Kaon and Pion Ratio Probes of Jet Quenching in Nuclear Collisions

Energy loss of high energy quark and gluon jets penetrating dense matter produced in ultrarelativistic heavy ion collisions leads to jet quenching and thus probes the quark-gluon plasma formed in those reactions [1,2]. The non-abelian radiative energy loss, ∆E(E, L), suppresses the moderate 2−3 GeV < pT < 10−15 GeV distributions of hadrons in a way that can also influence the jet fragmentation pattern into different flavor hadrons. This is because quark and gluon jets suffer different energy losses proportional to their color Casimir factors (4/3, 3). First estimates[1,2] suggested that ∆E ≈ 1 − 2GeV(L/fm) would depend linearly on the plasma thickness, L, as in abelian electrodynamics. In BDMS[3], however, nonabelian (radiated gluon final state interaction) effects were shown to lead to a quadratic dependence on L with a much larger magnitude of ∆E. The analysis of jetquenching in Pb + Pb at √ s = 20 AGeV, however, indicated a negligible energy loss at that energy [4,5]. In GLV[6,7] finite kinematic constraints were found to reduce greatly the energy loss at moderate jet energies. In this letter we apply the GLV energy loss to estimate more quantitatively the effect of jet quenching on the hadronic ratios at moderate p⊥ < 10 GeV at the Relativistic Heavy Ion Collider (RHIC) energy, √ s ≤ 130 AGeV. An advantage of looking into particle ratios is that uncertainties in the absolute normalization due to acceptance tend to cancel. The disadvantage is of course that high p⊥ particle identification is increasingly difficult. As we show below, the kinematically suppressed GLV energy loss turns out to depend approximately linearly on the jet energy, E. This linear dependence, ∆E ∝ E, leads unfortunately to only a very weakly p⊥ dependent suppression of the transverse momentum distributions for the kinematic range accessible experimentally at RHIC. Our focus here is to investigate whether the p⊥ dependence of the particle ratios can help further pin down the jet quenching mechanisms. Our primary candidates are the measurable K/π and K−/K+ ratios. Non-abelian energy loss in pQCD has been calculated analytically in two limits. In the “thick plasma” limit, the mean number of jet scatterings, n̄ = L/λ, is assumed to be much greater than one. For asymptotic jet energies the eikonal approximation applies and the resummed energy loss (ignoring kinematic constraints) reduces to the following simple form [3,8,9]