Phenomenological models of two-particle correlation distributions on transverse momentum in relativistic heavy-ion collisions
Two-particle, pair-number correlation distributions on two-dimensional transverse momentum ($p_{t1},p_{t2}$) constructed from the particle production in relativistic heavy-ion collisions allow access to dynamical processes in these systems beyond what can be studied with angular correlations alone. Only a few measurements of this type have been reported in the literature and phenomenological models, which facilitate physical interpretation of the correlation structures, are non-existent. On-going effort at the Relativistic Heavy-Ion Collider (RHIC) will provide a significant volume of these correlation measurements in the future. In anticipation of these new data two phenomenological models are developed which describe two-dimensional 2D correlation distributions on transverse momentum. One model is based on a collision event-by-event fluctuating blast wave. The other is based on event-by-event fluctuations in fragmenting color-flux tubes and in jets. Both models are shown to be capable of accurately describing the measured single-particle $p_t$ distributions for minimum-bias Au+Au collisions at $\sqrt{s_{\rm NN}} = 200$~GeV. Both models are then applied to preliminary, charged-particle correlation measurements on 2D transverse momentum. The capabilities of the two models for describing the overall structure of these correlations, the stability of the fitting results with respect to collision centrality, and the resulting trends of the dynamical fluctuations are evaluated. In general, both phenomenological models are capable of qualitatively describing the major correlation structures on transverse momentum and can be used to establish the required magnitudes and centrality trends of the fluctuations. Both models will be useful for interpreting the forthcoming correlation data from the RHIC.