Signatures of Quark-gluon-plasma/3 Direct photons

1. Signatures of Quark-gluon-plasma/3 Direct photons

2. Photon production in the QGP In the quark-gluon-plasma a quark may interact with an antiquark to produce a photon and a gluon (annihilation process) The probability for the process going into 2 photons is lower by a factor (αe/αs)=0.02, the ratio between the electromagnetic fine structure constant and the strong interaction coupling constant (g2/4π).

3. A gluon can also interact with a quark or with an antiquark to produce a photon by the process After a photon is produced, it must escape the interaction region before being detected. It interacts through the e.m. interaction, so the interaction is not strong. The mean free path is then large for the photon. The production rate and its momentum distribution depend on the momentum distributions of quarks, antiquarks and gluons in the QGP. Photons produced in the QGP then carry information on the state of the medium at the moment of production.

4. The cross section of the process quark+antiquark -> γ+ g is related to that of the process quark+antiquark -> γ + γ = = Using the Mandelstam variables

5. it can be shown (Wong, 16.2) that = so that

6. Such cross section is also linked to the e+e- -> γγcross section In terms of the Mandelstam variables From previous equations, the photon cross section has a maximum at photon momenta for which |t-m2|or |u-m2| is a minimum.

7. Since |t-m2|has a minimum when i.e. when the photon momentum is aligned with the quark momentum. Similarly which has a minimum for i.e. when the photon momentum is aligned with the antiquark momentum.

8. Thus, the photon differential cross section for the process quark + antiquark -> γ + g has 2 peaks, along directions of quark and antiquark. The produced photon is found in narrow cones along the directions of the two annihilating particles, with a width of such cones of the order of = = For relativistic particles (Eq >> m) the produced photon is mostly found along the direction of the two annihilating particles.

9. The most likely photon energy is such that the photon 4-momentum is The invariant cross section is Total cross section given by

10. Photon production by quark-antiquark annihilation The momentum distribution of produced photons per 4-volume element is quark distribution The integral of this quantity over the space-time volume element d4x gives the momentum distribution of the photons. This can be transformed into a 1-dimensional integral

11. which gives

12. For a QGP with u,d quarks (Nf=2) =

13. Photon production by Compton process The other processes to be considered are In such case Eγ and the same basic result is found: The photon differential cross section has a peak in the direction of the initial quark, within an angular cone =

14. with a cross section Similarly to the annihilation photon distribution with the 1-dimensional integral

15. For a QGP with u,d quarks (Nf=2)

16. Total photon distribution in the QGP = Annihilation process + Compton process Once produced, photons have a long mean-free path and are unlikely to interact with quark matter before being detected. Therefore, they carry information on the state in which they were created

17. Which other mechanisms contribute to photon production? Photon productions by hadrons Photon production by parton collisions

18. Photon production by hadrons Possible processes Moreover:

19. Differential cross sections for such processes have been calculated (J.Kapusta et al., Phys.Rev.D44(1991)2774). As an example which leads to expressions of the form

20. The QGP is expected to be formed at a temperature higher than the critical temperature Tc, while hadrons should have a temperature lower than Tc. So, photons from QGP should have a different energy spectrum If the QGP and hadron temperatures are the same, energy spectra will be similar, especially at high photon energies.

22. Photon production by parton collisions Photons can also be emitted by the collisions between a constituent of one nucleon with a constituent of the other nucleon, by processes similar to the annihilation or Compton in the QGP. The cross section for photon production from parton collisions may be calculated in a similar way as for the QGP. The main differences consist in the different constituent distributions QGP Thermal distribution of q, q, g Parton collisions Structure function of q, q, g in the nucleon

23. The result is a photon distribution ≈ proportional to the quark distribution in a nucleon, multiplied by a slowly varying function of Eγ ) The photon distribution appears as with an effective temperature At √s=200 GeV the temperature is about 25 GeV. This large value implies that the photon yield from parton collisions will be greater than the photon yield from QGP at large Eγ

24. From an experimental point of view, a lot of correlated photons come from the decay of Π0 -> γγη -> γγ Moreover, single photons (especially low energy photons) may be produced by 1. Heavy-ion bremmstrahlung at forward angles 2. Decay of hadrons (10-100 times more abundant than from other sources) Experimental challenge: Separate out single photons (from hadron decay) and single photons (from other sources)

25. The experimental situation

26. Experiments to measure photon yields from A+A collisions at SPS have employed • The “direct” method, to detect gammas in Pb-glass detectors (WA80,WA93, WA98) • The “conversion” method, where the photon is converted into an electron-positron pair measured in Cherenkov Ring Imaging Electron Spectrometers (NA45)

27. The WA98 set up @CERN SPS

29. The upper half of the Pb-glass array (about 10000 modules)

30. How to get direct photons • Get clean inclusive-photon sample • e.g. subtraction of charged particle background • Measure pT spectrum of π0 and η mesons with high accuracy • Calculate number of decay photons per π0 • Usually with Monte-Carlo • mT scaling for η’, ω, … • Finally:Subtract decay background from inclusive photon spectrum

31. Preliminary results from WA80 found no excess photon yield beyond that which can be attributed to resonance decays in central O+Au at 200 A GeV. An upper limit of 15% was set for the ratio between (direct photons) and (photons from neutral pions) In S+Au collisions at 200 A GeV no excess was found in peripheral collisions, while an excess was found for central events.

32. WA80: A small excess (in the order of 5%) is found at large transverse momenta. However, at the level of 1 σ, the results are consistent with the hypothesis of no-excess observed.

33. When a small effect is searched for, it is important to correctly evaluate all the sources of systematic errors.

34. In WA80, the yield from neutral pions and from η-mesons was measured at the same time as the inclusive photon yield, to minimize systematic errors on the ratios. The yield from neutral pions and η-mesons was taken as the reference background, since it amounts to more than 98% of the total yield.

37. WA98, more recent results (Phys.Rev.Lett., 2000) • 20% direct photon excess at high pT in central Pb+Pb collisions at CERN SPS • No signal within errors in peripheral collisions

39. WA98 Result: Just Hard Scattering and kT Broadening? • High pT part of the spectrum explained by pQCD + nuclear kT broadening • p+p: • A+A: • Intermediate pT range cannot be explained regardless of amount of kT Dumitru et al., Phys. Rev. C 64, 054909 (2001)

40. QGP + HG rates convoluted with simple fireball model plus pQCD hard photons Data described with initial temperature Ti=205 MeV + some nuclear kT broadening (Cronin-effect) Data also described without kT broadening but with high initial temperature (Ti=270 MeV) WA98 Interpretation: T or kT ? Turbide, Rapp, Gale, Phys. Rev. C 69 (014902), 2004

43. What have we learned from SPS? • Evidence for thermal photons • Consistent with QGP scenario • But • Temperature and kT competing contributions • Pure hadronic scenario cannot be ruled out