Predictions for Bottom Production in Quark-Gluon Plasma

1. Predictions for Bottom Production in Quark-Gluon Plasma Deqiang Sun Advisor: Dr. Rapp Cyclotron Institute & Physics Department, TAMU April 8, 2005

2. History of the Universe Where I work

3. What’s different and QCD phase diagram QGP: a fireball consists of deconfined quarks and gluons. • To study a QGP, physicists first have to make one. We need high Temperature and high density condition which simulates the early universe. The machine which produces QGP is… Confinement Deconfinement • Quarks and gluons (both called partons) usually confined in matter, e.g. proton, neutron. Only when energy is high enough, the protons and neutrons are melt and quarks are then “free”. QCD Phase diagram QGP phase Colour Super conductor

4. A Multi-Accelerator Complex- Brookhaven National LaboratoryThe Relativistic Heavy Ion Collider -- RHIC • Accelerates each gold ( Au ) nuclei to 197*200 GeV or 99.996% of the speed of light. Two Au hit each other. A Little Bang (heavy ion collision) is created in LAB! And bigger LHC in CERN ~~ Pb + Pb

5. Evolution of the little bang time Before collision. Incoming Lorenz contracted Nuclei Hitting. Hard parton collisions Hadron Gas Phase: particles stream to detector QGP phase? Probably!!! Even if plasma at RHIC is formed, it exists for 3~4 fm only.

6. How particles stream to detectorfrom a Au+Au Collision Look form beam direction Look perpendicular to beam direction

7. QGP formed? • Final observed products from heavy-ion collisions are hadrons. End result looks same whether or not QGP is formed. • QGP can not be detected directly so far, and can only be inferred from collision products by comparing with the other experiments to see whether some property is significantly changed. (And hence we need know what properties plasma has.) • No single experiment proved QGP existence. Existence will be inferred by a comprehensive set of signatures. • There are many signatures if a QGP existed during the collisions. We are interested in heavy quarks as signatures.

8. If we are given the experimental initial conditions, can we just use the QCD theory to predict the formation of QGP? • Yes, lattice QCD predicts that Karsch, Laermann, Peikert ‘99 Tc ~ 170 ± 10 MeV e ~ 3 GeV/fm3

9. Thermal Fireball T(t)

10. What we do • Bottomonium lifetimes and abundances calculated. • We investigate properties of bottomonium in QGP. • We try to understand in detail the interaction between bottomonium and QGP , and try to understand heavy quark as a probe.

11. heavy quarks as hard Probes • Significance of heavy quarks • Mc=1.3Gev>> Tc=0.18GeV, Mb=4.5GeV>>> Tc. Only produced in initial parton collisions, secondary production is negligible. Approx allowed. • Charmonium has been extensively studied by comparing its production in heavy ion collisions to p+p collisions and p+Au collisions. • J/Ψ suppression was originally suggested as QGP signature, but recently regeneration is shown to be dominant at RHIC. • Now we investigate the Bottomonium as a probe • Once the Bottom quarks are produced in the primordial collisions, what’s their fate in the QGP? • Is Upsilon suppression a good QGP signature? Or regeneration?

12. Suppression and Regeneration 1. 2. • Put a Y in a sea of color charges, maybe the plasma. • The color lines attach themselves to other gluons or quarks. This forms a pair of open bottom mesons. • These bottom mesons “wander off” from each other, and the Y is dissolved. • But, there’s still chance for two open bottom mesons to recombine to Y. Called Regeneration 3. c.f. Matsui &Satz (1986)

13. Initial Production of Bottomonium Where, Ry denotes the fraction of b and anti-b quark pairs within a given rapidity interval，and parameter b is the impact parameter. [42mb at RHIC, 78mb at LHC] denotes the total inelastic pp crossection. [8ub at RHIC, 160ub at LHC] For the Au+Au collisions at RHIC, there are about one b-bbar produced per 10 central collisions and 0.1% of b-bbar form Upsilons. For Pb (lead nuclei) +Pb at LHC, the corresponding numbers are about ten times larger than those in RHIC.

14. Quarkonium Potential A not-too-bad model of the quark-antiquark force law: B< 0, a spring-like part This model is mostly used There are MUCH better potential models than what I have shown. These models use the quarkonia spectra to fit their parameters. A< 0, a coulomb-like part For Bottomonium, due to big mass r is so small that we even could throw item B*r away: i.e. we derive the bottomonium’s wave function and hence cross section in the hydrogen model.

15. e0 >> L~0.3 GeV Cross sections Mechanism I: gluon dissociation LO pQCD using OPE, peskin NPB156, 79’ In medium, In vacuum, e0(j/psi)=0.6GeV e0(Y)=1.1GeV 0.6GeV At Tc=0.18GeV,u~0.40GeV

16. Cross sections NLO, but adjusted by exchanged propagators, has same order q q Mechanism II: quasifree dissociation. g g b g g g g b b b

17. Cross sections II : results gluon gluon

18. Dissociation Rate is the relative velocity between parton and Upsion is what we just calculated quasifree cross section

19. Gluon Dissociation Rate

20. Quasifree Dissociation Rate

21. Rate Equation: • If we don’t write term in this equation then we actually set a ZERO chance for two open bottom mesons recombining to a Upsilon. In other words, it accounts for the regeneration. • Solution is • Where S(t) is the survival probability for an Y to survive at time t, given as • can be achieved from statistical model of bottomonium production.

22. Equilibrium abundances from statistical model At each instant of time, Boltzmann Approximation, if equilibrium The b b_bar pairs are conserved, the thermal bottom production has to match with the initial b b_bar pairs. The statistical model introduced an fugacity factor to complete this. With the determined value of

23. Thermal Off-equilibrium effects

24. Rate Equation: • Regeneration is a small effect. Suppression is, roughly, 80% at LHC and 40% at RHIC. Although we see that at LHC there produces 10 times more Upsilons at initial primordial collisions but production is finally more suppressed than at RHC.

25. Conclusion • If QGP is formed we get a suppression for Upsilon production at both RHIC and LHC. • We invoked quasifree dissociation mechanism for bottomonium to overcome problems arising from gluon dissociation. For this process, cross sections, rates, lifetimes and abundances are quantified.

26. Acknowledgement • advisor Dr Ralf. Rapp • coworker Loic.Grandchamp, Hendrik van Hees，Sarah Lumpkins

27. Q2: if we compare our result with experiment what can we conclude?