Space-time Autocorrelation and Hubble Flow: Probing Small Length Scales in Heavy Ion Collisions

Two-particle momentum correlations have been applied extensively to the determination of particle source distributions and flow effects in nuclear collisions [1]. HBT interferometry employs variations of the detected pair intensity in a two-particle momentum space to estimate the conjugate space-time-momentum autocorrelation density of the emitting source. These established techniques depend directly on quantum-mechanical amplitude interference. We propose here an alternative source of momentum correlation induced by a combination of radial or Hubble flow and autocorrelation differences between particle pair types which should provide additional information on the two-particle space-time structure of the emitter. This new method is not primarily an interference effect. In the simplest interpretation it has a cosmological analog in the use of red shifts and a universal Hubble-flow hypothesis to map relative galactic positions. In this Letter we extend the usual treatment of two-particle momentum correlations to include the possibility of non-chaotic or correlated particle emission from the hadronic freeze-out surface. We adopt a modified two-particle emission density which permits description of nontrivial differences between pair autocorrelations for different pair types. Pair position autocorrelation determines how nuclear flow is sampled by pair partners. If different pair types sample flow in systematically different ways we predict a unique signature in two-particle momentum distributions. A general two-particle momentum distribution assuming independent pair emission can be written as P2(p1,p2) = ∫ dx1d x2 S2(x1, x2, p1, p2) |Φ2(x1, x2, p1, p2)| , where |Φ2| 2 may include a distorted-wave treatment to describe Coulomb and final-state interactions (FSI). In what follows we use x = (x1 + x2)/2 and y = x1 − x2. If we assume a factorizable Wigner density (chaotic or independent particle emission), smoothness [2, 3] and plane-wave propagation without final-state