STAR Pion Interferometry and RHIC Physics John G. Cramer Department of Physics University of Washington Seattle, Washington, USA John G. Cramer Department

STAR

Pion Interferometryand

RHIC Physics

Pion Interferometryand

RHIC Physics

John G. Cramer

Department of Physics

University of Washington

Seattle, Washington, USA

John G. Cramer

Department of Physics

University of Washington

Seattle, Washington, USA

Invited Talk presented atIX Mexican Workshop on Particles and Fields

Physics Beyond the Standard ModelUniversidad de Colima, Colima, Mexico

November 19, 2003

Invited Talk presented atIX Mexican Workshop on Particles and Fields

Physics Beyond the Standard ModelUniversidad de Colima, Colima, Mexico

November 19, 2003

November 19, 2003

John G. Cramer2STAR

Part 1Part 1

About RHIC

The Relativistic Heavy Ion Collider

and STAR

Solenoidal Tracker At RHIC

at BNL

Brookhaven National Laboratory

About RHIC

The Relativistic Heavy Ion Collider

and STAR

Solenoidal Tracker At RHIC

at BNL

Brookhaven National Laboratory

November 19, 2003

John G. Cramer3STAR

Systems:

Au + Au

CM Energies:

130 GeV/A

200 GeV/A

1st Collisions:

06/13/2000

Location:

BrookhavenNationalLaboratory,

Long Island,NY

Brookhaven/RHIC/STAR OverviewBrookhaven/RHIC/STAR Overview

pp

AGS

TandemVan de Graaff

RHICBlue Ring

Yellow Ring

Booster

Ring

November 19, 2003

John G. Cramer4STAR

What does RHIC do?What does RHIC do?

RHIC accelerates gold nuclei in twobeams to about 100 Gev/nucleon each(i.e., to kinetic energies that are over100 times their rest mass-energy)and brings these beams into a200 GeV/nucleon collision. Four experiments, STAR,PHENIX, PHOBOS, andBRAHMS study these collisions. In the year 2000 run, RHICoperated at a collision energyof 130 Gev/nucleon. In 2001-2 it operated at 200 GeV/nucleon.

November 19, 2003

John G. Cramer5STAR

ZDC

Barrel EMC

Endcap EMC

Magnet B= 0.5 T

ZDC

FTPCs

Vertex Position Scintillators (TOF)

Trigger Barrel(TOF)

Time Projection Chamber

Silicon Vertex Tracker

RICH

2 m

4 m

24 sectors x 5692 r pads x 350 t bins= 47,812,800 pixels

y1

The STAR Detector

November 19, 2003

John G. Cramer6STAR

Run: 1186017, Event: 32, central

colors ~ momentum: low - - - high

Central Au +Au Collision at sNN = 130 GeVCentral Au +Au Collision at sNN = 130 GeV

November 19, 2003

John G. Cramer7STAR

Part 2Part 2

RHIC Physics ExpectationsRHIC Physics Expectations

November 19, 2003

John G. Cramer8STAR

A Metaphor for RHIC Physics Understanding

A Metaphor for RHIC Physics Understanding

November 19, 2003

John G. Cramer9STAR

Surprises from RHICSurprises from RHIC

1. The “Hydro Paradox”: Relativistic hydrodynamic calculations work surprisingly well, while cascade string-breaking models have problems.

2. Strong absorption of high pT pions: There is evidence for strong “quenching” of high momentum pions.

3. The “HBT Puzzle”: The ratio of the source radii Rout/Rside is ~1, while the closest model predicts 1.2, and most models predict 4 or more. RLong is smaller than is consistent with boost invariance. In essence, all models on the market have been falsified by HBT.

In the remainder of this talk we will focus on theRHIC HBT Puzzle.

November 19, 2003

John G. Cramer10STAR

In Search of the Quark-Gluon Plasma (QGP)

In Search of the Quark-Gluon Plasma (QGP)

A pion gas should have few degrees of freedom.

A quark-gluon plasma should have many degrees of freedom and high entropy.

Entropy should be roughly conserved during the fireball’s evolution.

Hence, look in phase space for evidence of:

Large source size, Long emission lifetime, Extended expansion,

Large net entropy …

November 19, 2003


The Hanbury-BrownTwiss Effect and

Bose-Einstein Interferometry

The Hanbury-BrownTwiss Effect and

Bose-Einstein Interferometry

Part 3Part 3

November 19, 2003


A Happy Coincidence of ScalesA Happy Coincidence of Scales

For the Hanbury-Brown Twiss Effect to work, we must have ab/L 1, where

a = size of object,b = separation of detectors = wavelength of correlated

particlesL = object-detector distanceStars:

a = 2 Rsun = 1.5 x 109 m L = 10 light years = 1017 m

= 500 nm = 5 x 10-7 m

Therefore, need b = L/a = 33 m (OK!)

Pions:a = 10 fm

L = 1 m = 4.4 fm

Therefore, need b = L/a = 44 cm (OK!)

So the same technique can be used on stars and on RHIC collision fireballs!

November 19, 2003


The Hanbury-Brown-Twiss EffectThe Hanbury-Brown-Twiss Effect

y

X

1

2

Source

For non-interacting identical bosons:

S(x,p)=S(x)S(p)

Coherent interference between incoherent sources!

The “bump” results fromthe Bose-Einstein statistics ofidentical pions (J=0).

Width of the bump in theith momentum direction isproportional to 1/Ri.

November 19, 2003


Bertsch-Pratt Momentum CoordinatesBertsch-Pratt Momentum Coordinates

beam direction

p1 p2

Q T

Q

Q L

beam direction

p2p1

Q T

Q S

Q O

)qqR2qRqRqRexp(1 longout2ol

2long

2long

2side

2side

2out

2out

)q,q,q(C longsideout

)T2

PT1

P(2

1T

K

(long) (out, side)x

November 19, 2003


A Bose-Einstein Correlation “Bump”A Bose-Einstein Correlation “Bump”

This 3D histogram is STARdata that has been corrected forCoulomb repulsion ofidentical pairs andis a projection slice nearqlong=0 .

The central “bump” resultsfrom Bose-Einstein statisticsof identical pions (J=0).

November 19, 2003


+ - + - 0 p p ++ +

0 -

+

-

Sergei's HBT matrix 0

Y1 p

Y1 ? p

Y2

“traditional”HBT axis

STAR HBT Matrix (circa Nov. 2000)

STAR HBT Matrix (circa Nov. 2000)

Year 1

From the beginning - studycorrelations of nonidentical particlesand resonance production

Goal: reconstruct complete picture with full systematics

Year 1 ??

Year 2 AnalysisIn progress

November 19, 2003


STAR HBT Matrix (circa 2003)STAR HBT Matrix (circa 2003)

+ - + - 0 p p ++ +

0 -

+

-

Sergei's HBT matrix 0

Y1 p

Y1 ? p

Y2

“traditional”HBT axis

Analysisin progress

published

3 Correlations (accepted PRL)asHBTPhase space densityCorrelations with CascadesdAu, ppCascades

submittedNot shown:

November 19, 2003


The RHIC HBT PuzzleThe RHIC HBT Puzzle

Part 4Part 4

November 19, 2003


Pre-RHIC HBT PredictionsPre-RHIC HBT Predictions

“Naïve” picture (no space-momentum correlations):

Rout2 = Rside

2+(pair)2

One step further: Hydro calculation of Rischke &

Gyulassy expects Rout/Rside ~ 2->4 @ kt = 350 MeV.

Looking for a “soft spot” Small Rout/Rside only for

TQGP=Tf (unphysical)).

Rout

Rside

November 19, 2003


• p-space observables well-understood within hydrodynamic framework

→ hope of understanding early stage

• x-space observables not well-reproduced• correct dynamical signatures with

incorrect dynamic evolution?

Heinz & Kolb, hep-ph/0204061


November 19, 2003

John G. Cramer21STAR time

dN/dt

PCM & clust. hadronization

NFD

NFD & hadronic TM

PCM & hadronic TM

CYM & LGT

string & hadronic TM

• p-space observables well-understood within hydrodynamic framework

→ hope of understanding early stage

• x-space observables not well-reproduced• correct dynamical signatures with

incorrect dynamic evolution?

• Over-large timescales are modeled?• emission/freezeout duration (RO/RS)• evolution duration (RL)

Heinz & Kolb, hep-ph/0204061


November 19, 2003


RO

(fm

)R

L (f

m)

λ

RS

(fm)

RO / R

S

<kT> GeV/c

centrality

6

6

6

4

4

4

1

1.2

0.8

0.2

0.4

0.6

0.2 0.20.3 0.30.4 0.40.5 0.5

STAR PRELIMINARY

• HBT radii increase with increasing centrality

• HBT radii decrease with kT (flow)

• RO / RS ~ 1 (short emission time) problem persists

HBT at 200 GeVHBT at 200 GeV

November 19, 2003


• HBT radii increase with increasing centrality

• HBT radii decrease with kT (flow)

• RO / RS ~ 1 (short emission time) problem persists

Longitudinal radius

• Modified Sinyukov fit

M. Herrmann and G.F. Bertsch, Phys. Rev. C51 (1995) 328

<tfo>central ≈ 9 fm/c

<tfo>peripheral ≈ 7 fm/c

Tfo = 90MeV/c (spectra)

TmK

TmKmT

tRT

T

TfoL /

/

1

2

HBT at 200 GeVHBT at 200 GeV

RO

(fm

)R

L (f

m)

λ

RS

(fm)

RO / R

S

<kT> GeV/c

centrality

6

6

6

4

4

4

1

1.2

0.8

0.2

0.4

0.6

0.2 0.20.3 0.30.4 0.40.5 0.5

STAR PRELIMINARY

November 19, 2003


HBT Source Radius Excitation Function

HBT Source Radius Excitation Function

Source radii from HBT interferometry do not show a significant increase between CERN energies and RHIC energies.

However, we would still liketo fill the gapwith future RHIC runs.

November 19, 2003


Conclusions from HBT AnalysisConclusions from HBT Analysis

1. The pion-emission source size is smaller than expected, with little growth from a factor of 10 increase in collision energy from the CERN SPS.

2. The time from initial collision to emission is also about the same as observed at the SPS, about 9 fm/c.

3. The emission duration is also very short, at most 1-2 fm/c.

4. These results imply an explosive system with a very hard equation of state.

We were expecting to bring the nuclear liquid to a gentle boil.

Instead, it is exploding in our face!

November 19, 2003


Part 5Part 5

Pion Phase Space Density

and Entropy

Pion Phase Space Density

and Entropy

November 19, 2003


Phase Space Density: Definition & Expectations

Phase Space Density: Definition & Expectations

Phase Space Density - The phase space density f(p,x) plays a fundamental role in quantum statistical mechanics. The local phase space density is the number of pions occupying the phase space cell at (p,x) with 6-dimensional volume p3x3 = h3.

The source-averaged phase space density is f(p)∫[f(p,x)]2 d3x / ∫f(p,x) d3x, i.e., the local phase space density averaged over thef-weighted source volume. Because of Liouville’s Theorem, for free-streaming particles f(p) is a conserved Lorentz scalar.

At RHIC, with about the same HBT source size as at the CERN SPS but with more emitted pions, we expect an increase in the pion phase space density over that observed at the SPS.

November 19, 2003


hep-ph/0212302

Entropy: Calculation & ExpectationsEntropy: Calculation & ExpectationsEntropy – The pion entropy per particle S/N and the total pion entropy at midrapidity dS/dy can be calculated from f(p). The entropy S of a colliding heavy ion system should be produced mainly during the parton phase and should grow only slowly as the system expands and cools.

Entropy is conserved during hydrodynamic expansion and free-streaming. Thus, the entropy of the system after freeze-out should be close to the initial entropy and should provide a critical constraint on the early-stage processes of the system.

nucl-th/0104023 A quark-gluon plasma has a large number of degrees of freedom. It should generate a relatively large entropy density, up to 12 to 16 times larger than that of a hadronic gas.

At RHIC, if a QGP phase grows with centrality we would expect the entropy to grow strongly with increasing centrality and participant number.

Can Entropy provide the QGP “Smoking Gun”??

November 19, 2003


Pion Phase Space Density at Pion Phase Space Density at MidrapidityMidrapidity

Pion Phase Space Density at Pion Phase Space Density at MidrapidityMidrapidity

The source-averaged phase space density f(mT) is the dimensionless number of pions per 6-dimensional phase space cell h3, as averaged over the source. At midrapidity f(mT) is given by the expression:

λ

1

RRR

πλ

ymmπ2

N

E

1)m(

LOS

3

TT

2

πT

)(

c

dd

df

Momentum Spectrum HBT “momentumvolume” Vp

PionPurity

Correction

Jacobianto make ita Lorentz

scalar

Average phasespace density

November 19, 2003


RHIC Collisions as Functions of Centrality

RHIC Collisions as Functions of Centrality

50-80% 30-50% 20-30% 10-20% 5-10% 0-5%

At RHIC we can classifycollision events by impact parameter, based on charged particle production.

Participants

Binary Collisions

Frequency of Charged Particlesproduced in RHIC Au+Au Collisions

of Total

November 19, 2003


0.05 0.1 0.15 0.2 0.25 0.3

150

200

300

500

700

1000

1500

2000

016

Vp

VeG

3 Corrected HBT Momentum Volume

Vp /½

Corrected HBT Momentum Volume Vp /½

LOS

3

p RRR

πλλV

)( c

STAR Preliminary

Central

Peripheral

mT - m (GeV)

0-5%

5-10%

10-20%

20-30%

30-40%

40-50%

50-80%

Centrality

Fits assuming:

Vp ½=A0 mT3

(Sinyukov)

November 19, 2003


0.1 0.2 0.3 0.4 0.5 0.6mT m

5

10

50

100

500

1000

d2 N2m Tmd

Tyd

Global Fit to Pion Momentum Spectrum

Global Fit to Pion Momentum Spectrum

We make a global fit of the uncorrected pion spectrum vs. centrality by:

(1) Assuming that the spectrumhas the form of an effective-TBose-Einstein distribution:

d2N/mTdmTdy=A/[Exp(E/T) –1]

and

(2) Assuming that A and T have aquadratic dependence on thenumber of participants Np:

A(p) = A0+A1Np+A2Np2

T(p) = T0+T1Np+T2Np2

Value ErrorA0 31.1292 14.5507A1 21.9724 0.749688A2 -0.019353 0.003116T0 0.199336 0.002373T1 -9.23515E-06 2.4E-05T2 2.10545E-07 6.99E-08

STAR Preliminary

November 19, 2003


0.1 0.2 0.3 0.4mTm

0.1

0.2

0.3

0.4

f

Interpolated Pion Phase Space Density f at S½ = 130 GeV

Interpolated Pion Phase Space Density f at S½ = 130 GeV

Central

Peripheral

NA49

STAR Preliminary

Note failure of “universal” PSDbetween CERN and RHIC.}

HBT points with interpolated spectra

November 19, 2003


0.05 0.1 0.15 0.2 0.25mTmGeV

0.05

0.1

0.2

0.5

fp

Fits to Interpolated Pion Phase Space Density

Fits to Interpolated Pion Phase Space Density

Central

Peripheral

STAR Preliminary

Warning: PSD in the region measured contributes only about 60% to the average entropy per particle.

HBT points using interpolated spectra fittedwith Blue-Shifted Bose Einstein function

November 19, 2003


fdxdp

fffffLogfdxdp

xpfdxdp

xpdSdxdp

NS

33

49653

612

2133

33

633 )([

),(

),(

Converting Phase Space Density to Entropy per Particle (1)


...)(

)1()1()();,(4

9653

612

21

6

fffffLogf

fLogffLogfdSpxff

Starting from quantum statistical mechanics, we define:

To perform the space integrals, we assume that f(x,p) = f(p) g(x),where g(x) = 23 Exp[x2/2Rx

2y2/2Ry2z2/2Rz

2], i.e., that the source hasa Gaussian shape based on HBT analysis of the system. Further, we make theSinyukov-inspired assumption that the three radii have a momentum dependenceproportional to mT

. Then the space integrals can be performed analytically.This gives the numerator and denominator integrands of the above expressionfactors of RxRyRz = Reff

3mT(For reference, ~½)

An estimate of the average pion entropy per particle S/N can be obtainedfrom a 6-dimensional space-momentum integral over the local phase spacedensity f(x,p):

O(f)

O(f2)

O(f3) O(f4)

f

dS6(Series)/dS6

+0.2%

0.2%

0.1%

0.1%

November 19, 2003




0

31

0

4

22453

3942

2)8(5

2131

33

4

22453

3942

2)8(5

2133

33

633

][

][

),(

),(

fmpdp

fffffLogfmpdp

fmdp

fffffLogfmdp

xpfdxdp

xpdSdxdp

NS

TTT

LogTTT

T

LogT

The entropy per particle S/N then reduces to a momentum integralof the form:

We obtain from the momentum dependence of Vp-1/2 and performthe momentum integrals numerically using momentum-dependent fits to for fits to Vp-1/2 and the spectra.

(6-D)

(3-D)

(1-D)

November 19, 2003


50 100 150 200 250 300 350Npparticipants

3.6

3.8

4

4.2

4.4

4.6

S N

Entropy per Pion from Two Fit MethodsEntropy per Pion from Two Fit Methods

Central

PeripheralSTAR

Preliminary

Green = BSBE2: ~ T

Red = BSBE1: Const

Blue = BSBE3: Odd 7th order Polynomial in T

Black = Combined fits to spectrum and Vp/1/2

November 19, 2003


0 0.5 1 1.5 2 2.5 3Tm

2

4

6

8

10

SN

= 0

= m

Thermal Bose-Einstein Entropy per Particle

Thermal Bose-Einstein Entropy per Particle

1]/)[(

1 where

)]()1()1[(S/N

0

0

TmExpf

fdppm

fLnffLnfdppm

TBE

BETT

BEBEBEBETTT

0. 0.3 0.6 0.90.2 7.37481 5.86225 4.30277 2.431810.4 5.13504 4.33169 3.45065 2.251660.6 4.46843 3.89106 3.23476 2.288370.8 4.16727 3.70431 3.16747 2.369671. 4.00256 3.61107 3.15191 2.458511.2 3.90175 3.56032 3.15728 2.543751.4 3.83522 3.53137 3.17146 2.621951.6 3.78887 3.51456 3.18916 2.692441.8 3.75521 3.50489 3.20786 2.755532. 3.72997 3.49958 3.22638 2.8119

The thermal estimate of the entropy per particle can beobtained by integrating a Bose-Einstein distribution over3D momentum:

/mT/m

Note that the thermal-model entropy per particle usually decreases with increasing temperature T and chemical potential .

November 19, 2003


50 100 150 200 250 300 350Npparticipants3.4

3.6

3.8

4

4.2

4.4

4.6

S N

T90 MeV

T120 MeV

T200 MeV

Landau Limit: m0

BPB

Entropy per Particle S/N with Thermal EstimatesEntropy per Particle S/N with Thermal Estimates

Central

Peripheral STAR Preliminary

Dashed line indicates systematicerror in extracting Vp from HBT.

Dot-dash line shows S/N from BDBE2 fits to f

Solid line and points show S/Nfrom spectrum and Vp/1/2 fits.

For T=110 MeV, S/N impliesa pion chemical potential of=44.4 MeV.

November 19, 2003


50 100 150 200 250 300 350Np

500

1000

1500

2000

2500

Sdyd

Snuc

Total Pion Entropy dS/dyTotal Pion Entropy dS/dy

STAR Preliminary

Dashed line indicates systematicerror in extracting Vp from HBT.

Dot-dash line indicates dS/dy fromBSBEx fits to interpolated <f>.

Solid line is a linear fit through (0,0)with slope = 6.58 entropy unitsper participant

Entropy content ofnucleons + antinucleons

P&P

P&P

Why is dS/dylinear with Np??

November 19, 2003


0 50 100 150 200 250 300 350Npparticipants

20

25

30

35

40

45

Sd ydN p23

Initial collision overlap area is roughlyproportional to Np

2/3

Initial collision entropy is roughlyproportional to freeze-out dS/dy.

Therefore, (dS/dy)/Np2/3

should be proportionalto initial entropydensity, a QGPsignal.

Initial Entropy Density: ~(dS/dy)/Overlap Area

Initial Entropy Density: ~(dS/dy)/Overlap Area

Data indicates that the initialentropy density does grow withcentrality, but not very rapidly.

Solid envelope =Systematic errors in Np

Our QGP “smoking gun” seems to beinhaling the smoke!

STAR Preliminary

November 19, 2003


Conclusions from PSD/Entropy Analysis

Conclusions from PSD/Entropy Analysis

1. The source-averaged pion phase space density f is very high, in the low momentum region roughly 2 that observed at the CERN SPS for Pb+Pb at Snn=17 GeV.

2. The pion entropy per particle S/N is very low, implying a significant pion chemical potential (~44 MeV) at freeze out.

3. The total pion entropy at midrapidity dS/dy grows linearly with initial participant number Np, with a slope of ~6.6 entropy units per participant. (Why?? Is Nature telling us something?)

4. For central collisions at midrapidity, the entropy content of all pions is ~5 greater than that of all nucleons+antinucleons.

5. The initial entropy density increases with centrality, but forms a convex curve that shows no indication of the dramatic increase in entropy density expected with the onset of a quark-gluon plasma.

November 19, 2003


The useful theoretical models that has served us so well at the AGSand SPS for heavy ion studies have now been overloaded with a largevolume of puzzlingnew data from HBTanalysis at RHIC.

Things are a bitup in the air.

We need moretheoretical helpto meet the challengeof understandingwhat is going on inthe RHIC regime.

In any case, thisis a very excitingtime for the STARexperimentalistsworking at RHIC!

Overall ConclusionsOverall Conclusions

November 19, 2003


The

End

Documents

STAR Pion Interferometry and RHIC Physics John G. Cramer Department of Physics University of Washington Seattle, Washington, USA John G. Cramer Department