Photon production in a QGP, collinear and infrared
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
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
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
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
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,
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
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?
Last modified: Nov. 19 1999