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following the well known _ rhetoric _ , photons are weakly coupled to the strongly interacting quarks and gluons .
photons emitted in a qgp will immediately escape without further interactions in the plasma .
this immediate `` escape '' will carry useful information on the nature of the supposedly formed plasma , at the emission stage .
hence the comparison between the _ calculated _ photon spectrum from a qgp and that from a hadron gas medium with the measured photon spectrum in heavy ion collision , after background subtraction , will constitute an evidence in favor of either state of matter .
+ in an optimistic scenario , the plasma will live long enough for thermalization to occur . at a suitable high temperature ( @xmath2 ) , which is not so realistic in present heavy ion collisions ,
the running strong coupling constant @xmath0 will be small .
+ the above framework can be summarized as follows : we have a system in thermal equilibrium with an exact microscopic description in terms of quarks and gluons . in the small coupling constant regime
, the calculation of the photon spectrum seems to be a straightforward application of perturbation theory .
this is seemingly a simple situation compared to photon production in proton - proton collision where form - factors show up .
although photons are weakly coupled to the plasma this description is oversimplified , since the quark that emits the photon is affected by medium effects such as debye screening ; it also acquires a thermal mass which plays a central role in screening infrared divergences .
medium effects are well described by the hard thermal loop ( htl ) effective theory @xcite .
so , the htl theory is the natural scheme for calculating the photon production rate in a thermalized qgp .
+ for present ( rhic ) , and near future ( lhc ) , heavy ion collision experiments a more realistic prediction should go beyond the small coupling constant regime .
this will be briefly discussed at the end of this article .
in a qgp in local thermal equilibrium , the photon production rate or the number of photons , with momentum @xmath3 , produced per unit time and per unit volume is conveniently expressed in terms of the imaginary part of the photon two point function , calculated in the plasma @xmath4 this formula is valid at lowest order in the electromagnetic coupling , and to all orders in the strong coupling constant . in other words ,
the two point function encodes the essential physics of the plasma , relevant for photon emission . + as mentioned in the previous section , to obtain the photon two point function in a perturbative procedure , the htl theory should be used . the one loop calculation in the effective theory
was performed some time ago @xcite .
it was believed that the one loop result gave * the * leading order @xmath0 photon spectrum .
this belief was based on the success of the effective theory .
the essence of the effective theory is to reorder the perturbation theory to give a meaning to the equivalence between the loop - wise expansion and the successive orders in the coupling constant .
the loophole in this equivalence comes from collinear configurations .
the effective theory does not incorporate a ready - to - use remedy for collinear problems .
collinearity is kinematical , _
i.e. _ it depends on the particular problem of interest , so it is not surprising if the effective theory fails to treat such problems systematically .
+    it worth mentioning that the underlying physical processes in the one loop diagram are the @xmath5 processes , compton and annihilation . however , it was shown @xcite that bremsstrahlung and the new process of annihilation of an off - shell quark ( on the left of figure [ fig : processes ] ) contribute to leading order .
these processes appear only at the two loop level in the effective theory .
the breakdown of the effective theory , two loop is of the same order as one loop , is traced back to the appearance of collinear divergences ( _ i.e. _ the collinear emission of the photon by a quark ) .
this collinearity is soften by the use of the effective theory which gives a kinematical cutoff denoted by @xmath6 where @xmath7 is the thermal mass of fermions , provided by the effective theory , and @xmath8 is the quark energy .
the present form of the cut - off is valid for real and small mass virtual photons ( the real photon case is obtained for @xmath9 ) .
the dependence of this cut - off on the coupling constant , although it regularizes what would be a collinear singularity , renders the two loop diagrams equally important as the one loop contribution . since , after phase space integration the cut - off @xmath10 appears linearly in the denominator , its @xmath11 dependence cancels the extra powers of the couplings in the two - loop diagrams .
+ it is thus natural to ask whether this breakdown of the effective theory does not propagate to higher loop orders ?
+ simple power counting @xcite indicates that the collinear configuration persists for all ladder diagrams . as a consequence , higher loop diagrams do contribute to the leading @xmath0 order for real photon production .
hence a resummation of a whole set of gauge invariant diagrams is mandatory .
in attempt to focus on the underlying physical mechanism which renders higher loop diagrams equally important as the one loop diagram , we calculated @xcite the imaginary part of the photon polarization tensor at two loop level with quarks having a finite width .
this study leads to a simple physical picture .
photon emission from a quark gluon plasma gives rise to two natural physical scales ( figure [ fig : lpm ] ) :    * the formation length ( time ) @xmath12 , also called the coherence length @xmath13 : @xmath14\;,\ ] ] where @xmath15 is the quark transverse ( compared to photon momentum ) momentum , * the mean free path ( width)@xmath16 : @xmath17    the interplay between these two scales leads to the emergence of different physical regimes :    * the perturbative regime ( @xmath18 ) , where the dominant mechanisms of photon production are compton and annihilation appearing at one loop order in the htl effective theory .
high dilepton mass spectrum is a typical example of this regime . *
the landau - pomeranchuk - migdal regime ( @xmath19 ) : it is the region where the formation length is much longer than the mean free path .
inelastic processes like bremsstrahlung should be considered .
this leads to coherent photon production , which is responsible for the lpm suppression of the photon spectrum . in this region
a further resummation is needed to include rescattering .
real photon production exemplifies this regime .
the finite width study cited in the previous section , although it provides a nice physical picture , is far from giving the complete photon spectrum .
a correct approach would consist in re - summing the ladder diagrams mentioned above together with quark propagators with a finite width ( self - energy corrections ) .
this has been recently carried out @xcite .
the authors of @xcite showed that important cancellations of long ranged interactions occured between vertex and self - energy diagrams and derived an integral equation with a simple physical interpretation .
the bottom line of their resummation is to consider the rescattering of an almost on - shell quark in a random gaussian background field .
the imaginary part of the two point function was found to be : @xmath20\ ; { { p_0 ^ 2+(p_0+q_0)^2}\over{2(p_0(p_0+q_0))^2 } } \nonumber\\ & & \qquad\qquad\qquad\times{\rm re}\,\int { { d^2{\bf p}_\perp}\over{(2\pi)^2}}\ ; { \bf   p}_\perp\cdot{\bf f}({\bf p}_\perp ) \nonumber \label{eq : amy}\end{aligned}\ ] ] with @xmath21\ ; , \ ] ] @xmath22 is the same as the inverse of the formation time defined before .
this integral equation reflects the following features :    * the combination @xmath23 $ ] guarantees the cancellation of all infrared behavior ( _ a priori _ non - perturbative ) when @xmath24 .
* iteration is equivalent to rescattering in the medium with a collision term @xmath25 . *
the width , discussed in the previous section , could be seen as a part of the collision term .
we notice again that multiple scatterings are important when the collision integral is of the same order as the @xmath22 term , as was predicted by the model discussed in the previous section .
the above equation is solved numerically and it is found that rescattering leads to about 25 % suppression of the photon spectrum coming from bremsstrahlung and off - shell scattering .
hence , although the `` next to one loop '' processes are not as enhanced as was thought originally @xcite they still give important contribution which should be included beside the strict one loop processes to obtain the complete order @xmath0 photon spectrum . +
recently the collision term was obtained analytically using new sum rules at finite temperature @xcite .
the collision term is found to be @xmath26 this analytical form allows to circumvent the evaluation of complicated integrals in the original form of the collision term .
it is also useful for the extension of the above study to the production of low mass dileptons .
photon production nowadays is known to complete order @xmath0 .
it is among the rare theoretical calculations going beyond the leading logarithm approximation .
the resummation done by arnold _ et al _ leads to a picture where one averages over a gaussian background field which goes beyond the classics of static scattering centers extensively used in the literature to model rescattering .
+ it must be emphasized that bremsstrahlung and off - shell annihilation are among the dominant mechanisms for photon production .
although the resummation has led to a 25 % suppression , the next to one loop processes still give significant contributions which will enhance the photon production rate in a quark - gluon plasma .
thermal photon production is not the unique source of photons .
pions , for example , decay into photons giving a very important background . this background should be subtracted in order to isolate the thermal photon production and compare it to photon production in a hadron gas model . on the other hand
, dilepton production has a different background to be subtracted .
hence a compilation of photon and dilepton will constitute a tractable mean for `` plasma detection '' .
+ the resummation done in @xcite includes only the transverse photon polarization .
however , dilepton could receive contributions from the longitudinal polarization sector , hence the extension of the above resummation to dilepton case requires some precautions .
the necessary resummation for low mass dilepton leads to @xcite ( preliminary results ) @xmath27\int   \left[2{\bf p}_{\perp}.{\bf f}({\bf p}_{\perp})\oplus q^2 g({\bf p}_{\perp})\right]\ ] ] the new scalar function @xmath28 satisfies an equation analogue to that satisfied by @xmath29 .
the preliminary results for the dilepton rate indicates an lpm type suppression which does not rule out the contribution coming from bremsstrahlung and off - shell annihilation found recently in @xcite .
+ we should stress that the small coupling constant regime is an idealized situation .
a more realistic coupling constant should not be so small .
recall that photon emission is dominated by collinear emission , this occurs for almost on - shell quarks . hence quarks can be treated to a good approximation in a quasi - particle model , with masses derived from lattice calculation .
this is under investigation @xcite .    9 , nucl . phys . * b * * 337 * , 569 ( 1990 ) ; e. braaten , r.d .
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* b * * 339 * , 310 ( 1990 ) ; j. frenkel , j.c .
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long time ago , photon production was proposed as a probe and a thermometer for quark - gluon plasma ( qgp ) . 
 however , only recently has the complete @xmath0 order photon spectrum been obtained . in this paper 
 we give a brief review of the problematic as well as discuss the @xmath1 result .