1. 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.

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

3. G. Toledo Motivation Hadrons - quarks New phases of matter [Gerlach PR68, Glendenning AAstrophys00, Greiner NPA00] S.S. Adler nucl-ex/0305030 M. Gyulassy nucl-th/0403032 Nuclear modification factor R CP for ( p + p )/2 and π 0 at s 1/2 =200 GeV. PHENIX Coll. S.S. Adler et al, Phys. Rev. Lett. 91, 172301 (2003).

4. 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 P T, for an exponential quark spectrum, fragmentation is always suppressed with respect recombination. At large P T, 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).

5. 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 time In 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

6. 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.

7. G. Toledo The string flip model Horowitz, Moniz, Negele 80’s Quarks as degrees of freedom Colors: red, blue green Flavors: Up, Down PropertyThe model ConfinementYes Cluster separabilityYes Gauge invariance, SU(3)No Exchange symmetryYes Lorentz invariance and qq productionNo 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.

8. 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 V baryon =V RB +V RG +V GB V meson =V RR +V GG +V BB

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

10. G. Toledo Monte Carlo Simulation W=∑ (x n –y n ) 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

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

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

13. G. Toledo

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

15. G. Toledo Correlation Function Correlation Function and probabilities Baryons Mesons

16. G. Toledo Transition 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 screening Color screening G. Toledo & J. Piekarewicz PRC 70, 3526(04) Heavy quark-antiquark potential at zero temperature and finite barion density

17. 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

18. G. Toledo Correlation evolution