zbigniew chaj ę cki ohio state university

Z. Ch. - RHIC & AGS Annual Users' Meeting, June 2, 2009 1

Zbigniew ChajęckiOhio State University

Collectivity in p+p Collectivity in p+p collisions?collisions?

Z. Ch. & M. Lisa, PRC 78 064903 (2008)Z. Ch. & M. Lisa, PRC 79 034908 (2009)Z. Ch., Acta Phys.Polon.B 40 1119 (2009) Z. Ch. & M. Lisa, to be published


Outline & MotivationOutline & Motivation common understanding of heavy ion collisions [soft sector]

p+p as a reference to heavy ion collisions

Effect of the phase-space constraints due to energy and momentum conservation

Results from 2-pion correlations in HIC and p+p Femtoscopic correlations

Re-examining multiplicity-evolution of pT spectra, considering evolution of available phase space postulate of unchanging parent distribution

Consistent treatment of the phase-space constraints and bulk in femtoscopy and spectra

Summary


Heavy-ion collisions - A Heavy-ion collisions - A systemsystem

A+A a system


STAR PRL 91 262301 (2003)

R (fm

)

mT (GeV/c2)

Spectra v2

Femtoscopy€

mT ≈ T + mβ flow2

Spectrav2

fast

Femtoscopy : two-pion correlations

slow

Femtoscopy : identical particle correlations

R (fm

)

mT (GeV/c2)

Femtoscopy : non-id particle correlations

K

STAR PRL 91 262301 (2003)

Heavy Ion Collisions : Explosive flow Heavy Ion Collisions : Explosive flow revealed through revealed through specific fingerprints specific fingerprints on soft-sector observableson soft-sector observables


Importance of referenceImportance of reference

?=


p+p as a reference: p+p as a reference: hard hard sectorsector

=

STAR, PRL93 (2004) 252301


p+p as a reference: p+p as a reference: soft sectorsoft sector

= “flow”?

STAR PRL 92 112301 (2004)

p+p

Au+Au

eliptic flow

radial flow


Phase-Space varies with Phase-Space varies with multiplicitymultiplicity

Phase-space constraintsExtreme case, N=3, easily calculable with Dalitz plot

What about the effect for higher number of particles?

Dalitz plot for a three-body final state. (p at 3 GeV), PDG 2008Pn ∝ SnRn

W ( ′1)d3 ′1 ∝ d 3 ′1S ′1( )Rn

Phase-space factor: Hagedorn/FermiPhase-space factor: Hagedorn/Fermi

€

Sn - dynamicsRn - kinematics


Correlations arising (only) from Correlations arising (only) from conservation laws (PS constraints)conservation laws (PS constraints)

€

˜ f (pi) = 2E idN

d3 pi

single-particle “parent” distributionw/o P.S. restriction

%fc (p1,..., pk ) : %f (pi )i=1

k∏( )⋅ d 4 id(i2 −m i

2 )%f(i)i=k+1

N∏( )∫ d 4 ii=1

N

∑ −P⎛⎝⎜

⎞⎠⎟

≅ %f(i)i=1

k∏( ) N

N −k⎛⎝⎜

⎞⎠⎟2

ex −i,m − m( )

i=1

k

∑⎛⎝⎜⎞⎠⎟2

2(N −k)σ m2

m=0

3

∑

⎛

⎝

⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟

k-particle distribution (k<N)

no othercorrelations

what wemeasure

%fc (p1,..., pk ) ≡ %f(i)i=1

k∏( )

with P.S. restriction

CLT approximation works best for N>10 & Ei < 23<E>

“distortion” due to PS constraints–Danielewicz et al, PRC38 120 (1988)–Borghini, Dinh, & Ollitraut PRC62 034902 (2000)–Borghini, Eur. Phys. J. C30:381-385, (2003)–Chajecki & Lisa, PRC 78 064903 (2008), PRC 79 034908 (2009)


N=5

N=40

Z.Ch, M

.Lisa, PR

C 79 034908 (2009)

1-particle PS effect1-particle PS effect

Phase-space effect on kinematic Phase-space effect on kinematic observablesobservables

%fc (pi ) =%f(i)×

×N

N −1⎛⎝⎜

⎞⎠⎟2

ex −1

2(N −1)2T,i

2

T2

+z,i2

z2

+Ei − E( )

2

E2 − E 2

⎛⎝⎜

⎞⎠⎟

⎛

⎝⎜⎜

⎞

⎠⎟⎟

Finite-particle constrains

C(p1, p2 ) ≅1−

1N

2rT ,1 ⋅

rT ,2T2

+z,1 ⋅z,2

z2

+E1 − E( )⋅ E2 − E( )

E2 − E 2

⎛⎝⎜

⎞⎠⎟

NA49 pions Borghini et al, PRC 66 014901 (2002)- also, Danielewicz, PLBB157:146 (1985)


CF (GenBod)

EMCICs

Z. Ch, M. Lisa, PRC 78 064903 (2008)

N. Borghini, PRC75:021904 (2007)


C(p1,..., pk ) ≡%fc(1,..., k)

%fc(1)....%fc(k)

=

NN−k

⎛⎝⎜

⎞⎠⎟2

NN−1

⎛⎝⎜

⎞⎠⎟2k

ex −1

2(N −k)

x,ii=1

k∑( )2

x2 +

y,ii=1

k∑( )2

y2

+z,ii=1

k∑( )2

z2 +

Ei − E( )i=1

k∑( )2

E2 − E 2

⎛

⎝⎜⎜⎜

⎞

⎠⎟⎟⎟i=1

k

∑⎛

⎝

⎜⎜⎜

⎞

⎠

⎟⎟⎟

ex −1

2(N −1)x,i2

x2 +

y,i2

y2

+z,i2

z2 +

Ei − E( )2

E2 − E 2

⎛⎝⎜

⎞⎠⎟

i=1

k

∑⎛

⎝⎜⎜

⎞

⎠⎟⎟


k-particle correlation k-particle correlation functionfunction

€

C(p1,...,pk ) ≡˜ f c(p1,...,pk )

˜ f c(p1)....̃ f c(pk )

=

NN − k ⎛ ⎝ ⎜

⎞ ⎠ ⎟2

NN −1 ⎛ ⎝ ⎜

⎞ ⎠ ⎟2k

exp − 12(N − k)

px,ii=1

k∑ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟2

px2

+py,ii=1

k∑ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟2

py2

+pz,ii=1

k∑ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟2

pz2

+E i − E( )

i=1

k∑ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟2

E 2 − E 2

⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟i=1

k

∑ ⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟

exp − 12(N −1)

px,i2

px2 +

py,i2

py2 +

pz,i2

pz2 +

E i − E( )2

E 2 − E 2

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

i=1

k

∑ ⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

Dependence on “parent” distrib f vanishes,except for energy/momentum means and RMS

2-particle correlation function (1st term in 1/N expansion)

€

C(p1,p2) ≅1− 1N

2r p T,1 ⋅

r p T,2

pT2 +

pz,1 ⋅pz,2

pz2 +

E1 − E( ) ⋅ E 2 − E( )E 2 − E 2

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟


What’s the effect of PSD – nontrivial !What’s the effect of PSD – nontrivial !

• structure not confined to large Q• kinematic cuts have strong effect

event generator (genbod)with only E&M conservation

Genbod N=18 <K>=0.9 GeV; PRF - ||<0.5

C(p1, p2 ) ≅1−

1N

2rT ,1 ⋅

rT ,2T2

+z,1 ⋅z,2

z2

+E1 − E( )⋅ E2 − E( )

E2 − E 2

⎛⎝⎜

⎞⎠⎟

€

Detailed shape depends on :

N, E , E 2 , pT2 , pZ

2


The Complete Experimentalist’s The Complete Experimentalist’s RecipeRecipe

€

C( p1, p2 ) = Norm ⋅ 1+ λ ⋅ Kcoul (Qinv ) 1+ exp −Rout2 Qout

2 − Rside2 Qside

2 − Rlong2 Qlong

2( )( ) −1[ ]{ } ×

1− M1r p 1,T ⋅

r p 2,T{ } − M2 p1,Z ⋅ p2,Z{ } − M3 E1 ⋅E2{ } + M4 E1 + E2{ } −

M4( )2

M3

⎡

⎣

⎢ ⎢

⎤

⎦

⎥ ⎥

or any other parameterization of CF

9 fit parameters

- 4 femtoscopic

- normalization

- 4 EMCICs

Fit this ….

€

M1 = 1N pT

2

M2 = 1N pz

2

€

M3 = 1

N E 2 − E2 ⎛

⎝ ⎜ ⎞ ⎠ ⎟

M4 =E

N E 2 − E2 ⎛

⎝ ⎜ ⎞ ⎠ ⎟


Fits to STAR p+p dataFits to STAR p+p data

kT = [0.15,0.25] GeV/c kT = [0.25,0.35] GeV/c

kT = [0.35,0.45] GeV/c kT = [0.45,0.60] GeV/c

STAR preliminary


Fit results: STAR p+p@200 GeVFit results: STAR p+p@200 GeVST

AR

pre

limin

ary

€

M1 = 1N pT

2= 0.43

M2 = 1N pz

2= 0.22

M3 = 1

N E 2 − E2 ⎛

⎝ ⎜ ⎞ ⎠ ⎟= 1.51

M4 =E

N E 2 − E2 ⎛

⎝ ⎜ ⎞ ⎠ ⎟= 1.02

€

⎫

⎬ ⎪ ⎪

⎭ ⎪ ⎪⇒ E = 0.68 GeV

€

E 2 > pT2 + pz

2

€

⇒ N > 13.6

Five physical variables - four fit parameters

Can we verify whether kinematic variables showing up in fit parameters have physical values?

€

⇒ N > M3

M4

⎛ ⎝ ⎜

⎞ ⎠ ⎟2

1M1

+ 1M2

− 1M3

⎛ ⎝ ⎜

⎞ ⎠ ⎟

€

C( p1, p2 ) = Norm ⋅ 1+ λ ⋅ Kcoul (Qinv ) 1+ exp −Rout2 Qout

2 − Rside2 Qside

2 − Rlong2 Qlong

2( )( ) −1[ ]{ } ×

1− M1r p 1,T ⋅

r p 2,T{ } − M2 p1,Z ⋅ p2,Z{ } − M3 E1 ⋅E2{ } + M4 E1 + E2{ } −

M4( )2

M3

⎡

⎣

⎢ ⎢

⎤

⎦

⎥ ⎥


femtoscopy in p+p @ STAR

DELPHI

Z0 decay @ LEP

m, mT (GeV)

R (fm

)R

Z(fm

)

hep-ph/0108194

π

K

p Λ

1. Heisenberg uncertainty?• e.g. G. Alexander• “plausible” in z-direction• unlikely in transvrse• inconsistent with mult-dep

2. String fragmentation? (Lund)• essentially no quantitative

predictions• pT dependence maybe (??)• mass dependence no

[Andersson, Moriond 2000]

3. Resonance effects?• e.g. Wiedemann & Heinz ‘97• maybe, but will be significantly

different effect than for Au+Au

p+p and A+A measured in same experiment, same acceptance, same techniques

•unique opportunity to compare physics•what causes pT-dependence in p+p?•same cause as in A+A?

4. Flow???• Increasingly suggested in HEP

experiments

HBT+ “conservation”

HBT

Z. Ch., Acta Phys.Polon.B 40 1119 (2009)

mmTT dep. of HBT radii - World Systematcs dep. of HBT radii - World Systematcs


E735 Collaboration, PRD48 1931 (1993)also PLB 2002consistent with an expanding shell model.

NA22 Collaboration Z. Phys. C 71, 405–414 (1996)(hadron-hadron collisions)[based on shape of C(q)…]Our data do not confirm the expectation from the string type model… A good description of our data is, however, achieved in the framework of the hydrodynamical expanding source model.

W. Kittel Acta Phys.Polon. B32 (2001) 3927 [Review article]… and suggests the existence of an important “collective flow”, even in the system of particles produced in e+e− annihilation!

A 1/√m T scaling first observed in heavy-ion collisions is now also observed in Z fragmentation and may suggest a “transverse flow” even there!

OPAL Collaboration, Eur.Phys.J.C52:787-803,2007; arXiv:0708.1122 [hep-ex]

R2tside , R2tout and, less markedly, R2long decrease with increasing kt . The presence of correlations between the particle production points and their momenta is an indication that the pion source is not static, but rather expands during the particle emission process.

RHIC: “comparison machine”Vary size. All else fixed. [acceptance, technique…]• spectra• femtoscopy

compare with a system we “know” is flowing


STAR PRL 91 262301 (2003)

R (fm

)

mT (GeV/c2)

Spectra v2

Femtoscopy

Heavy Ion Collisions : Explosive flow Heavy Ion Collisions : Explosive flow


Apples:apples Apples:apples comparison…comparison…

STAR preliminary

Ratio of AuAu HBT radii by pp

R(pT) taken as strong space-timeevidence of flow in Au+Au• clear, quantitative consistency

predictions of BlastWave

“Identical” signal seen in p+p• cannot be of “identical” origin?

(other than we “know it cannot”...)


Blast-wave fit to spectra:• much less explosive flow in p+p collisions

STAR PRL 92 112301 (2004)

Au+Au 0-5%

Au+Au 60-70%

p+p minbias


1-particle phase-space 1-particle phase-space effect effect

€

˜ f c(pi ) = ˜ f (pi )N

N −1 ⎛ ⎝ ⎜

⎞ ⎠ ⎟2

exp − 12(N −1)

2 pT ,i2

pT2 +

pz ,i2

pz2 +

Ei − E( )2

E2 − E 2

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

“distortion” of single-particle spectra

What if the only difference between p+p and A+A collisions was N?

measured

“matrix element”

€

same ˜ f p( ) , pT2 , E , E2

STAR PRL 92 112301 (2004)

Au+Au 0-5%

Au+Au 60-70%

p+p minbias

STAR PRL 92 112301 (2004)

Then we would measure:

€

˜ f cpp pT ,i( )

˜ f cAA pT ,i( )

=NAA −1( )N pp

N pp −1( )NAA

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

2

exp 12 NAA −1( )

− 12 N pp −1( )

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟2pT ,i

2

pT2

+E i − E( )

2

E 2 − E 2

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟


Multiplicity evolution of spectra - p+p to A+A (soft Multiplicity evolution of spectra - p+p to A+A (soft sector)sector)

N evolution of spectra dominated by PS “distortion”

p+p system samples same parent distribution, but under stronger PS constraints

€

˜ f cpp pT ,i( )

˜ f cAA pT ,i( )

∝ exp 12 NAA −1( )

− 12 N pp −1( )

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟2pT ,i

2

pT2 +

E i − E( )2

E 2 − E 2

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

STAR PRL 92 112301 (2004)


Kinematic scales of “the Kinematic scales of “the system”system”

postulate of same parent consistent with all spectra• magnitude• pT dependence (shape)• mass dependence

Fit results for p+p consistent with expectations from Maxwell-Boltzman equation, Blast-wave, Pythia, …


Consistency check ….Consistency check ….

€

N, E , E 2 , pT2 , pZ

2

Characteristic scales of relevant system in which limited energy-momentum is shared

€

Blastwave, T =100 MeV ρ 0 = 0.9

pT2

π= 0.240 GeV2 pT π

= 0.405 GeV( )

mT π= 0.435 GeV

mT2

π= 0.259 GeV2

€

Maxwell - Boltzmann parent d3Nd3 p

~ e−E /T

non - rel ultra - rel if T = .15 ÷ .35pT

2 2mT 8T 2 0.045 ÷ 0.98 GeV/c( )2

E 2 154 T 2 + m2 12T 2 0.10 ÷1.5 GeV2

E 32 T + m 3T 0.36 −1 GeV


By By popular popular demanddemand

Almost universal “flow” & “temperature”parameters in a BlastWave fit

Apparent changes in β, T with dN/dη caused by finite phase-space effect

p+p

STAR PRL 92 112301 (2004)

Blast-Wave Model: F. Retiere, M. Lisa, PRC70:044907,2004.


Fits to pion CF in p+p by STARFits to pion CF in p+p by STAR

C(p1, p2 ) =a 1+ λ ⋅ Kcouλ(Qinv) 1+ ex −Rout2 Qout

2 −Rσide2 Qσide

2 −Rλong2 Qλong

2( )( )−1⎡⎣ ⎤⎦{ } ×

1−2⋅

r1,T ⋅r2,T

N T2

−1,Z ⋅2,Z

N z2

−E1 − E( )⋅ E2 − E( )

N E2 − E 2( )

⎡

⎣⎢⎢

⎤

⎦⎥⎥

N =14

T2 =0.17 (GeV / c)2

z2 =0.32 (GeV / c)2

E =0.68 GeV

E2 =0.50 GeV 2

STAR Preliminary

kT = [0.35,0.45] GeV/c

STAR preliminary

kT = [0.35,0.45] GeV/c

Use parameters obtained from the fit to STAR femtoscopic correlation function and use them to “correct” spectra

%fc (pi ) =%f(i)

NN −1

⎛⎝⎜

⎞⎠⎟2

ex −1

2(N −1)2T ,i

2

T2

+z,i2

z2

+Ei − E( )

2

E2 − E 2

⎛⎝⎜

⎞⎠⎟

⎛

⎝⎜⎜

⎞

⎠⎟⎟


Combined fit: consistent flow-based Combined fit: consistent flow-based descriptiondescription

Blast-Wave Model: F. Retiere, M. Lisa, PRC70:044907,2004.

€

T =106 ± 3 MeVβ = 0.48 ± 0.03

R = 2.09 ± 0.04 fmτ 0 = 2.25 ± 0.05 fm/cΔτ = 0.1± 0.2 fm/c


Combined fit: consistent flow-based Combined fit: consistent flow-based descriptiondescription

“raw” (ignoring PS effets)

“raw” (ignoring PS effects)

PS effects fixed by correlationsJoint spectra/HBT BW fit

PS effects free adjustedto spectra & fit to spectra

PS effects fixed by correlationsJoint spectra/HBT BW fit

p+p collisions show same radial flow signals as A+A collisions


STAR PRL 91 262301 (2003)

R (fm

)

mT (GeV/c2)

Spectra v2

Femtoscopy

Heavy Ion Collisions vs p+pHeavy Ion Collisions vs p+p


SummarySummary Energy and momentum conservation induces phase-space

constraint that has explicit multiplicity dependence– should not be ignored in (crucial!) N-dependent comparisons– significant effect on 2- (and 3-) particle correlations [c.f. Ollitrault, Borghini, Voloshin…]

– …and single-particle spectra (often neglected because no “red flags”)

Femtoscopy & Spectra– in H.I.C., well understood, detailed fingerprint of flow– RHIC – first opportunity for direct comparison with p+p

– accounting for finite phase-space effects identical flow signals in p+p

?

HBT

exp CF

HBT+ “conservation”

STAR PRL 92 112301 (2004)

STAR Preliminary


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zbigniew chaj ę cki ohio state university

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