XXXV Int. Symposium on Multiparticle Dynamics August 9-15, 2005, Kro měříž, Czech Republic

Michal Šumbera, NPI ASCR, Prague, Czech Republic HEP Seminar, Department of Physics, University of Arizona 10/10/05


XXXV Int. Symposium on Multiparticle Dynamics August 9-15, 2005, Kroměříž, Czech Republic

Nobel laureate 2005Nobel laureate 2005

STAR spokespersonSTAR spokesperson

Tucson physicistsTucson physicists

FemtoscopistsFemtoscopists

StudentsStudents

ParPartticle Correlations icle Correlations and and

Femtoscopy at RHICFemtoscopy at RHIC


Workshop on ParticleCorrelations and Femtoscopy,

August 15-17, 2005Kroměříž, Czech Republic


Relativistic Heavy-Ion Collider Relativistic Heavy-Ion Collider ((RHIC) @ BNL, 11973 NYRHIC) @ BNL, 11973 NY

Long Island

Long Island

Long Island

Long Island

2 concentric rings of 1740 superconducting magnets

2.4 mile (3.8 km) circumference

counter-rotating beams of:

p+p @ √smax= 500 GeV p+A @ √smax= 200 GeVA+A @ √sNN = 200 GeVL = 2·1026 cm-2 s-1

STAR

PHENIX

BRAHMS

2000-2005• p+p (polarized): sNN=200, 410 GeV• d+Au: sNN=200 GeV

• Cu+Cu: sNN= 62, 200 GeV• Au+Au: sNN= 20, 62, 130, 200 GeV


The RHIC ExperimentsThe RHIC Experiments

Ring Counters

Paddle Trigger Counter

Spectrometer

TOF

Octagon+Vertex

BRAHMS

PHOBOS (terminated)

STAR PHENIX


Delivered Luminosity (Physics Weeks)

Summary of RHIC Runs 1-5Summary of RHIC Runs 1-5

2000



1. Quark–gluon plasma and color glass condensate at RHIC? The perspective from the BRAHMS experiment

2. The PHOBOS perspective on discoveries at RHIC

3. Experimental and theoretical challenges in the search for the quark–gluon plasma: The STAR Collaboration’s critical assessment of the evidence from RHIC collisions

4. Formation of dense partonic matter in relativistic nucleus–nucleus collisions at RHIC: Experimental evaluation by the PHENIX Collaboration p. 184–283p. 184–283

p. 102–283p. 102–283

p. 1–27p. 1–27

p. 28–101p. 28–101

Nuclear Physics A 757, issues 1-2 8 August 2005Nuclear Physics A 757, issues 1-2 8 August 2005


Correlation function of two identical pions shows effect of quantum statistics (Bose-Einstein enhancement)when their momentum difference q=p1–p2 is small.

Height of the BE bump equals the fraction (½) of pions participating in the BE enhancement. Its width scales with the emission radius as R-1.

Correlation Correlation ffemtoscopyemtoscopyin a nutshell (1/2)in a nutshell (1/2)

0 50 100 150 200

0

0.2

0.4

0.6

0.8

1

C(q

)-1

q (MeV/c)

1/R

))N(pN(p)p,N(p

)p,C(p21

2121


CorrelationCorrelation femtoscopy femtoscopy in a nutshell (2/2)in a nutshell (2/2)

x1

x2

p1

p2

R

0.0 0.5 1.0 1.5 2.00.0

0.5

1.0

1.5

2.0

~1/R BE

~1/R FD

Maximum/minimum of the CF at small Maximum/minimum of the CF at small q q is is due to quantum interference two particles due to quantum interference two particles emitted from points emitted from points xx11 and and xx22 of the source of the source with space-time extension with space-time extension RR


A brief historyA brief history of CF (1/2)of CF (1/2)

G.Goldhaber, S.Goldhaber, W.Lee and A.Pais (60): • observed ++ , vs + enhancement at small

opening angles

• interpreted it as Bose-Einstein enhancement

Distribution of the pion pair angles Cos for like (a) and unlike (b) pions compared to Fermi statistical model with (solid line) and without (dashed line) the effect of Bose–Einstein correlations.

G.Goldhaber, S.Goldhaber, W.Lee and A.Pais, Phys.Rev 120 (1960) 300


G.I.Kopylov, M.I.Podgoretsky (71-75): •found deep analogy with HBTHBT effect in astronomy •introduced CF= Ncorr /Nuncorr •settled basics of correlation femtoscopy

R.Hanbury-Brown and R.Q.Twiss, Nature 178 (1956) 1046G.I.Kopylov and M.I.Podgoretsky. Sov. J. Nucl. Phys. 15 (1972)219 G.I. Kopylov, Phys. Lett. 50, 472 (1974)

Astronomy: space-time correlation measurementsource momentum picture p= star angular radius

Particle physics: momentum correlation measurement

source space-time picture x

A brief historyA brief history of CF (2/2)of CF (2/2)


(Some) recent reviews(Some) recent reviews1. M.A.Lisa, S.Pratt, R.Soltz,U.Wiedemann: Femtoscopy in Relativistic Heavy

Ion Collisions: Two Decades of Progress, Submitted to Ann.Rev.Nucl.Part.Sci. e-Print Archive: nucl-ex/0505014

2. R.Lednický: Correlation femtoscopy of multiparticle processes, Phys.Atom.Nucl.67(2004)72, e-Print Archive: nucl-th/0305027

3. G.Alexander: Bose–Einstein and Fermi–Dirac interferometry in particle physics, Rept. Prog.Phys. 66(2003)481

4. B.Tomášik and U.Wiedemann: Central and Non-central HBT from AGS to RHIC, e-Print Archive: hep-ph/0210250

5. T. Csorgo: Particle Interferometry from 40 MeV to 40 TeV, Heavy Ion Phys. 15(2002)1

6. R. M. Weiner: Introduction to Bose-Einsterin Correlations and Subatomic

Interferometry, Chichester, UK: Wiley (2000) 244 p. 7. R. M. Weiner: Boson Interferometry in High Energy Physics,

Phys.Rept.327(2000)249

8. U.Wiedemann and U.W. Heinz: Particle Interferometry for Relativistic Heavy-Ion Collisions, Phys. Rept.319(1999)145

LPSW 2005LPSW 2005


Distribution of relative positions of particles with identical velocities and total momentum P

Two-particle correlation Two-particle correlation functionfunction

CP

ab(q )

d6Nab /(dpa3dpb

3)

d3Na /dpa3 d3Nb /dpb

3 ba

ba

ppq

ppP

),(),(

),(),()(

44

44

bbbaaaba

babbbaaabaabP xpsxpsxdxd

xxrxpsxpsxdxdrS

23 ),()()( rqrSrdqC abP

abP

N.B. prime means in the pair CMS frame

: Space-time emission function of particle i

),( iii xps

Two particle wave funcion(QS+FSI)


Source Source imagingimaging

23 ),()()( rqrSrdqC abP

abP

),()()( rqKrSdrqC Geometric information from imaging.

General task:

From data w/ errors, C(q), determine the source S(r ). Requires inversion of the kernel K(q,r).

C:

S:

Any determination of source characteristics from data, unaided by reaction theory, is an imaging.

P.Danilelewicz

WPCF’05

P.Danilelewicz

WPCF’05

Optical recognition: K - blurring function, max entropy method


rderrqqC rqiabP

3)()cos(1)(

CF: No final state interaction CF: No final state interaction casecase

)cos(1),(2

rqrq No FSI :

)cos()(1)( 3 rqrSrdqC abP

abP

baabPba

ba

abP rrrSrdrr

dqdq

qCd

)(

)0( 32

LPSW 2005

LPSW 2005

ji ji

ji

R

rr

abP

erS ,2,2

~)(

Gaussian parametrization:


Rsi

de

R long

Rout

x1

x2

p1

p2

q

qout

qside

qlong

Parametrizing the Parametrizing the source source

Particles on mass shell & azimuthal symmetry 5 variables:

q = (qx , qy , qz) (qout , qside , qlong), pair velocity v = P/P0 ={vx,0,vz} y side

x out transverse pair velocity v

z long beam

Podgoretsky (‘83)-Bertsch-Pratt(‘95) parametrizationPodgoretsky (‘83)-Bertsch-Pratt(‘95) parametrization

cos qx1-½ (qx)2 exp(-Rx2qx

2 –Ry2qy

2 -Rz

2qz2)

Rx2 = R

2 +v22, Ry

2 = R2, Rz

2 = R||2 +v||

22 2

22

1sideside

out

R

v

R

R


Femtoscopy: Femtoscopy: what is actually measured?what is actually measured?

Femtoscopy measures size, shape, and orientation of homogeneity regions

LPSW 2005

LPSW 2005

The correlation is determined by the size of region from which particles with roughly the same velocity are emitted

S. V. Akkelin and Yu. M. Sinyukov Phys. Lett. B356:525–530, 1995

S. V. Akkelin and Yu. M. Sinyukov Phys. Lett. B356:525–530, 1995


Out

Side Long

Example: Example: 3D 3D gaussian gaussian fit to 5% fit to 5% most most central central Au-Au at Au-Au at 200GeV200GeV

kT=(0.15,0.25)GeV/c

M. Bysterský, WPCF 2005



Out

Side Long

kkTT=(0.25,0.35)GeV/c=(0.25,0.35)GeV/cExample: Example: 3D 3D gaussian gaussian fit to 5% fit to 5% most most central central Au-Au at Au-Au at 200GeV200GeV




Out

Side Long





Out

Side Long





kkTT--dependence of dependence of identicalidentical

correlationcorrelation function function• New (2004) high statistics data 11M events, i.e. 6x increase, but still only 10% of full dataset

• Bowler-Sinyukov fit to data

C(q)=(1-λ)+λ Kc(1+exp(- ∑ R

ij2q

iq

j ))

• 3D CF fit using Podgoretsky-Bertsch-Pratt parametrization in LCMS frame without crossterms in azimuthally integrated analyses

• Radii consistent within errors with published STAR PRC71 data

• Difference in in the lowest kT

bin resuts from improved purity of the pion sample

Out Side

Long

M. Bysterský WPCF 2005M. Bysterský WPCF 2005

STAR preliminary STAR preliminary


•x2 expansion in AuAu

•Cu bridges dAu and AuAu

Expansion in Heavy Ion CollisionsExpansion in Heavy Ion Collisions

S. Panitkin, ISMD’05

S. Panitkin, ISMD’05

Rside = R

@sNN=200GeV


•Heavy and light ion data from AGS, SPS, RHIC

•Generalize A1/3 Npart1/3

•Connection with initer-action size?

•~s-ordering in “geometrical” Rlong, Rside

•What is the source of residual s dependence?

Connection with iConnection with initialnitial//finalfinal geometry?geometry?

LPSW 2005LPSW 2005

•Final geometry - particle density (entropy)- drives the radii, not the initial geometry!!

•Breaks down s < 5 GeV


•CuCu bridges multiplicity range between dAu and AuAu

•Radii scale with multiplicity fromperipheral dAu to central AuAu

•Scaling holds with kT

•62 GeV AuAu data follow the sameSystematics

Multiplicity scaling of pion radii Multiplicity scaling of pion radii at RHICat RHIC S. Panitkin,

ISMD’05

S. Panitkin,

ISMD’05STAR preliminary


•AuAu (PbPb)•y 0 & <kT> 170 MeV/c•~10% most central

Energy dependence of Energy dependence of pion source parameterspion source parameters

RHIC HBT Puzzle #0:Smooth energy dependence

•For collectively streaming matter (e.g. with Hubble type flow) the strong x-p correlation makes emission region smaller than total size of the source. (homogeneity region shrinks)Expanding system may develop mechanical instability.


Strong flow predicted by the Strong flow predicted by the hydro and confirmed by all hydro and confirmed by all

expts...expts...LPSW 2005

LPSW 2005

112

22

sideside

out

R

v

R

R

RHIC HBT Puzzle #1:Hydro predicts long emmision time


Comparison to Comparison to hadronic and hadronic and partonic partonic cascade modelscascade models

LPSW 2005

LPSW 2005


Dependence of emission radii Rlong, Rside and ratio Rout/Rside on kT=(pT1+pT2)/2 Full stars – experimental data, dashed line - weighting method, full line – charge reassigning algorithm.

charge reassigning algorithm:

O.V. Utyuzh, G. Wilk, Z. Wlodarczyk, Phys.Lett. B522 (2001) 273O.V. Utyuzh, G. Wilk, Z. Wlodarczyk, Phys.Lett. B522 (2001) 273

Two different implementations of BE in

UrQMD final stateM. Bysterský, thesis 2004

M. Bysterský, thesis 2004

weighting metod:

)cos(1)( rqqC


Beyond the imaging:Beyond the imaging:Trying to understand the Trying to understand the

puzzlepuzzle……Further modification of the apparent source size arises if particles are often rescattered within the source. For such opaque source particle emission points lie within a thin surface layer.

Introduce complex optical potential U:

absorbs pions;

deflects pion trajectories

steals kinetic energy from the emerging pions

J.G.Cramer,G.A.Miller, J. M. S. Wu, J.-H.Yoon, Phys.Rev.Lett.94:102302,2005 J.G.Cramer,G.A.Miller, J. M. S. Wu, J.-H.Yoon, Phys.Rev.Lett.94:102302,2005

… Or just the mean filed only

S. Pratt, nucl-th/0508029 S. Pratt, nucl-th/0508029


Checks with kinetic modelChecks with kinetic model

System cools & expands but initial Boltzmann momentum distribution & interferomety radii are conserved due to developed collective flow

N.S. Amelin, R. Lednický, L. V. Malinina1, T. A. Pocheptsov and Yu.M. Sinyukov, nucl-th/050704

N.S. Amelin, R. Lednický, L. V. Malinina1, T. A. Pocheptsov and Yu.M. Sinyukov, nucl-th/050704

Even for large elastic cross sections (1000mb) leading to huge number of collisions kinetic evolution can be close to free streaming and thus


•observe the source from all angles with respect to reaction plane

•oscillations in the emission radii are expected to show up

Femtoscopy of Femtoscopy of azimuthaly asymetric sourceazimuthaly asymetric source

big RS

small RS

•observe the source from all angles with respect to reaction plane

•expect oscillations in HBT radii (including “new” cross-terms)


Measured Measured finalfinal source source shapeshape

centralcollisions

mid-centralcollisions

peripheralcollisions

STAR, PRL93 012301 (2004)


+ - K+ K- K0S p p

+

-

- K+

K-

- - K0S

p

p

!

R(√SNN, b, Npart, A, B, mT, y, , PID1, PID2)

prelim or final result available

RHIC femtoscopy matrixRHIC femtoscopy matrix


correlations at RHICcorrelations at RHIC

• (as well as other multi strange baryons) may have thermal freeze-out behaviour differing from the other hadrons: e.g. early decoupling?

•Why is elliptic flow comparable to other hadrons?

•Is that all suggesting early partonic collectivity?


Measuring production Measuring production offset by kinematic offset by kinematic

selectionselection

• If space-time ordering, select between two configurations– One particle catching up– Particles moving away from

each other

• Final state interactions yield different correlations for these two configuration – Always for Coulomb – Sometimes for strong

• Interaction time Interaction time shortershorter• Weaker correlationWeaker correlation

A) faster particle flying away

B) faster particle catching up

• Interaction time Interaction time longerlonger• Stronger correlationStronger correlation R.Lednický, V. Lyuboshitz, B. Erazmus,

D. Nouais, Phys.Lett. B 373 (1996) 30.

R.Lednický, V. Lyuboshitz, B. Erazmus, D. Nouais, Phys.Lett. B 373 (1996) 30.

F.Retière

F.Retière


pion

Kaon

proton

Distribution of emissionpoints at a given emission momentum.

Particles are correlated when their velocities are similar.

Keep velocity constant: - Left: vx = 0.73c, vy = 0 - Right: vx = 0.91c, vy = 0

Dashed lines: average emission radius.

<Rx()> < <Rx(K)> < <Rx(p)>

px = 0.15 GeV/c

px = 0.53 GeV/c px = 1.07 GeV/c

px = 2.02 GeV/cpx = 1.01 GeV/c

px = 0.3 GeV/c

Looking at Looking at different different particlesparticles


““Thermal” spectra and Thermal” spectra and flowflow•Final state spectra reflect the

system at thermal freeze-out•Two components

• “temperature” T• collective radial (transverse) flow vT

Stronger is the flow less appropriate are the simple exponential fits:

• Hydrodynamic models • Hydro inspired parameterizations (Blastwave)

mT

1/m

T d

N/d

mT light

heavyT

purely thermalsource

Central AuAu √s = 200 GeV

explosivesource

T,

mT

1/m

T d

N/d

mT light

heavyLow-pt spectra mostly plotted versus:mT = (pT

2+m2)1/2

Hydro (P. Kolb & U. Heinz)

With initial flow kick


mmT

1/m

T d

N/d

mT

(a.u

.)

E.Schnedermann et al., Phys.Rev.C48 (1993) 2462.E.Schnedermann et al., Phys.Rev.C48 (1993) 2462.

Blast wave Blast wave parametrization parametrization of collective flowof collective flow

)0 ,sinh ,(cosh )0,,( rezrtu

tanh 1r )( rfsr

f(r) = (r/Rmax)0.5

+

R

s

Parameterizationof the final state

–Boost invariant longitudinal flow–Transverse flow with azimuthal dependence –Tunable system size, shape and life time

M.A.Lisa&F.Retière, Phys.Rev.C70(2004) 044907 M.A.Lisa&F.Retière, Phys.Rev.C70(2004) 044907


• ,K, p <T> at 200 GeV > 62 GeV Tth at 200 GeV =62 GeV

• <T> at 200 GeV = 62 GeV Tth at 200 GeV >62 GeV

Tth from a Blast-Wave is not same as the Temperature from a Hydro Model.

• Temperature Tth is higher for baryons with higher strange quark content for Blast-wave fits.

• Spectral shapes are different.

Most Central Collisions

0.13

T=100 MeV

T=132 MeV

productionproduction @RHIC @RHIC (1/2)(1/2)

Sevil Salur QM’05Sevil Salur QM’05

Tem

per

atu

re T

th (G

eV)


What does the hydro tell us What does the hydro tell us about the about the production at production at

RHICRHIC

Heavy hadrons, which are particularly sensitive to radial flow effects, require the additional collective “push” created by resonant (quasi)elastic interactions during the fairly long-lived hadronic rescattering stage between Tcr and Td

U. Heinz, J. Phys. G31,S717, 2005U. Heinz, J. Phys. G31,S717, 2005


x

z

y

Elliptic Flow or

Squeeze-out

Radial Flow (Slope systematics)

Reaction plane

Non-central collisions

• radial flow and anisotropic flow

Central collisions• radial flow•“blast wave”

Two kinds of Two kinds of collective transverse flowcollective transverse flow


Phys. Rev. Lett. 92 (2004) 052302 Au+Au √sNN=200 GeV

Au+Au √sNN=62 GeV

STAR Preliminary

productionproduction @RHIC @RHIC (2/2)(2/2)

pT/n (GeV/c)0 1 2

2

2

2

1 2 ( )cos(2 )

1 2 ( )cos(2 )

1 2 cos(2 )

q

T

nq qT

q Tq

q

dNv p

d

v p

pn v

n


Au+Au √sNN=200 GeV


pT= (1 , 3)

GeV/c

pp

Topological reconstruction Topological reconstruction ofof

: y = (-0.5 , 0.5) pT= (0.15 , 0.8) GeV/c


like-sign vs unlike-sign

central vs peripheral

++ & --•consistent•Coulomb-dominated

+- & -+•consistent•Coulomb + strong

Expected centralitydependence • “*” sensitive! *

Wonderful...but there’s more!...

-- correlations in Au+Aucorrelations in Au+Au @ @ 200 GeV200 GeV

P. Chaloupka, QM’05

P. Chaloupka, QM’05*) first observation of * in heavy ion collisions !!!


Spherical harmonics Spherical harmonics decomposition of nondecomposition of non--identical identical

particle correlationsparticle correlations

• A00 - monopole size

• A11 - dipole shift

• A2m – quadrupole

shape

• .....Z. Chajecki , T.D. Gutierrez , M.A. Lisa and M. López-Noriega, nucl-ex/0505009

Z. Chajecki , T.D. Gutierrez , M.A. Lisa and M. López-Noriega, nucl-ex/0505009


Accessing asymmetryAccessing asymmetry

• A11 ≠ 0 in

correlation regions

Asymmetry in the average emission point between

and

• Correct ordering, i.e. in the “right” direction (cf BW)

P. Chaloupka, WPCF’05

P. Chaloupka, WPCF’05


Model comparisonModel comparison

FSI: S.Pratt & S.Petricioni,

Phys.Rev. C68,054901(2003)

Emission points from:

• BW constrained by CF data

• RQMD

• Difference between measured and calculated CF in the * region is under investigation

• Observed shift agrees qualitatively with flow scenario.

l


Early freeze-out ?Early freeze-out ?

• Is this due to early freeze-out? (Could we tell?)

• Competing changes – small overall effect

• Assumed early freeze-out scenario – small effect on CF BW parameters

T[Mev] 103 103 150 0,93 0,93 0,75

R[fm] 10,3 10,3 96,9 6,9 52 2 2

early freeze-out

[fm]fm]


Summary• First five years at RHIC provided us with a

wealth of excellent femtoscopic data

• Some analyses are very challenging experimentally

• Some experimental results are very challenging theoretically

• Stay tuned!


Back up slides


Pij(1) = exp(-½r²q²) vs. wij = 1+cos(r·q)

Problem:Correlation strength λ > 1 seems unphysical

Possible solution:Try different forms of the weigth function Pij

(gauss,exp), which is used to produce correlations.


Pij(2) = exp(-1 r²q²) vs. wij = 1+cos(r·q)


Pij(3) = exp(- 1 |r·q| ) vs. wij = 1+cos(r·q)


Pij(4) = exp(- 2|r·q|) vs. wij = 1+cos(r·q)








• The correlation is determined by the size of the region from which particles with roughly the same velocity are emitted.

For collectively streaming matter the strong correlation between the momenta and the emission points of the particles makes this region smaller than the total source.

• A further modification of the apparent source size arises if particles are often rescattered within the source. For such opaque source particle emission points lie within a thin surface layer.

How big part of the whole source we really measure


Final State InteractionSimilar to Coulomb distortion of -decay Fermi’34:

RL, Lyuboshitz’82 eq. time condition |t*| r*2

e-ikr -k(r) [ e-ikr +f(k)eikr/r ]

eicAc

F=1+ _______ + …kr+krka

Coulomb

s-wavestrong FSIFSI

fcAc(G0+iF0)

}

}

Bohr radius}

Point-likeCoulomb factor

k=|q|/2

CF nnpp

Coulomb only

|1+f/r|2

FSI is sensitive to source size r and scattering amplitude fIt complicates CF analysis but makes possible

Femtoscopy with nonidentical particles K, p, .. &

Study relative space-time asymmetries delays, flow

Study “exotic” scattering , K, KK, , p, , ..Coalescence deuterons, ..

|-k(r)|2


Does entropy drive the strangeness yield?

Is there a universal scaling?

Enhancements are the same or even bigger at RHIC than at SPS !

Yes!!

Npart dNch/dη

Correlated to the entropy of the system!


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XXXV Int. Symposium on Multiparticle Dynamics August 9-15, 2005, Kro měříž, Czech Republic

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