Quark-gluon densities in the nuclear fragmentation region in heavy ion collisions at LHC

At the LHC, the leading partons in the nuclei are expected to interact with the maximal possible strength black disk limit up to transverse momenta of the order of few GeV. We demonstrate that in this limit the densities of the quark gluon systems produced in the central AA collisions in the nucleus fragmentation regions should exceed 300GeV/ f m3 which is at least as high as the densities discussed for the central region. Experimental signatures of such a regime are also discussed. The focus of most studies of the quark-gluon state produced in heavy ion collisions is the central region where one expects generation of high gluon densities at sufficiently high energies. The first estimates of the hadron matter densities produced in the nuclear fragmentation region were presented in [1] in the framework of the soft hadronic dynamics. The first estimate of the quark-gluon densities in this kinematics was presented within the framework of the onset of the black disk limit (BDL) of QCD in [2] which found densities at least a factor of ten larger. The purpose of this talk is review and update analysis the analysis of [2]. The starting point of [2] is the observation [3] that the transverse momenta of partons propagating through a high gluon density medium should become much larger than the scale of soft interactions. This is due to the possibility for a quark with given large x1 to interact with partons with very small x2 = 4p2 t /x1s where pt is the resolution scale. As a result, for the case of a gluon with x ≥ 10−2 propagating through the center of the heavy nucleus we find an average of pt ≥ 4GeV/c at the LHC energies, see review in [4]. Let us consider nucleus nucleus scattering in the rest frame of one of the nuclei. First let us determine the emission angle, θ , of the parton belonging to the nucleus which was at rest. Since the energy losses are small, the light-cone fraction carried by the parton is approximately conserved: (Ei − p z i ) = xmN , (1) leading to pz = (μ2 + p2 t )/2xmN − xmN/2 ≈ p2 t /2xmN . Here in the last step we have neglected μ2 compared to p2 t which is legitimate in the leading order. Since μ2 ≥ 0, neglected terms would increase pz making the emission angles, θ , even smaller. Thus, in the BDL the angles θ ≃ pt/pz ∼ 2xmN/pt are small. So, the length of the produced wave package is reduced from the naive value of 2RA by the large factor S = 1/(1− cosθ) ≈ p2 t /2x mN . However, we must also take into account that the products of the nucleon fragment as a whole move forward in the target rest frame. Since the knocked out partons carry practically the whole light cone fraction of the nucleon, the mass squared of the produced system, M2 and its longitudinal momentum, pz can be determined from ( √ M2 + pz − pz)/mN = 1,M2 = ∑i pi, t/xi, where xi, pi, t are light cone variables for produced partons. Hence, pz = M/2mN , and the Lorentz factor γ = E/M = √ M2 +(M/2mN)/M ≈ M/2mN . As a result we find the total reduction in the volume: D = (2mN/M)· < p 2 t /2m 2 Nx 2 > . (2) Since the energy of the system in its rest frame is M, we find for the overall enhancement as compared to the nuclear density: RE = 1 Nq +Ng ∑ i pit mNx 2 i . (3) To illustrate the dependence of RA on the total number of involved partons, N, and on average transverse momenta we can take all xi and all pit . In this case D = N pt/mN, RE = D2, and energy density depends quadratically on the average transverse momentum of partons. Our estimates indicate that at LHC for the gluons with x ≥ 0.0.5, 〈 pgt 〉 ≥ 16GeV 2 (and growing with increase of x), and that for quarks 〈 pqt 〉 is a factor of two smaller [4]. Taking for illustration Nq = 3,Ng = 6,xq = 1/6,xg = 1/12 and 〈 pgt 〉 = 20GeV 2 we find RE = 2300. This corresponds to ”energy density” ∼ 370GeV/ f m3, which is at least as large as the one expected for the central region. It is much larger than our initial estimate where a very conservative value of 〈 pgt 〉 was taken. If we assume the proximity of BDL at RHIC for the fragmentation region for pt ∼ 1GeV/c, we find quark-gluon energy densities ∼ 10GeV/ f m3. These densities are at least a factor of 10 higher than in [1] due to much larger release of energy in the BDL and due to significantly larger longitudinal compression of the interaction volume. Our estimate neglects the conversion of the released partons into hadrons before they reach the back edge of the fragmenting nucleus. If pt generated in the collision is small enough, this effect may become important. Using the logic similar to the one we used for estimating hadron formation in the color transparency phenomenon [5] we can estimate the distance over which a parton (not interacting with a medium) converts to hadrons. One finds