1. Quark recombination in high energy collisions for different energies Steven Rose Worcester Polytechnic Institute Mentor: Dr. Rainer Fries Texas A&M University

2. Motivations Understand the mechanisms that allow for particle creation in high energy collisions Understand QCD (strong force interactions) at high temperatures and densities  Quark-Gluon Plasma is such a system

3. Quarks/Partons Quark- elementary particle that carries a color charge There are three color charges and their opposites Quarks also have one of six ‘flavors’ Strong interactions conserve color and flavor Gluons are the strong force carriers  Both quarks and gluons make up hadrons

4. Hadrons Hadrons are particles constructed of quarks (Anti)-Baryons have three (anti)-quarks Mesons have a quark-anti-quark pair All hadrons are color neutral due to confinement

5. Sea Quarks and Virtuality Quantum Mechanics allows for qqbar pairs to be created by violating energy conservation for short periods of time These pairs are always opposite in color and flavor Violation of CoE is an attribute of virtuality

6. The Collision – What Happens? Impact- Temperature and pressure are raised and cause a phase transition. QGP- Hadrons “melt” as quarks become relevant degrees of freedom System expands, reaches a thermal freeze out and hadrons are recreated, but how?

7. The Collision – Characteristic Quanitities

8. Jets

9. Fragmentation Partons may escape the QGP before freeze out, but confinement must hold true. The ‘freed’ quark is virtual, but it loses it’s own energy to create many qqbar pairs that form hadrons. Each qqbar pair brings the quarks collectively closer to the mass shell, until there is no virtuality.

10. Diagrams for Fragmentation Feynman diagram model describes fragmentation with a perturbative approach The gluon-string model gives a better insight as to how confinement plays a role

11. Recombination Fragmentation built on the idea of a single quark in a vacuum, doesn’t consider many quarks Recombination describes hadronization of many quarks  Applicable in QGP Recombination argues that only quarks close in phase space will be able to form hadrons

12. Hadron Ratio - Evidence P+P Collisions have nearly constant, and small ratios Large nuclei exhibit a growth in the same ratio

13. Fragmentation and Recombination Fragmentation is dominant in p+p and electron- positron annhilations for pt > 1 GeV/c Fails at intermediate pt (1..6 GeV/c) for heavy ions Fragmentation has to win for high pt Recombination wins at intermediate pt, if phase space is densely populated

14. Methodology- Fragmentation Perform perturbative calculations to create jet spectra for various collisions/energies/nuclei  Many integrals, best speed with FORTRAN Calculation is Leading Order, so fits the shape well, but not the size- scale by an appropriate “k-factor”  Simple least squares fit, done easily with Mathematica Used KKP fragmentation functions

15. Methodology- Nuclear Effects Experimental data has no control over impact parameter, but generalizes ‘centrality bins’ This determines fireball geometry for calculated jet path length With path length, we allow interactions to drain energy from the jet, changing apparent momentum  Gluons lose more energy than quarks!

16. Methodology- Recombination We assume thermal quark spectra (fq = distribution) with temperature T and radial flow v t Example: A meson in terms of recombination

17. Resulting pt spectra Au+Au 200 GeV Au+Au 62.4 GeV Central

18. More pt spectra Au+Au 62.4 GeV Peripheral Cu+Cu 22.5 GeV

19. Other Observables – P/Pi, RAA

20. Conclusions In high energy, massive nuclei collisions,  Recombination is a critical mechanism for hadron production in the range of 1 – 6 GeV/c.  Fragmentation is the dominant process for hadron production above 6 Gev/c Recombination contributes less to smaller collisions (low A, large b)

21. Always under construction Need better fragmentation functions Experimental data on mid- to light-ion collisions Systematic study of parameters and comparison to hydrodynamics