multi-hadron correlations and the space-time structure of (heavy ion) collisions

mike lisa - University of Rochester nuclear seminar - 4oct2005 1

Multi-hadron correlations and the space-time structure of (heavy ion) collisions

Mike Lisa

Ohio State University

Featuring Work of:Zbigniew Chajeçki, Mercedes López-Noriega, Dan Magestro, Randy Wells


Outline

• R.H.I.C. / RHIC - what and wherefore?

• geometry and bulk physics in p-space - brief

• ... & in x-space: pion femtoscopy at RHIC

• Au+Au

• d+Au , p+p

• new puzzles, new techniques, global conservation laws

• Summary


• Vary signal ()• constrain multi-dimensional models• requires flexible detectors, broad approach

• Vary colliding system• does physics change?• requires dedicated program

• Vary kinematic variables• dynamics and different regimes• requires large acceptance

• Vary particle type• consistent picture?• unique probe of dynamical structure• requires good particle identification & acceptance

(√SNN, b, Npart, A, B, mT, y, , PID)

mass

|b|

pT


RHIC BRAHMSPHOBOS

PHENIXSTAR

AGS

TANDEMS

1 km

v = 0.99995c = 186,000 miles/sec

Possibilities in a dedicated program: 5 years @RHIC

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

Also: p+p @ 62.4 & 200 GeV

Gunther Roland, QM05





Also: p+p @ 62.4 & 200 GeV

Gunther Roland, QM05


RHIC BRAHMSPHOBOS

PHENIXSTAR

AGS

TANDEMS

STAR ~600 Collaborators



The STAR Experiment

STAR: Solenoidal Tracker at RHIC

multipurpose detector system for hadronic measurements

• large coverage (geometrical acceptance)• tracking of charged particles in high multiplicity environment• measure correlations of observables• study of hard processes (jet physics)

Solenoidal Tracker At RHIC

goal: track “all” charged hadrons (bags of quarks) emitted in each collision


Operation of a Time Projection Chamber

SCA/ADCDAQ

Copper pads ~ 1cm2

Amplifying and digitizing electronics connected to each pad

Anode wires with +HVsitting ~5 mm above pads

Charged particle fliesthru TPC gas…

..generating a clusterof liberated electrons

Electricfield

“Avalanche” as electronsapproach anode wire...

..capacitively inducinga signal on nearby pads... ..which is amplified, digitized, and recorded for later analysis

V

t AD

Cbucket #


One collision seen by STAR TPC

Momentum determined by trackcurvature in magnetic field…

…and by direction relative to beam


Generating a “deconfined” (?) state

Nuclear Matter(confined)

Hadronic Matter(confined)

Quark Gluon Plasmadeconfined !

“Present” understanding of Quantum Chromodynamics (QCD)• heating• compression deconfined color matter !


Expectations from Lattice QCD

/T4 ~ # degrees of freedom

confined:few d.o.f.

deconfined:many d.o.f.


baryon densityvacuum

Te

mp

era

ture

Neutron stars

Early universe

nucleinucleon gas

hadron gascolour

superconductor

quark-gluon plasmaTc

0

critical point ?

CFL

The phase diagram of QCD


baryon densityvacuum

Te

mp

era

ture

Neutron stars

Early universe

nucleinucleon gas

hadron gascolour

superconductor

quark-gluon plasmaTc

0

critical point ?

CFL

The phase diagram of QCD

?

Au+Au

99.5%

• understanding a theory or

phenomenon (superconductivity...)

focus on phase transitions

• RHIC studies:

partonic condensed matter physics

• the crucial feature of QCD (theory):

long-range behaviour

• confinement, etc:

soft-sector crucial


Spacetime - the defining aspect of RHI physics

• Non-trivial space-time - the hallmark of rhic• Initial state: dominates further dynamics• Intermediate state: impt element in exciting signals• Final state:

• Geometric structural scale is THE defining feature of QGP

STAR, PRC66 (2002) 034904 STAR, PRL93 (2004) 252301


Spacetime - the defining aspect of RHI physics

• Non-trivial space-time - the hallmark of rhic• Initial state: dominates further dynamics• Intermediate state: impt element in exciting signals• Final state:

• Geometric structural scale is THE defining feature of QGP

• Temporal scale sensitive to deconfinement transition (?)



Ann.Rev.Nucl.Part.Sci. 46 (1996) 71


Is it bulk? Is it a “system?”

br

1) Superposition of independent p+p:momenta pointed at randomrelative to reaction plane



br

1) Superposition of independent p+p:

2) Evolution as a bulk system

momenta pointed at randomrelative to reaction plane

highdensity / pressure

at center

“zero” pressurein surrounding vacuum

Pressure gradients (larger in-plane) push bulk “out” “flow”

more, faster particles seen in-plane



1) Superposition of independent p+p:

2) Evolution as a bulk system

momenta pointed at randomrelative to reaction plane

Pressure gradients (larger in-plane) push bulk “out” “flow”

more, faster particles seen in-plane

N

-RP (rad)0 /2 /4 3/4

N

-RP (rad)0 /2 /4 3/4


Azimuthal distributions at RHIC

STAR, PRL90 032301 (2003)

b ≈ 4 fm

“central” collisions

b ≈ 6.5 fm

midcentral collisions


Azimuthal distributions at RHIC

STAR, PRL90 032301 (2003)

b ≈ 4 fmb ≈ 6.5 fmb ≈ 10 fm

peripheral collisions


Elliptic flow – collectivity& sensitivity to early system

STAR, PRL90 032301 (2003)

“v2”

“Elliptic flow”

• evidence ofcollective motion

• quantified by v2

• geometrical anisotropy momentum anisotropy

• sensitive to early pressure

• evidence for• early thermalization

• QGP in early stage

Hydrodynamiccalculation ofsystem evolution


Perfect...?


v2 - huge systematics...

Art’s talk. Compiled byA. Wetzler (2005)

6 decades of E/A(2 decades of sNN)Gyulassy 1995

Just oneevent!

Finally, weunderstand it!


It starts... ideal hydro: sharp 1st-order rather than lattice EOS ?

P. Houvinen, nucl-th/0505036

Also: Hirano, Gyulassy...


More direct connection to geometric substructure

• Two-particle correlation functions probe femtoscopic scales

• “HBT” etc.


222111 p)xr(i22

p)xr(i11T e)p,x(Ue)p,x(U

rrrrrr rrrr ⋅−⋅−=ψ

probing source geometry through interferometry

12 ppqrrr −=

2

21

2121 )q(~1

)p(P)p(P)p,p(P

)p,p(C +== C (Qinv)

Qinv (GeV/c)

1

2

0.05 0.10

Width ~ 1/R

Measurable! F.T. of pion source

( ))xx(iq2

*21

*1T

*T

21e1UUUU −⋅+⋅⋅=ψψ

Creation probability (x,p) = U*U5 fm

1 m source(x)

r1

r2

x1

x2

{2

1

}e)p,x(Ue)p,x(U 212121 p)xr(i21

p)xr(i12

rrrrrr rrrr ⋅−⋅−+

p1

p2

The Bottom line…if a pion is emitted, it is more likely to emit another

pion with very similar momentum if the source is small

experimentally measuring this enhanced probability: quite challenging


Correlation functions for different colliding systems

C2(

Qin

v)

Qinv (GeV/c)

STAR preliminary p+pR ~ 1 fm

d+Au

Au+AuR ~ 6 fm

Different colliding systems studied at RHIC

First opportunity to directly compare AA, pp, (&pA)


beam directi

on

More detailed geometry

Relative momentum between pions is a vector can extract 3D shape information

1 2q p p= −r r r

p2

p1

q

12Kpp=+rrrR long

RsideRout

Rlong – along beam direction

Rout – along “line of sight”

Rside – “line of sight”


• “observe” the source from all angles relative to the reaction plane

• expect oscillations in radii for non-round sources

big RSIDE

small RSIDE

Source shapeR

SID

E

-RP (rad)0 /2 /4 3/4

reaction plane

6Li released from an asymmetric trapO’Hara, et al, Science 298 2179 (2002)


STAR, PRL93 012301 (2004)

Measured final source shape

centralcollisions

mid-centralcollisions

peripheralcollisions

Expected evolution:

initi

al= fin

al

Bulk shape evolution


Disintegration timescale

Relative momentum between pions is a vector can extract 3D shape information

1 2q p p= −r r r

p2

p1

q

12Kpp=+rrr

Rout

Rlong – along beam direction

Rout – along “line of sight”

Rside – “line of sight”

Rside

increases with emission timescale

OUT

SIDE

R

R↔ τ


Disintegration timescale - expectation

3D 1-fluid Hydrodynamics Rischke & Gyulassy, NPA 608, 479 (1996)

withtransition

withtransition

“” “”

Long-standing favorite signature of QGP:

• increase in τ, ROUT/RSIDE due to deconfinement confinement transition

• expected to “turn on” as QGP energy threshold is reached


N(τ)

Heinz & Kolb, hep-ph/0204061

Hirano ‘02

HBT puzzle(s)


Why do the radii fall with increasing momentum ??


It’s collective flow !!

Direct geometrical/dynamical evidencefor bulk behaviour

Amount of flow consistent with p-space

Why do the radii fall with increasing momentum ??


Flow-dominated model w/ “hand-tuned” short timescales

• Blast-wave model (latest in long series) reproducesp- and x-space

• Also non-id, asHBT...

F. Retiere & MAL, PRC 70 (2004)

F. Retiere, QM04


Bulk size evolution - collisions at 200 GeV

• Au+Au reaction zone:two-fold expansion

• Preliminary Cu+Cu, d+Au, p+p:smooth interpolation

• central Cu+Cu = periph Au+Au

• Little expansion for small system• shorter timescales

or...• less bulk collectivity...?


femtoscopy in p+p @ STAR

DELPHI

Z0 decay @ LEP

m, mT (GeV)

R (

fm)

R Z

(fm

)

hep-ph/0108194

K

p

STAR preliminary

mT (GeV) mT (GeV)

1. Heisenberg uncertainty?

• e.g. G. Alexander• “plausible” in z-direction• unlikely in transvrse

2. String fragmentation? (Lund)

• pT dependence maybe (??)

• mass dependence probably no

[Andersson, Moriond 2000]

3. Resonance effects?

• e.g. Wiedemann & Heinz ‘97

• maybe, but presumably significantly different effect than for Au+Au

• under investigation

Zbigniew Chajecki QM05

p+p and A+A measured in sameexperiment• great opportunity to compare physics• what causes pT-dep in p+p?• same cause as in A+A?


femtoscopy in p+p @ STAR

DELPHI

Z0 decay @ LEP

m, mT (GeV)

R (

fm)

R Z

(fm

)

hep-ph/0108194

K

p

STAR preliminary

mT (GeV) mT (GeV)

1. Heisenberg uncertainty?

2. String fragmentation? (Lund)

3. Resonance effects?

Zbigniew Chajecki QM05

p+p and A+A measured in sameexperiment• great opportunity to compare physics• what causes pT-dependence in p+p?• same cause as in A+A?

d+Au : Rlong doesn’t change with centrality

flow not expected in such a small system as p+p

e.g. Shuryak: hep-ph/0405066

Csorgo et al.: Buda-Lund treatment of p+p collision as bulk system(w/ temperature gradients)hep-ph/0406042

ROUTRSIDE RLONG

mT-m (GeV)

1/(2m

T)d

2n

/(d

mTd

y)

K

p

mT (GeV)

4. Bulk system („hydro”) in pp?


Surprising („puzzling”) scaling

first-ever pp/AA comparison yields a surprise!

similar underlying physics?

HBT radii scale with pp

Scary coincidence or something deeper?

pp, dAu, CuCu - STAR preliminary

Ratio of (AuAu, CuCu, dAu) HBT radii by pp


• pp appears to be blasting system (?!)

• AA ≠(pp)• would mean local x-p correlations

(giving identical p-space...)

• More like pp = “little AA” !!

What the “coincidence” does NOT mean


Don’t forget where the “radii” come from...

long-range correlations for small systems


• Usual 1D out-side-long “Cartesian projections”

• limited view of data• ~set of zero measure of 3D CF

• Fit-violating trends may be hidden

• Salient geometrical effects non-trivially convoluted

• acceptance-dependent (unlike 3D CF)

1D projections: a limited view

“Gaussian fit”(remember: notGaussian CF)

out

side long

STAR PRC71 044906 (2005)

Harmonic Decomposition Analysis• exploits full symmetry of q-space

• explicit isolation of femtoscopic(& non-femtoscopic) effects

• full 3D CF seen clearly in few plots

• acceptance-robust (*)

• Cartesian HD Danielewicz & Pratt nucl-th/0501003nucl-th/0501003

• Spherical HD Chajecki,Gutierrez,MAL,Lopez nucl-ex/0505009nucl-ex/0505009

Michael Lisa:“Salient geometrical...” bullet just means: if I want to know “Rlong” or so, I *mostly* just look at width of long projection, but there are also acceptance effects

Michael Lisa:“Salient geometrical...” bullet just means: if I want to know “Rlong” or so, I *mostly* just look at width of long projection, but there are also acceptance effects


Spherical harmonic decomposition of CFSpherical harmonic decomposition of CF

∑→→ ΔΔ

=binsall

iiiiimlml QCYQA

.

,

cos

, ),cos|,(|),(|)(| φθφθπ

φθ

4QOUT

QSIDE

QLONG Q

• Cartesian-space (out-side-long) naturally encodes physics, but is “inefficient” representation

• Harmonic Moments -- 1::1 connection to source geometry [Danielewicz,Pratt: nucl-th/0501003]

• ~immune to acceptance

• full information content at a glance[thanks to symmetries]

OUT

SIDE

TOT

LONG

LONGSIDEOUT

Q

Q

Q

Q

QQQQ

arctan

)cos(

222

=

=

++=

φ

Chajecki., Gutierrez, MAL, Lopez-Noriega, nucl-ex/0505009


“Mental calibration” - a Gaussian CF

Simple, Gaussian source calculations

~acceptance freeRL < RT

RL > RT

RO < RS

RO > RS

• Full 3D structure

• (high-L (fine structure) coefficients drop off)

• Different geometrical aspects separate &

use “all” relevant information in the CF

• AL≠0 vanishes in non-femtoscopic region

Chajecki., Gutierrez, MAL, Lopez-Noriega, nucl-ex/0505009


STAR preliminary

A00

A20

A22

SH Moments

STAR Central Au+Au collisions -- Spherical HDSTAR Central Au+Au collisions -- Spherical HD

C(Qout)

C(Qside)

C(Qlong)

1D o-s-l projections

∑→→ ΔΔ

=binsall

iiiiimlml QCYQA

.

,cos

, ),cos|,(|),(4

|)(| φθφθπφθ

Chajecki., Gutierrez, MALLopez-Noriega, nucl-ex/0505009


Baseline problems with smallest systemsBaseline problems with smallest systems

STAR preliminary d+Au peripheral collisions

Gaussian fit

ad hoc, but try it...



NA22 fit

Try NA22 empirical formTry NA22 empirical form

NA22 fit

data

Spherical harmonics

L =1M=0

L =2M=0

L =1M=1

L =2M=2


““account for” constant offset in L=2 account for” constant offset in L=2 componentscomponents


Gaussian fit

|Q| |Q|

|Q|

A02

A22

A00

Gaussian

+ constant A02, A2

2

also ad-hoc, but withcorrect symmetries, “simple” Q-dep


With L=2 shifts, message remains

Ratio of (AuAu, CuCu, dAu) HBT radii by pp

Fit w/o baseline parameterization NEW fit w/ baseline parameterization

STAR preliminary

• Ad hoc formulation not satisfying...

• Detector-induced? No.

• Potential physical non-femtoscopic effects at low multiplicity• jet-induced? Studies so far: no• global conservation laws...?


A00

A20

A22

EPOS v1.4 (Nexus++)K. Werner

(Gaussian HBT only)

Conserves momentum...... somehow

Long-range correlationnot reproduced


HEP’s secret weapon: GENBOD (CERNLIB F. James 1968)

A. Stavinskiy, WPCF Aug ‘05

3He(e, +-)X

Phasespace weightingfactor - modified by global conservation laws

Unknown (?) in RHI circles !


GenBod...Only p-conservation

A00 A20

A22

Phasespace distortion

calculation

(Gaussian HBT only)

Very promising !!


Summary• Extracting subtle signals at RHIC

• dedicated, systematic, broad program• comparison to “elementary” p+p crucial

• understanding source of any differences also crucial (e.g. v2 in pp?)

• Bulk, collective physics• crucial for QGP study• well-established at RHIC: p- and x-space• really understood at RHIC? (coffee cup time?)• AA is “bulk” : AA ≠ (pp) .... but... AA = K(pp) ? [ pp = AA/K ?]

• pp collisions at RHIC• first direct comparison HEP with RHI• x-p correlations indistinguishable from AA - coincidence or deep?• long-range correlations important

• useful harmonic analysis of CF developed

• accounting for non-femtoscopic correlations - on the way...


THEEND


pp (non?-)flow

non-flow (?)

flow

“v2”


The phase diagram of water

Analogous graphs• superfluids• superconductors• metal/insulator• …

multi-hadron correlations and the space-time structure of (heavy ion) collisions

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