# Presentation: 350404

## Thermal photons in A+A collisions at RHIC energies 

- D.Peressounko
-             RRC “Kurchatov Institute”

## How to calculate thermal photon yield

- Pre-equilibrium contribution:
-  Neglect it;
-  Use cascade models;
-  Model with hydro.

- d3N

- dy d2Pt

- = ∫ R(T,u) d4x

**Key features of calculations:**
** ****Emission rates for QGP and RHG**
** ****Dynamic model: **
** ****Fireball; **
** ****2+1 Bjorken hydrodynamics;**
** ****3+1 hydro;**
** ****Initial conditions: ********0**** (********0**** or T****0****)**
** ****EoS**

****

**R** – emission rate from the unit 4-volume
-        at a temperature **T(x)** and
-        chemical potential ******(x)**,
-        boosted with 4-velocity **u(x)**;
****– space-time volume, occupied by the system.

- 6/21/2005

## Thermal photon emission rate from QGP

**Compton and annihilation (qg****→****q********,qq****→****g********) processes in HTL framework**
-      J.I. Kapusta, P. Lichard, D. Seibert, Phys. Rev. **D44**, 2774 (1991); Erratum, *ibid ***D47**, 4171 (1993).
-      R. Baier, H. Nakkagawa, A. Niegawa, K. Redlich, Z. Phys. **C53**, 433 (1992).
**Annihilation with rescattering and bremsstrahlung **
-      P. Aurenche, F. Gelis, R. Kobes, E. Petitgirard, Z. Phys. **C75**, 315 (1997).
-      P. Aurenche, F. Gelis, R. Kobes, H. Zaraket, Phys. Rev **D58**, 085003 (1998).
-      P. Aurenche, F. Gelis, H. Zaraket, JHEP **0205**, 043 (2002).
-      P. Aurenche, F. Gelis, H. Zaraket, Phys. Rev. **D62**, 096012 (2000).
**Inclusion of the LPM effect**
-      P. Arnold, G.D. Moore, L.G. Yaffe, JHEP **0111**, 057 (2001).
-      P. Arnold, G.D. Moore, L.G. Yaffe, JHEP **0112**, 009 (2001).
-      P. Arnold, G.D. Moore, L.G. Yaffe, JHEP **0206**, 030 (2002).

- Complete calculations in  and s

- 6/21/2005

## Thermal photon emission rate from hadron gas 

- Photon emission in reactions in  gas
-      J. I. Kapusta, P. Lichard, and D. Seibert, Phys. Rev.D 44, 2774 (1991);
- Added a1 as a intermediate state in →a1→
-      L. Xiong, E. V. Shuryak, and G.E. Brown, Phys. Rev.D 46, 3798 (1992).
- Consistent treatment of contribution of a1 resonance
-      C. Song, Phys. Rev. C 47, 2861 (1993).
- Exploring effects of hadron mass modifications in hot matter
-      P. Ko and S. Rudaz, Phys. Rev. D 50, 6877(1996).
-      J.K. Kim, P. Ko, K. Y. Lee and S. Rudaz, Phys. Rev.D 53, 4787(1996).
-     S. Sarkar, J. Alam, P. Roy, A. K.Dutt-Mazumder, B. Dutta-Roy and B. Sinha, Nucl. Phys. A 634, 206 (1998);
-     P. Roy, S. Sarkar, J. Alam and B. Sinha, Nucl. Phys. A 653, 277 (1999).
-     Y. C. Shin, M. K. Cheoun, K. S. Kim and T. K. Choi, Eur. Phys. J. A 14, 87 (2002).
- Inclusion of the contribution of strange mesons,  in t-channel and baryons
-     S. Turbide, R. Rapp and C. Gale, hep-ph/0308085.
-     Jan-e Alam, Pradip Roy and Sourav Sarkar, hep-ph/0310168

- Extensive set of reactions involving a1,K,N

- 6/21/2005

## Calcutta group

- J. e. Alam, S. Sarkar, T. Hatsuda, T. K. Nayak
- and B. Sinha, Phys. Rev. C 63 (2001) 021901.

**QGP emission rate:**
-    Two loop, no  LPM effect
**HG emission rate:**
-    a1 within different models
**Model:**
-    2+1 Bjorken hydrodynamics
**In. Cond:**
-    Ti = 265 MeV, i=1 fm/c
**EoS:**
-    Bag model (a1,N in HG)
- Evolution is not fitted neither to
- hadron multiplicity nor to hadron
- spectra.

- 6/21/2005

## D.K.Srivastava

- D. K. Srivastava,
- Pramana 57 (2001) 235.

**QGP emission rate:**
-    Two loop, no  LPM effect
**HG emission rate:**
**   **emission from** **,a1 gas
**Model:**
-    2+1 Bjorken hydrodynamics
**In. Cond:**
-    Ti = 670-390 MeV,
-     i = 0.2-1 fm/c
**EoS:**
-    Bag model (a1,N in HG)

- 6/21/2005

## Montreal group

- S.Turbide, R.Rapp and C.Gale,
- Phys. Rev. C 69, 014903 (2004).

- QGP emission rate:
-     two loop with LPM effect
- HG emission rate:
-     emission from** **a1,K,N gas
- Model:
-      Fireball model with fixed
-      longitudinal and transverse
-      accelerations.
- In.Cond.:
-      Ti~500 MeV (?)
- i=0.2 fm/c

- 6/21/2005

## Jyvaskyla group

- S.S.Rasanen, Nucl.Phys.A 715 (2003) 717.
- F.Gelis, H.Niemi, P.V.Ruuskanen, S.S.Rasanen, J.Phys.G30:S1031-S1036,2004

- QGP emission rate: two loop with LPM effect
- HG emission rate:  emission from** **,a1 gas
- Model:     2+1 Bjorken hydrodynamics
- In. Cond: Ti = 580 MeV, i=0.17 fm/c
- EoS:        Bag model (rich hadronic gas)

- Evolution fit to reproduce
- hadron spectra

- 6/21/2005

## BNL-Moscow group

- D.d'Enterria and D.Peressounko,nucl-th/0503054

**QGP emission rate:** two-loop with LPM effect
**HG emission rate:** emission from a1,K,N gas
**Model:**    2+1 Bjorken hydrodynamics;
**In.Cond:** i=0.15 fm/c; Ti=610 MeV
**EoS:**       Bag model (~400 species in HG)

- Evolution is fit to
-  ,K,p spectra

- 6/21/2005

## BNL-Moscow group

- D.d'Enterria and D.Peressounko,nucl-th/0503054

**pQCD: L.E. Gordon and W. Vogelsang, Phys. Rev. D 48 (1993) 3136; **
**            ****Phys. Rev. D 50 (1994) 1901.**
**PHENIX data: S.S.Adler et al., Phys. Rev. Lett. 94, 232301 (2005)**

- 6/21/2005

## Comparison of predictions to PHENIX data

- Calculations with similar
- initial time (temperature)
- result in similar spectra.
- Dependence on used
- emission rates and details
- of description of evolution
- is modest.

- All calculations predict
- considerable thermal
- contribution below 3 GeV

- All calculations agree with
- data within errors.

- 6/21/2005

## What is next?

- Calculate centrality dependence of the thermal photon spectrum:
-      Exploring dependence on the initial energy density.

-    Since thermal photons reflect temperature in the medium, can we extract this temperature directly by measuring slope?
-    Can we extract the number of effective degrees of freedom in hot matter by comparing thermal photon slope and entropy or energy density?

- Can we go further?

- 6/21/2005

## Correlation between apparent and initial temperature

- EoS ***with***
- phase transition

- EoS ***without***
- phase transition

- Smearing of effective temperature:
- Final thickness of matter
- Temperature gradients T(r)
- Collective velocity
- Does correlation survive?

- D.d'Enterria and D.Peressounko,nucl-th/0503054

- 6/21/2005

## Correlation between apparent temperature and dNch/d

- EoS ***with***
- phase transition

- EoS ***without***
- phase transition

**Au+Au, 200 AGeV**

- D.d'Enterria and D.Peressounko,nucl-th/0503054

- 6/21/2005

## Correlation between apparent temperature and dNch/d

**Au+Au, 62 AGeV**

- i=4R/= 0.45 fm/c

- D.d'Enterria and D.Peressounko,nucl-th/0503054

- 6/21/2005

## Conclusions

- At top RHIC energy thermal photons contribute to direct photon spectrum at Pt<3 GeV: more precise data are necessary to make any conclusion.
- Thermal photon spectrum depends mainly on initial temperature and in much smaller extend on details of evolution and emission rates.
- Correlation between apparent temperature of thermal photons and maximal initial temperature in the collision is not destroyed by evolution: maximal temperature can be extracted just by measuring inverse slope at as high Pt as possible.
- One can directly explore phase transition by confronting apparent slope of thermal photons and charged hadron multiplicity.

- 6/21/2005