Date post: | 02-Jan-2016 |
Category: |
Documents |
Upload: | katherine-matthews |
View: | 214 times |
Download: | 0 times |
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
G. Toledo
Variational ParameterVariational Parameter
Drop of the clustering efficiency
Proton/pion ratioPHENIX Coll PRL 91 172301(03)
G. Toledo
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