- Physics and the Quark-Gluon Plasma

1. -Physicsand the Quark-Gluon Plasma Björn Schenke 05/12/2003

2. Overview • Facts about RHIC • Deconfinement in Heavy Ion Collisions • Phase transition • Signatures of the Quark Gluon Plasma

3. What is RHIC? • Relativistic Heavy Ion Collider at Brookhaven National Laboratory • It‘s purpose is to gain information about how the universe may have looked in the first few moments after its creation. • RHIC drives two intersecting beams of (usually) gold ions head-on.

4. Some facts • Purpose:To study the fundamental properties of matter from elementary particles to the evolution of the universe. • Sponsor: U.S. Department of Energy's Nuclear Physics Division • Cost: $600 million • Operating Costs: $130 million per year • Features: Two crisscrossing rings in a tunnel 2.4 miles in circumference 1,740 superconducting magnets 4 experiments: BRAHMS, PHENIX, PHOBOS, STAR • Users: 1,000 per year from national and international laboratories, universities and other research institutions.

5. Where is RHIC? map from http://www.bnl.gov/

6. RHIC picture from http://www.bnl.gov/rhic/

7. Map map from http://www.bnl.gov/rhic/

8. Energies

9. Heavy ion collision

10. Confinement →Deconfinement • A hadron gas consists of separated bags in which the quarks are • confined. (Outside lies the true vacuum of QCD) (b) Under high pressure and temperature the bags overlap and a macroscopic region of perturbative vacuum is created. Here the quarks and gluons are deconfined – colored particles are allowed. This is the quark-gluon plasma (QGP).

11. Do we have QGP at RHIC? • Lattice QCD predicts phase transition at ε ~ 1 GeV/fm³ • RHIC: ε~4.5 GeV/fm³ Energy density for QGP formation reached !

12. Thermodynamic properties

13. Equation of state • Take quarks and gluons as essentially massless • First neglect all interactions among the constituents of the plasma • Count degrees of freedom: • Calculate the energy density of each degree of freedom

14. Equation of state • Gluons form an ideal relativistic Bose gas of temperature :

15. For quarks and antiquarks, introduce a chemical potential , because generally there will be a surplus of quarks in the QGP. Equation of state

16. splitting this integral in the way and substitute the latter becomes Combinig the expressions for the energy densities, we get Equation of state

17. Equation of state • This can be solved and one gets: • To get a feeling for the energy densities involved in the QGP, let‘s consider the case of baryon number symmetric quark-gluon matter, i.e. the case • Then

18. Equation of state is only valid for an infinite plasma. For a finite system, that is surrounded by the usual vacuum, one has to modify the equation by the bag constant B. The pressure of the QGP then is

19. That leads to a transition temperature of beyond which the quark-gluon plasma is thermodynamically favored. Phase transition For a gas of 3 massless pions ( ) we get At the phase transition we have

20. Phase transition For and assuming that the plasma phase is stable if the internal pressure can balance the external vacuum pressure B, we can obtain a relation for the critical values of and This is a very simplified model assuming 0 quark mass and no interactions between the quarks! But it gives an idea of the range of stability of the QGP phase.

21. Phase transition

22. Phase transition

23. Signatures of the QGP

24. Signatures of the QGP One must identify signals to test whether or not the system was in a ‘primordial’ plasma phase. We are looking for • signals for deconfinemt • signals for restoring of chiral symmetry • observables, that depend on the thermodynamics of the different phases

25. The experiments PHENIX detects collision products that can reveal information about the initial collision temperature, as well as the time evolution during its later stages. STAR obtains fundamental data about the microscopic structure of the ion interactions, tracking thousands of particles emerging from the collisions. PHOBOS examines a very large number of collisions to detect rare and unusual collision events. BRAHMS measures a small number of particles emerging from a specific set of angles, and precisely measures characteristics such as momentum and energy. map from http://www.bnl.gov/rhic/

26. End view of a collision of two gold beams in the STAR detector

27. Signals for deconfinement 1) Strangeness enhancement Amount of strangeness in the hadronic phase: Production of strange hadrons in nucleon-nucleon collisions: Srange quarks are usually produced together with a K-meson: In the cm system the threshold for this reaction is

28. Strangeness enhancement Production of strange antibaryons is very rare: with threshold of 2.23 GeV in the cm system (> 8 GeV in laboratory) or with threshold of 2.55 GeV (> 9 Gev in laboratory) these reactions are also suppressed because at least three quark-antiquark pairs need to be produced in a single reaction and with very similar momenta. Results from the SPS (p+p reactions) show the ratios and

29. Strangeness enhancement Amount of strangeness in the QGP phase: Assume all quark flavors (uds) take on their thermal and (hadro-)chemical equilibrium distributions. Setting we estimate Compare to hadronic phase =0.05 And still twice as large as the ratio for p+p collisions. However, recent experimental ratios can also be explained on the basis of HG without QGP formation.

30. Strangeness enhancement

31. Signals for deconfinement 2) J/Ψ suppression At lower (SPS) energies, pairs of charmed quarks can only be formed in the beginning of a collision. If QGP is formed, the charm quarks have less chance of forming a charmonium state due to interactions with the gluons (hinder their binding or break the bound state) and color screening by the other quarks. So if a QGP-phase is formed, one should (and does) measure a suppression of the J/Ψ compared to lighter colliding systems (like p-p)

32. J/Ψ suppression

33. J/Ψ suppression At RHIC energies, considering only the absorptive effect of the QGP, no J/Ψ should be detected at all. But now, both break-up and creation should be possible: So, we should await a J/Ψ enhancement depending on the abundance of open charm.

34. Signals for deconfinement 3) Jet quenching Hard scattering of primary partons produces a pair of quarks or gluons with large transverse momenta In free space, hadronization of these high energy partons would result in back-to-back jets of hadrons. In the plasma environment, however, the partons will suffer significant energy loss and this would suppress the high energy jet components and/or destroy the balance of jets.

35. Jet Quenching First Hints for Jet Quenching at RHIC pt spectra from peripheral collisions seem well reproduced by extrapolations from p-p pt spectra from central collisions show clear deviation from p-p extrapolation high-pt data are consistent with “jet quenching” scenarios

36. So we can write: In order to have a massterm, both helicities must be present. A pure chiral state must be massless! Signals for restoring of chiral symmetry Review on chiral symmetry: Define righthanded particles through and lefthanded particles through

37. Signals for restoring of chiral symmetry HG phase: quarks acquire huge constituent mass. → chiral symmetry broken QGP phase: quarks are free and have current quark mass →chiral symmetry is restored We still do not know whether the critical line for chiral symmetry restoring phase transition should coincide with the one for the deconfining phase transition.

38. Signals for restoring of chiral symmetry The disoriented chiral condensate: Consider the linear σ-model: then the Lagrangian becomes:

39. The disoriented chiral condensate DCC: The formation of a chiral condensate in an extended domain, such that the direction of the condensate is misaligned from the true vacuum direction. The vacuum state looks like the situation in (a) Restored chiral symmetry in the QGP is shown in (b) Phase transition back to the symmetry-broken phase is shown in (c).

40. The disoriented chiral condensate DCC: The formation of a chiral condensate in an extended domain, such that the direction of the condensate is misaligned from the true vacuum direction. This will lead to a sort of domain structure in the physical space where each domain will have the chiral field aligned in a given direction. (But the directions in different domains vary randomly.)

41. The disoriented chiral condensate A signature of the DCC is the distribution for the ratio of neutral pions to all pions: If pions are incoherently produced,the probability distribution of f will be a Gaussian, peaked at the value 1/3. If all the pions are produced from a single DCC, one can show that

42. The disoriented chiral condensate Significant departures from the value 1/3 for f can then provide the cleanest evidence for the formation of a DCC. As the number of DCC domains becomes large, one will again recover the Gaussian distribution centered at 1/3. This makes it difficult to experimentally detect signals from each DCC domain. Though the width of the Gaussian will directly depend on the DCC size and hence may provide a somewhat indirect evidence for DCC formation.

43. Observables depending on the thermodynamics of the phases Direct photons and dileptons After their production, photons usually don‘t interact with their surroundings anymore. (The mean free path of photons in nuclear matter is about 600 fm. So about 98% of the photons leave the zone of reaction without interacting) So these photons should be a good measure for the early stages of the reaction.

44. Direct photons Photons in the QGP-phase are mainly produced via the following processes: We have to deal with background problems because of hadronic decays into photons, especially by and In principle, these photons can be distinguished by invariant mass analysis. But this is very difficult, if 100 neutral pions or more are produced in the reaction.

45. Direct photons One believes, that because of the additional processes in the QGP phase, there should be an increase of direct photons, if the QGP is formed. That‘s not obvious, but calculations of the temperature development for the different phases show that there are differences (especially because of the different number of degrees of freedom in the two phases). So calculations for a QGP and a HG can be compared to the experimental data. But the HG background contributions almost match with the QGP contribution and one cannot draw any conclusive evidence regarding QGP formation.

46. Dileptons Dilepton production by quark-antiquark annihilation in the QGP phase Main background process in the HG phase (invariant mass of this lepton pair is concentrated around 770±100 MeV) Calculations indicate, that lepton pairs from the QGP should be quite dominant in the lower mass region between 300 and 500 MeV.

47. Dileptons

49. Conclusion • Most likely there happens a phase transition to the QGP-phase in heavy ion collisions at RHIC • Lots of different signatures (way more than I introduced) have been studied. • But there is still no perfect signal for the creation of the Quark Gluon Plasma