Photon and dilepton emission from the quark-gluon plasma: Some general considerations

The emission rates for photons and dileptons from a quark-gluon plasma are related to the thermal expectation value of an electromagnetic current-current correlation function. This correlation function possesses an invariant-tensor decomposition with structure functions entirely analogous to $W_1$ and $W_2$ of deep-inelastic scattering of leptons from hadronic targets. The thermal scaling properties of the appropriate structure functions for thermal emission are derived. The thermal structure functions may be computed in a weak-coupling expansion at high plasma temperature. The rates for thermal emission are estimated, and for dileptons, using conservative estimates of the plasma temperature, the thermal-emission process is argued to dominate over the Drell-Yan process for dilepton masses 600 MeV<M<1–2 GeV. We argue that higher temperatures are entirely possible within the context of the inside-outside cascade model of matter formation, perhaps temperatures as high as 500–800 MeV. If these high temperatures are achieved, the maximum dilepton masses arising from thermal emission are argued to be 5 GeV. Pre-equilibrium emission might dominate over Drell-Yan emission at somewhat higher masses. Signals for thermal emission are presented as the relative magnitude of invariant thermal structure functions, thermal scaling relations, and transverse momenta of thermal dilepton pairs which increase with and are proportional to the dilepton-pair mass. The transverse-mass spectrum is shown to be dN/${\mathrm{dM}}^2$dy $d^2$$q_{\perp }$∝$M_{\perp }$${\mathrm{}}^{\mathrm{-}6}$ and upon integrating over transverse momentum ∝$M^{\mathrm{-}4}$, for a high-temperature plasma. The spectrum is power law, not exponential. The dependence of the spectrum of thermal emission upon the existence of a first-phase transition is studied, and the possibility that the spectrum might change its slope as a function of $M_{\perp }$ or have a sharp break is pointed out. We argue that if there is a first-order phase transition, as beam energy or nuclear baryon number is raised through the threshold for production of a plasma, the rate for photon or dilepton emission might dramatically increase. In the case of a first-order phase transition, in addition to the power-law spectrum of transverse mass, there is an additional contribution of $e^{\mathrm{-}{M}_{\perp }/T}$, where T is the phase-transition temperature.