Production of Transverse Energy from Minijets in Next-to-leading Order Perturbative Qcd

We compute in next-to-leading order (NLO) perturbative QCD the transverse energy carried into the central rapidity unit of hadron or nuclear collisions by the partons freed in the few-GeV subcollisions. The formulation is based on a rapidity window and a measurement function of a new type. The behaviour of the NLO results as a function of the minimum transverse momentum and as a function of the scale choice is studied. The NLO results are found to be stable relative to the leading-order ones even in the few-GeV domain. [email protected] [email protected] Below the transverse momenta of observable jets in hadronic collisions, pT <∼ 5 GeV, but still within the applicability domain of perturbative QCD, ΛQCD ≪ pT , there is a region of semi-hard parton production, pT ∼ 1..2 GeV. In ultrarelativistic heavy ion collisions this region is especially important in the formation of Quark Gluon Plasma at the future colliders BNL-RHIC and CERN-LHC/ALICE: at high collision energies, the few-GeV QCD-quanta, minijets, dominate the initial transverse energy production [1, 2, 3] at central rapidities during the first fractions of fm/c. The initial energy densities for further evolution of the system can thus be estimated based on perturbative QCD (pQCD)[4]. As work pdV is done during the expansion of the system, the initial transverse energy is not, however, directly measurable in AA collisions: the final state ET in the central rapidity unit has been estimated to be only 1/6 (1/3) of the initially produced ET at the LHC (RHIC) [4]. The final ET depends practically linearly on the initial one, so for making reliable estimates of the measurable ET the initial ET needs to be computed as accurately as possible. The average initial transverse energy produced perturbatively in the central rapidity unit ∆Y of an AA collision at an impact parameter b can be computed as [3] E AA T (b, √ s, p0,∆Y ) = TAA(b)σ〈ET 〉p0,∆Y . (1) The standard nuclear overlap function TAA(b) accounts for the nuclear collision geometry (TAA(0) ≈ A/(πR A) for A ∼ 200 [3]). The first moment of the semi-inclusive ET distribution, σ〈ET 〉p0,∆Y , is the pQCD quantity we formulate and compute in NLO below. The scale p0 is the smallest transverse momentum scale in the computation. It also governs the formation time of the system through τ0 ∼ 1/p0. To compute the actual values of initial ET , p0 has to be determined dynamically by introducing additional (nonperturbative) phenomenology, see e.g. [4]. We emphasize that in this work we do not discuss this but aim to show that the NLO pQCD formulation is field-theoretically well defined and perform a rigorous pQCD computation of σ〈ET 〉p0,∆Y . Therefore, at this level p0 is a fixed external parameter with no other physical significance than p0 ≫ ΛQCD. The dependence of σ〈ET 〉 on p0 will be explicitly studied and the rigorous NLO computation presented here then sets the stage for more phenomenological analyses. We generalize the LO formulation [3] of σ〈ET 〉 to NLO by introducing a new type of infrared (IR) safe measurement functions [5] which contain both the rapidity acceptance and the definition of perturbative collisions. In getting from the 4 − 2ε dimensional squared matrix elements to the physical quantities we apply the procedure by S. Ellis, Kunszt and Soper (EKS) [5, 6, 7, 8]. The new results obtained in our study can be summarized as follows: A consistent and well-defined NLO pQCD formulation of σ〈ET 〉p0,∆Y exists. Eventhough towards the few-GeV region the NLO results could grow rapidly relative to the LO, a stable behaviour of the NLO results is discovered in the range 1...2GeV<∼ p0<∼ 10GeV. This