Comment on "Transverse-mass Mperp dependence of dilepton emission from preequilibrium and quark-gluon plasma in high energy nucleus-nucleus collisions"

In a recent Letter [1], Geiger presents calculations of the dilepton emission from the early stage of ultrarelativistic heavy ion collisions using the parton cascade model (PCM). He shows that the M ⊥ scaling [2] found in Ref. [3] is not observed. In this Comment, we point out that this is largely due to a defect in the PCM. The PCM is based on the perturbative QCD and inevitably contains two infrared cutoffs. In particular, it has the lower limit of the timelike virtuality of partons, µ 0 = 1GeV. As a result, each parton has an effective mass larger than 1GeV. During the nuclear collision, many partons acquire large timelike virtuality and it decreases gradually to µ 0. In the PCM, once the virtuality reaches µ 0 , it is kept unchanged. This is expected to happen typically by τ ≃ 1/µ 0 = 0.2fm ≡ τ cut , where the proper time τ is defined as τ = sgn(t − t 0) (t − t 0) 2 − z 2 [1] and in the center of mass frame, at z = 0, the maximum density is achieved at τ = 0. In reality, the virtuality of partons continues to decrease below µ 0 as time increases according to the uncertainty principle. Therefore, the partons in the PCM have inappropriately large virtualities after τ ≃ τ cut. This unphysical virtuality drastically affects the dilepton production, especially that from ¯ qq annihilations with M comparable to ∼ 2µ 0 or less, where M is the invariant mass of the dilepton. A remarkable feature in Fig. 3 of Ref. [4], on which the formalism of Ref. [1] is based, is strong suppression of the dilepton yield from ¯ qq annihilations 1