Haitham Zaraket
(LAPTH  Annecy, France)
                               Photon production in a QGP, collinear and infrared divergences
The quark gluon plasma being transparent to photons, will allow those photons produced in the plasma to escape without further interactions. Hence photon production rate constitute a good signature of the plasma formation.
Photon production rate in a QGP can be calculated using the Hard Thermal Loop scheme (HTL) which takes into account the collective phenomena of the plasma. Doing the calculation using HTL reveals strong collinear and infrared divergences:
Collinear divergences are related to the fact that we look at on shell photons. Those photons can be emitted parallel to the quark that emits it. Collinear singularities start to appear at one loop level  (logarithmic divergence only) in HTL loop expansion as found by   Baier et al.  and  Aurenche et al.  for soft photon production. The two loop diagram suffers from a more serious linear collinear divergences [see  Aurenche et al. ]. In this talk I will discuss this problem briefly, and give the method to regularize these collinear divergences by using the modified HTL approach a la Flechsig and Rehban . Within the same line of reasoning it may appear that higher loop diagrams do  contain additional collinear divergences. In a  recent work  done in collaboration with P. Aurenche and F. Gelis,  we show that no additional collinear divergences could appear at higher loop order, i.e.  higher loop diagrams contain only the two loop collinear structure.
Although higher loop diagrams do not give rise to new collinear divergences, infrared divergences are crucially present. We know that thermal field theories with bosons have stronger infrared singularities compared to their counterparts at zero temperature. This is due to the singular behavior of the Bose-Einstien statistical weight at zero energy, which affects massless bosonic fields. In our particular situation we can show by simple power counting that we have linear infrared divergences, especially  due to the exchange of static magnetic gluons, which are not screened even after using the HTL resummation. This power counting is not the end of the story, there are cancellations between different physical processes. We show that any n-loop diagram (with abelian topology only i.e. we did not included three or four gluon  vertices ) is infrared finite when adding the contributions from all physical processes, a thermal field theory version of Kinoshita, Lee and Nauenberg theorem at zero temperature.
By explicitly calculating the three loop ladder diagram we see that these infrared cancellation are partial. The final finite  three loop result, after these partial cancellation, depends on a kinematical cutoff that is proportional to photon energy,  where we can distinguish to separate cases:
1- For hard photon production  (with energy > T), the three loop diagram is suppressed by a  factor of temperature over energy compared to the two loop diagram, and hence hard photon production is given by the one and two loop diagrams only.
2- soft photon production ( with energy <T), where the kinametical cutoff start to be less efficient to screen infrared divergences, than the magnetic mass which is a non perturbative quantity, and hence soft photon production seem to  be nonperturbative.
Finally the question is how to resum all the higher loop diagrams, and include the non perturbative effects in the case of soft photons?

e-mail:  zaraket@lapp.in2p3.fr
Last modified:  Nov. 19 1999