STAR Preliminary

1. † † † † REAL MIXED Rside is a fairly clean transverse size scale y y x x Rout contains any transverse dynamics as carried by Kt Rlong contains information about longitudinal dynamics Radii vs. Mt for pp, dAu, and AuAu Rout (fm) Rside (fm) STAR Preliminary Mt (GeV/c) Rlong (fm) E735 (ppbar) STAR Preliminary STAR R(fm) UA1 (ppbar) dN/d Thomas D. Gutierrez, January 2004 Pion HBT from pp and dAu Collisions at STAR Thomas D. Gutierrez Department of Physics, University of California, Davis for the STAR Collaboration Coulomb corrected (CC) Hanbury-Brown Twiss Interferometry (HBT) Provides geometric information about incoherent sources of identical particles Uncorrected (used for imaging) STAR Preliminary For two particle interference, the observable is the correlation function C2(Q). It is usually plotted as a function of the pair’s momentum difference, Q. HBT in 3-Dimensions The momentum difference vector, Q, used in C2(Q) can be projected into three dimensions. This provides a more complete picture of the correlation function than the 1D Qinv. The Bertsch-Pratt (BP) coordinate system (shown below) is commonly used. Each Q projection has its own corresponding conjugate size scale extracted from a fit. Studying the BP HBT fit parameters as a function of Kt provides information about space momentum correlations discussed in the following panel. g=0.410  0.007 Rg=1.02  0.013 fm e=0.756  0.015 Re=1.71  0.03 fm pp collisions  correlations C2 is sensitive to: quantum statistics (Boson, Fermion, q-boson, etc.) quantum field configuration (thermal, coherent, squeezed, etc.) source geometry (Gaussian, etc.) source dynamics (flow, jets, other space-momentum correlations, etc.) pairwise interactions (Coulomb, strong, etc.) The width of the correlation function in relative momentum is inversely related to the geometric source size. This is usually extracted from a fit to the correlation function.  correlations STAR Preliminary Ideally, for an incoherent source of bosons, C2(0)~2. C2(0) is usually measured to be less than 2 because of experimental effects (contamination, etc.) and physics effects (coherence, resonances, etc.). The fit parameter  reflects this correlation strength. The HBT effect is not small in pp and dAu collisions compared to AuAu pp (minbias) dAu (minbias) AuAu (central) STAR Preliminary dAu pp Out pp Side pp Long The 1D Qinv correlation functions, shown to the left, provide an angle-averaged view of the pion source from the pair’s rest frame. Qinv (GeV/c) dAu Space-Momentum Correlations Study of the BP HBT Gaussian radii vs. transverse mass dAu STAR Preliminary Longitudinal (beam) direction Because of boost-invariant expansion, a transverse mass dependence of Rlong is predicted. This is true even for very different mechanisms such as hydrodynamic Bjorken expansion (in AuAu) or inside-out string fragmentation (pp). It is therefore perhaps not surprising Rlong exhibits a similar Mt dependence in the pp, dAu, and AuAu systems at mid-rapidity. A graphical representation of a typical pion source function in the time-z (beam) plane 0 0.5 0 1 0 1 1 0 Q( GeV/c) Q( GeV/c) Q( GeV/c) Q( GeV/c) Show above are the 1D projections of the 3D  correlation function along the out, side, and long directions for dAu and pp collisions at STAR (the projections are 80 MeV/c wide in the “other” directions for pp and 30 MeV/c wide for dAu). The correlation projections are shown for 0.15<Kt<0.25 GeV/c. The fits are Gaussian: Transverse direction In pp collisions, the transverse dynamics are presumably driven by the independent fragmentation of (at most) a few strings, some of which will create jets. In AuAu collisions, the transverse dynamics are governed by bulk expansion such as flow. It seems strange that these two mechanisms give rise to similar Mt dependence of the transverse radii, as seen in the plots below. The effect is still under study. y (fm) Multiplicity and Centrality Dependence x (fm) Collective expansion in a AuAu collision Cartoon of multistring fragmentation in a pp collision In AuAu collisions, a more central collision has more initial state interactions which in turn produces more final state particles. This leads to a larger freezout region. The HBT radii are observed to increase with centrality Zoom on pp radii vs. Mt  correlations Ratios of AuAu and dAu radii to pp radii (from figure to the left) The horizontal lines are to guide the eye STAR Preliminary Rout/Rout_pp Rside/Rside_pp STAR Preliminary The result and interpretation are similar for dAu collisions. As the centrality increases the HBT radii are observed to increase as shown to the left. R (fm) STAR Preliminary In contrast to AuAu and dAu, the relationship between <Nch> and centrality isn’t as clear in pp collisions. The number of final state particles is subject to large fluctuations for the same impact parameter. Rlong Mt (GeV/c) Rlong/Rlong_pp Rside The flatness of these ratios is perhaps surprising (especially for the transverse radii) given the (presumably) very different mechanisms involved in producing these space-momentum correlations. Shown to the left is the one-dimensional Gaussian radius as extracted from C2(Qinv) for pp and ppbar collisions at STAR, UA1, and E735. While there is an upward trend in the radii for the other experiments, the radius as extracted at STAR appears to saturate. This is still under study. Rout Mt (GeV/c) Discussion The value of  versus dN/d appears constant at STAR. To the left, the smaller black points are from a 1D Gaussian fit to C2(Qinv). The larger black points are extracted from imaging methods, developed by Brown and Danielewicz. The larger value of lambda extracted from the imaging method indicates that C2(Qinv) is not Gaussian (as can be seen in the first panel on this poster). The flatness of  versus dN/d is observed in 3D as well (not shown). There is a long history of using HBT in elementary particle physics to study QCD and the space-time-momentum structure of hadronization. The multi-system capabilities of RHIC provides a unique link between what has historically been studied with HBT in elementary particle physics and what is known about HBT in heavy ion reactions. By studying the HBT of the pp system and dAu system in the context of AuAu collsions at STAR, we hope to gain a better understanding of the feezeout of nuclear matter under various extreme conditions: from hot and dilute pp collisions, where the space-time-momentum structure of hadronization itself is probed-- to the cooler, denser, highly interacting nuclear medium generated in AuAu reactions, where final state collective effects reign . STAR Preliminary  Future To fully characterize the system, the non-Gaussian nature of the source must be addressed. This is especially important in pp and dAu collisions where the correlation function visibly deviates from a Gaussian form. Edgeworth and Legendre fits as well as other non-fit methods such as imaging are being explored to fully characterize the correlation function. UA1: PLB 226, 410 1989 E735: PRD 48, 1931 1993 Images generated with Brown and Danielewicz’s HBT Progs v1.0 dN/d HBT with respect to the spin axis in polarized pp collisions is being explored as a means of studying final state shape asymmetries that may result from initial state polarization