STAR Preliminary

Coulomb corrected (CC)Uncorrected (used for imaging)

)1(22RQeN

)1( QReN 2GeV/c 200s

pp collisions correlations

pp (minbias)dAu (minbias)AuAu (central)

STAR Preliminary

2GeV/c 200s

Hanbury-Brown Twiss Interferometry (HBT)Hanbury-Brown Twiss Interferometry (HBT)Provides geometric information about incoherent sources of identical particles

The 1D Qinv correlation functions, shown to the left, provide anangle-averaged view of the pion source from the pair’s rest frame.

The HBTeffect is

not small in pp and

dAu collisionscompared to AuAu

221

22121 ppEEppQinv

RQ

1~

g=0.410 0.007 Rg=1.02 0.013 fm

e=0.756 0.015Re=1.71 0.03 fm

REAL

MIXED

3

233

13

32

31

6

2211

12122

// dpNddpNd

dpdpNd

aaTraaTr

aaaaTrC

pppp

pppp

† †

† †

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.

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.)

correlations

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.

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.

Pion HBT from pp and dAu Collisions at STARThomas D. Gutierrez

Department of Physics, University of California, Davisfor the STAR Collaboration

Pion HBT from pp and dAu Collisions at STARThomas D. Gutierrez

Department of Physics, University of California, Davisfor the STAR Collaboration

Thomas D. Gutierrez, January 2004

Qinv (GeV/c)

y (fm)

x (fm)

Longitudinal (beam) directionLongitudinal (beam) directionBecause 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

Transverse directionTransverse 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.

Cartoon of multistring fragmentation in

a pp collision

Collective expansion in a AuAu collision

Space-Momentum CorrelationsSpace-Momentum CorrelationsStudy of the BP HBT Gaussian radii vs. transverse mass

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.

HBT in 3-DimensionsHBT in 3-Dimensions

)1()( long2

long2

side2

side2

out2

out2

2RQRQRQeNQC

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:

Multiplicity and Centrality DependenceMultiplicity and Centrality Dependence

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

The result and interpretation are similar for dAu collisions.As the centrality increases

the HBT radii are observed to increaseas shown to the left.

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.

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.

DiscussionDiscussion

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 .

FutureFutureTo 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.

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

UA1: PLB 226, 410 1989E735: PRD 48, 1931 1993

Images generated with Brown and Danielewicz’s HBT Progs v1.0

Tsideside KQQ ˆ Rside is a fairly clean

transverse size scaley

x2Tp

21 TTT ppK

Tp

Toutout KQQ ˆ Rout contains any transverse

dynamics as carried by Kt

y

x

TKTp

zpQ zlong ˆ

Rlong contains information about longitudinal dynamics

0 1 0 1 0 1Q( GeV/c)Q( GeV/c)Q( GeV/c)

ppOut

ppSide

ppLong

STAR Preliminary

dAu

dAu

dAu

0 0.5Q( GeV/c)

STAR Preliminary

Rlong

Rside

Rout

Zoom on pp radii vs. Mt correlations

R (fm)STAR Preliminary

Rout (fm) Rside (fm)

Rlong (fm)

Radii vs. Mt for pp, dAu, and AuAu

Mt (GeV/c)

STAR Preliminary Rout/Rout_pp Rside/Rside_pp

Rlong/Rlong_pp

Ratios of AuAu and dAu radii to pp radii (from figure to the left)

Mt (GeV/c)

The horizontal lines are to guide the eye

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.

STAR Preliminary

dN/d

R(fm)STAR

E735 (ppbar)

UA1 (ppbar)

STAR Preliminary

dN/d

)1( QReN

STAR Preliminary

STAR Preliminary

Mt (GeV/c)

The value of versus dN/d appearsconstant 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).

2GeV/c 200s