1. With water up to the neck!

2. Alejandro Ayala, Mauricio Martínez, Guy Paic, Genaro Toledo
Proton to Pion Ratio at RHIC: Toward a dynamical picture of parton recombination
Alejandro Ayala,
Mauricio Martínez,
Guy Paic,
Genaro Toledo

3. Outline Baryon puzzle at RHIC
Static Quark Recombination + Fragmentation
String Flip Model: Dynamical Quark Recombination
Perspectives

4. PHENIX proton to pion ratios
Open points are for neutral 
Filled points are for charged 

5. Facts from RHIC
Strong suppression of pion and kaon (meson) at
pT > 2 GeV when comparing central to peripheral collisions.
Emission of protons and antiprotons does not appear to be similarly suppressed.
P/π ratio reaches or even exceeds 1 for pT > 2 GeV.
Jet quenching is not the mechanism because the fragmenting partons don’t lose energy in a different manner when forming mesons and baryons.

6. Why Puzzle?
For PT > 2 GeV in Au+Au Collisions there is a large amount of barions compared to mesons.
If hadrons were created by fragmenting partons, it would be easier to produce mesons than baryons!

7. Static Recombination+Fragmentation Basic assumptions:
At low pt, the quark and antiquark spectra are thermal. These recombine into hadrons locally “at an instant”:
At high pt, the parton spectrum is given by a pQCD power law, partons suffer jet energy loss and hadrons are formed via fragmentation of quarks and gluons

8. RECOMBINATION:
Choose a hypersurface Σ for hadronization
w(r,p): single particle Wigner function for quarks at hadronization
x, x’ & (1-x): momentum fractions carried by quarks
integrate out transverse degrees of freedom

9. Recombination+Fragmentation

10. R. J. Fries, B. Muller, C. Nonaka, S. A. Bass Phys. Rev. Lett
At intermediate PT baryon
to meson ratio depends
only on ratio of
degeneracy factors

12. Modifications to Recombination model
Greco, Ko, and Levai : Add coalescence of parton minijets and thermal partons
Hwa and Yang: Consider the effects from minijets and thermal soft partons in the thermal spectrum

13. But… The process of hadronization is intantaneous.
The model doesn’t satisfy the relation of the inverse slope parameter:
In the assumptions of the model, the four-momentum of the hadron is the sum of the four-momentum of the constituent quarks, but constituent quark masses are used.

14. Dynamical Recombination
We propose an alternative statistical model in which the evolution of the system with collision density is considered and the hadronization is not instantaneous.

15. Dynamical Recombination
Finite interval in temperature for phase transition from Lattice QCD.

16. Assumptions
At low densities, system of quarks described as isolated hadrons.
At high densities, system becomes a free Fermi gas.
The phase transition of the system occurs at finite interval of temperatures.

17. Statistical Model
In general, the statistical models obtain the spectrum of the produced particles by:
The proportionality is given by the degeneracy factor.

18. Dynamical Recombianation
Incorporate probability of forming a given hadron with proper time from an initial evolution
The information of the probability function P(τ) comes from MonteCarlo simulations using the string-flip model.

19. Many Body Potential
Gluonic Fluxes produce the minimal energy configuration in the system.
Color selection form color singlets.

20. Variational Wave Function

21. Energy minimization

22. Variational parameter as a function of energy density

23. Percentage of clusters of 3 quarks as a function of energy density

24. Perspectives
To give an dynamical mechanism for formation of mesons vs baryons
Implement this model to obtain the baryon/meson ratio and specifically p/π ratio.

26. Monte Carlo Simulation