We present results of analyses of two-pion interferometry in Au+Au collisions at $sqrt{s_{NN}}$ = 7.7, 11.5, 19.6, 27, 39, 62.4 and 200 GeV measured in the STAR detector as part of the RHIC Beam Energy Scan program. The extracted correlation lengths
(HBT radii) are studied as a function of beam energy, azimuthal angle relative to the reaction plane, centrality, and transverse mass ($m_{T}$) of the particles. The azimuthal analysis allows extraction of the eccentricity of the entire fireball at kinetic freeze-out. The energy dependence of this observable is expected to be sensitive to changes in the equation of state. A new global fit method is studied as an alternate method to directly measure the parameters in the azimuthal analysis. The eccentricity shows a monotonic decrease with beam energy that is qualitatively consistent with the trend from all model predictions and quantitatively consistent with a hadronic transport model.
In non-central collisions between ultra-relativistic heavy ions, the freeze-out distribution is anisotropic, and its major longitudinal axis may be tilted away from the beam direction. The shape and orientation of this distribution are particularly i
nteresting, as they provide a snapshot of the evolving source and reflect the space-time aspect of anisotropic flow. Experimentally, this information is extracted by measuring pion HBT radii as a function of angle with respect to the reaction plane. Existing formulae relating the oscillations of the radii and the freezeout anisotropy are in principle only valid for Gaussian sources with no collective flow. With a realistic transport model of the collision, which generates flow and non-Gaussian sources, we find that these formulae approximately reflect the anisotropy of the freezeout distribution.
Two-particle femtoscopy reveals the space-time substructure of the freeze-out configuration from heavy ion collisions. Detailed fingerprints of bulk collectivity are evident in space-momentum correlations, which have been systematically measured as a
function of particle type, three-momentum, and collision conditions. A clear scenario, dominated by hydrodynamic-type flow emerges. Reproducing the strength and features of the femtoscopic signals in models involves important physical quantities like the Equation of State, as well as less fundamental technical details. An interesting approximate factorization in the measured systematics suggests that the overall physical freeze-out scale is set by final state chemistry, but the kinematic substructure is largely universal. Referring to previous results from hadron and lepton collisions, we point to the importance of determining whether these universal trends persist from the largest to the smallest systems. We review theoretical expectations for heavy ion femtoscopy at the LHC, and point to directions needing further theory and experimental work at RHIC and the LHC.
It is important to understand, in detail, two-pion correlations measured in p+p and d+A collisions. In particular, one wishes to understand the femtoscopic correlations, in order to compare to similar measurements in heavy ion collisions. However, in
the low-multiplicity final states of these systems, global conservation laws generate significant N-body correlations which project onto the two-pion space in non-trivial ways and complicate the femtoscopic analysis. We discuss a formalism to calculate and account for these correlations in collisions dominated by a single particle species (e.g. pions). We also discuss effects on two-particle correlations between non-identical particles, the understanding of which may be important in the study of femtoscopic space-time asymmetries.
