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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
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Motivation
New states of matter
Hadronization and the proton/pion ratio
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The string-flip model
Dynamical hadron-quark transition
Variational montecarlo simulation
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Results and perspectives
Meson vs. Baryon Hadronization
G. Toledo
Motivation
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Hadrons - quarks
New phases of matter
[Gerlach PR68, Glendenning AAstrophys00, Greiner NPA00]
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
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 and recombination of quarks.
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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:
• 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(e)≈ P(τ), we use a Monte Carlo Simulation using the
String Flip Model
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QCD phenomenology
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Low density: Quarks confined into hadrons by gluons.
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Color singlets.
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No long range forces.
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High density: Gas of free quarks.
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Equation of state (EoS) at low densities. Degrees of freedom: Hadrons
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EoS at high densities. Degrees of freedom: Quarks
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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.
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Many-body potential
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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
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Increasing size clustering
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
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Variational parameter
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
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Potential energy
Results
Low density limit
Non rel. quark model prediction
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Energy per particle
Variational Parameter
Drop of the clustering efficiency
Proton/pion ratio
PHENIX Coll PRL 91 172301(03)
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Baryon fraction evolution
Clusters of 3 quarks / All possible
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Square radius
Correlation Function
and probabilities
Baryons
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Mesons
Transition to strange matter
G. Toledo and J. Piekarewicz,
PRC 65 045208(02)
Color screening
G. Toledo & J. Piekarewicz
PRC 70, 3526(04)
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Fermi gas transition continuos.
In the model, discontinuous.
Interaction effects are important
Heavy quark-antiquark potential at zero
temperature and finite barion density
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Summary
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Hadronic matter modeled in terms of quarks
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Dynamical interpolation between hadronic and quark matter
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We computed the hadron production as a function of the energy density
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Transition influenced by the interaction
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Radius, baryon fraction, correlation function, correlate with the transition.
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Substantial differences are found between the meson and baryon hadronization,
which may explain the observation of the proton/pion ratios.
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Candidates for the profile of P(e)≈ P(t).
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Calculation of the hadronic spectra is underway
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Correlation evolution
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