G. Toledo Mesons

Correlation Function and probabilities Baryons G. Toledo Mesons

Transition to strange matter G. Toledo and J. Piekarewicz, PRC 65 045208(02) Color screening

Transition to strange matter G. Toledo and J. Piekarewicz, PRC 65 045208(02) Color screening G. Toledo & J. Piekarewicz PRC 70, 3526(04) n n n Fermi gas transition continuos. In the model, discontinuous. Interaction effects are important Heavy quark-antiquark potential at zero temperature and finite barion density G. Toledo

Summary n Hadronic matter modeled in terms of quarks n Dynamical interpolation between hadronic

Summary n Hadronic matter modeled in terms of quarks n Dynamical interpolation between hadronic and quark matter n We computed the hadron production as a function of the energy density n Transition influenced by the interaction n Radius, baryon fraction, correlation function, correlate with the transition. n Substantial differences are found between the meson and baryon hadronization, which may explain the observation of the proton/pion ratios. n Candidates for the profile of P(e)≈ P(t). n Calculation of the hadronic spectra is underway G. Toledo

Correlation evolution G. Toledo

Correlation evolution G. Toledo