Femtoscopy in STAR vs world systematics

Z. Ch. for STAR - WWND 2009, Big Sky, MT, Feb. 1-8, 2009 1

Femtoscopy in STAR Femtoscopy in STAR vs world systematicsvs world systematics

Zbigniew Chajęcki, OSU

for the Collaboration


OutlineOutline

HBT in Heavy-Ion Collisions at RHIC

Multiplicity as universal scaling

R(mT) - direct probe of flow scenario

Femtoscopy in p+p [reminder]

mT scaling of HBT radii (AA/pp) [reminder]

Energy and Momentum Conservation Induced Correlations in p+p

STAR results from p+p (all fits)

world systematics : Rinv(N,mT), Ro,s,l(mT)

How different is pp from AA at the end?


Heavy ions at RHICHeavy ions at RHIC

Multidimensional analysis at RHIC

R(√SNN, mT, b, Npart, A, B, PID)

... but is there a scaling variable?


Multiplicity scaling of HBT radii at Multiplicity scaling of HBT radii at RHICRHIC

Radii scale with multiplicity

Lisa, Pratt, Soltz, Wiedemann, Ann.Rev.Nucl.Part.Sci. 55 (2005) 357-402


Flow is the most important bulk feature at RHIC mT-dependence of femtoscopy probes flow

the most directly quantitative agreement w/p-only observables

mmTT dependence of pion HBT dependence of pion HBT radiiradii


Femtoscopy - direct evidence of Femtoscopy - direct evidence of flowflow

Spectra

v2

HBT

Flow-dominated “Blast-wave”toy models capture main characteristicse.g. PRC70 044907 (2004)

KR

(fm

)

mT (GeV/c)

STAR PRL 91 262301 (2003)

space-momentum substructure mapped in detail

6


Id-pion correlations in p+pId-pion correlations in p+p

STAR preliminary

mT [GeV/c2] mT [GeV/c2]

p+p and A+A measured in thesame experiment

great opportunity to compare physics

what causes pT-dependence in p+p?

same cause as in A+A?

€

mT = kT2 + mπ

2


Femtoscopy in pp vs heavy Femtoscopy in pp vs heavy ionsions

pp, dAu, CuCu - STAR preliminary

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

Scary coincidence or something deeper?


Z.Ch., Gutierrez, Lisa, Lopez-Noriega, [nucl-ex/0505009]

Pratt, Danielewicz [nucl-th/0501003]

Non-femto correlations / SH Non-femto correlations / SH representationrepresentation

d+Au: peripheral collisions

STAR preliminary

∑→→ ΔΔ

=binsall

iiiiimlml QCYQA

.

,cos

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

|)(| φθφθπ

φθ

STAR preliminary


Decomposition of CF onto Spherical Decomposition of CF onto Spherical HarmonicsHarmonics

Au+Au: central collisions

C(Qout)

C(Qside)

C(Qlong)

∑→→ ΔΔ

=binsall

iiiiimlml QCYQA

.

,cos

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

|)(| φθφθπ

φθ

Z.Ch., Gutierrez, Lisa, Lopez-Noriega, [nucl-ex/0505009]

Pratt, Danielewicz [nucl-th/0501003]

Qx<0.03 GeV/c


Non-femtoscopic correlations in Non-femtoscopic correlations in STARSTAR

Baseline problem is increasing

with decreasing multiplicity

STAR preliminary

N-dep. of non-femtoscopic correlations in p+p

STAR preliminary


EMCICs in other experimentsEMCICs in other experiments

CLEO PRD32 (1985) 2294

NA22, Z. Phys. C71 (1996) 405

Qx<0.04 GeV/cOPAL, Eur. Phys. J. C52 (2007) 787-803

Qx<0.2 GeV/cNA23, Z. Phys. C43 (1989) 341

E766, PRD 49 (1994) 4373M

ultip

licity

incr

ease

s


€

C(qo,qs,ql ) = C femto(qo,qs,ql ) ⋅F(qo,qs,ql )

€

F(qo,qs,ql ) = 1+ δo qo + δs qs + δl ql

€

F(qo,qs,ql ) = 1+ δoqo + δsqs + δlql

• MC simulations

• ‘ad-hoc’ parameterizations

• OPAL, NA22, …

Common approaches to „remove” Common approaches to „remove” non-femtoscopic correlationsnon-femtoscopic correlations

• An alternative explanation:Energy and Momentum Conservation Induced Correlations, Z.Ch. and Mike Lisa [PRC 78 (2008) 064903, ArXiv:0803.022]

• “zeta-beta” fit by STAR [parameterization of non-femtoscopic correlations in Alm’s]

€

C( p1, p2 ) ≅ C femto p1, p2( ) 1−1

N2

r p T ,1 ⋅

r p T,2

pT2

+pz,1 ⋅ pz,2

pz2

+E1 − E( ) ⋅ E2 − E( )

E 2 − E2

⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟

⎡

⎣

⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥

|Q|

|Q|

|Q|


k-particle distributions w/ phase-space k-particle distributions w/ phase-space constraintsconstraints

€

˜ f ( pi) = 2E i f ( pi) = 2E i

dN

d3 pi

single-particle distributionw/o P.S. restriction

€

˜ f c(p1,...,pk ) ≡ ˜ f (pi)i=1

k

∏ ⎛ ⎝ ⎜ ⎞

⎠ ⎟⋅

d3pi

2E i

˜ f (pi)i= k +1

N

∏ ⎛

⎝ ⎜

⎞

⎠ ⎟∫ δ 4 pi

i=1

N

∑ − P ⎛

⎝ ⎜

⎞

⎠ ⎟

d3pi

2E i

˜ f (pi)i=1

N

∏ ⎛

⎝ ⎜

⎞

⎠ ⎟∫ δ 4 pi

i=1

N

∑ − P ⎛

⎝ ⎜

⎞

⎠ ⎟

= ˜ f (pi)i=1

k

∏ ⎛ ⎝ ⎜ ⎞

⎠ ⎟⋅

d4piδ(pi2 − mi

2)˜ f (pi)i= k +1

N

∏ ⎛ ⎝ ⎜ ⎞

⎠ ⎟∫ δ 4 pi

i=1

N

∑ − P ⎛

⎝ ⎜

⎞

⎠ ⎟

d4piδ(pi2 − mi

2)˜ f (pi)i=1

N

∏ ⎛ ⎝ ⎜ ⎞

⎠ ⎟∫ δ 4 pi

i=1

N

∑ − P ⎛

⎝ ⎜

⎞

⎠ ⎟

k-particle distribution (k<N) with P.S. restriction

observed

P - total 4-momentum


k-particle distributionk-particle distribution

€

˜ f c(p1,...,pk ) = ˜ f (pi)i=1

k

∏ ⎛ ⎝ ⎜ ⎞

⎠ ⎟ N

N − k

⎛

⎝ ⎜

⎞

⎠ ⎟2

exp −

pi,μ − pμ( )i=1

k

∑ ⎛

⎝ ⎜

⎞

⎠ ⎟

2

2(N − k)σ μ2

μ = 0

3

∑

⎛

⎝

⎜ ⎜ ⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟ ⎟ ⎟

where

σ μ2 = pμ

2 − pμ

2

pμ = 0 for μ =1,2,3

k-particle distribution in N-particle system

€

pμ2 ≡ d3p ⋅pμ

2 ⋅ ˜ f p( )unmeasuredparent distrib

{∫ ≠ d3p ⋅pμ2 ⋅ ˜ f c p( )

measured{∫N.B.

relevant later

–Danielewicz et al, PRC38 120 (1988)–Borghini, Dinh, & Ollitraut PRC62 034902 (2000)–Borghini Eur. Phys. J. C30:381-385, (2003)–Chajecki & Lisa, PRC78 (2008) 064903 arXiv:0803.0022

* “large”: N > ~10


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− M1

r 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 =1

N pT2

M2 =1

N pz2

€

M3 =1

N E 2 − E2 ⎛

⎝ ⎜

⎞ ⎠ ⎟

M4 =E

N E 2 − E2 ⎛

⎝ ⎜

⎞ ⎠ ⎟


EMCIC fit to STAR p+p dataEMCIC fit to STAR p+p data

STAR preliminary

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


Fit results: EMCIC parametersFit results: EMCIC parametersS

TA

R p

relim

inar

y

€

M1 =1

N pT2

= 0.43

M2 =1

N pz2

= 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

⎛

⎝ ⎜

⎞

⎠ ⎟

21

M1

+1

M2

−1

M3

⎛

⎝ ⎜

⎞

⎠ ⎟

€

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

2 − Rside2 Qside

2 − Rlong2 Qlong

2( )( ) −1[ ]{ } ×

1− M1

r p 1,T ⋅

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

M4( )2

M3

⎡

⎣

⎢ ⎢

⎤

⎦

⎥ ⎥


Various fits to STAR p+p dataVarious fits to STAR p+p data

STAR preliminary

STAR preliminary


mmTT scaling of HBT radii scaling of HBT radii

Various fits give different radii but mT scaling of HBT radii still holds

STAR preliminary


Multiplicity dependence in p+pMultiplicity dependence in p+p

200 GeV

Rin

v [

fm]

STAR preliminary


p+p vs heavy ions - R(N,mp+p vs heavy ions - R(N,mTT))STAR preliminary

Similar mT and multiplicity dependence of HBT radii in p+p and heavy ions in STAR

Is STAR p+p unique? Let’s look at world’s results on HBT in elementary particle collisions …

Z. Ch. for STAR - WWND 2009, Big Sky, MT, Feb. 1-8, 2009 23 Z.Ch. arXiv:0901.4078 [nucl-ex]

Femtoscopy in small systemsFemtoscopy in small systemsSystem √s [GeV] Facility Experiment

p-p 1.9 LEAR CPLEAR

1.9 CERN ABBCCLVW

7.2 AGS E766

17 SPS NA49 -prelim

26 SPS NA23

27.4 SPS NA27

31-62 ISR AFS

44,62 ISR ABCDHW

200 SPS NA5

200 RHIC STAR-prelim

p-p 53 ISR AFS

200 SPS NA5

200-900 SPS UA1

1800 Tevatron E735

- 126 ISR AFS

h-p 5.6 CERN ABBCCLVW

21.7 SPS EHS/NA22

System √s[GeV] Facility Experiment

e+e- 3-7,29 SLAC Mark-II

10 CESR CLEO

29 SLAC TPC

29-37 PETRA TASSO

58 TRISTAN AMY

91 LEP OPAL

91 LEP L3

91 LEP DELPHI

91 LEP ALEPH

e-p 300 HERA ZEUS

300 HERA H1

-p 23 CERN EMC-NA9

-N 30 Tevatron E665

-N >10 BBNC

R ≈ 0.5 - 1.5 fm


My first impression My first impression

€

C = 1+ λ exp −Rinv2 Qinv

2( )

€

C = 1+ λ exp −RG2 QG

2 + Q02τ 2

( )

€

C = 1+ λ2J1 qT RB( )

qT RB

⎡

⎣ ⎢ ⎢

⎤

⎦ ⎥ ⎥

2

1+ qocτ( )−1

€


2( )[ ] 1+ δ ⋅Qinv( )

€


2( )[ ] 1+ δ ⋅Qinv

2( )

€


2( )

€

C = 1+ λ2J1 qT RB( )

qT RB

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

2 ⎡

⎣

⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥1+ δB ⋅qT( )

€

C = 1+ λ exp −Re Qinv( )

€

C = 1+ λ1 exp −R12Q2

( ) + λ2 exp −R22Q2

( )

€


2( )[ ] 1+ ε ⋅Qinv + δ ⋅Qinv

2( )

€

C = 1+ λ2J1 qT RB( )

qT RB

⎡

⎣ ⎢ ⎢

⎤

⎦ ⎥ ⎥

2

1+ qocτ( )2 ⎛

⎝ ⎜

⎞ ⎠ ⎟−1

€


2( )[ ] 1+ δ ⋅Qinv

2( )

−1

€

C = 1+ λ2J1 qT RB( )

qT RB

⎡

⎣ ⎢ ⎢

⎤

⎦ ⎥ ⎥

2

1+ qLcτ( )−1

Can we do a direct comparison between experiments?


Parameterizations of 1D CF used in Parameterizations of 1D CF used in comparision b/w experimentscomparision b/w experiments

€


2( )

€


2 + Q02τ 2

( )

€

C = 1+ λ2J1 qT RB( )

qT RB

⎡

⎣ ⎢ ⎢

⎤

⎦ ⎥ ⎥

2

1+ qocτ( )−1

€

⎫

⎬

⎪ ⎪ ⎪

⎭

⎪ ⎪ ⎪

RB≈2·RG


R(N

) -

worl

d

R(N

) -

worl

d

syste

mati

cs

syste

mati

cs

€

s > 40GeV

R(N,<mT>)

- no point to compare the magnitude of the HBT radii between experiments since almost each experiment has different <pT>; e.g. <pT>(E735) > <pT>(STAR) -look for trends, instead!

STAR preliminary


1D R(p1D R(pTT))

*

**

€

pT = 2 / 3 ⋅r p

STAR preliminary


3D R(m3D R(mTT))

€

*RT ≈ RO ≈ RS

Leptonic results included!

STAR preliminary


• EMCICs seen in small systems• Femtoscopy similar in p+p as in Au+Au @ STAR

• “World results” show both pT and N dependence!

•Same physics in p+p as in Au+Au and the only difference due to phase-space effects?possibilities:

1.HBT signals are insensitive to underlying physics (flow etc)

2.they are sensitive & the very different physics of A+A and p+p look coincidentally identical

3.they are sensitive, and driving physics is the same

SummarySummary


RRinvinv(N,√s) - world systematics(N,√s) - world systematics7.21 GeV 21.7 GeV 27.4 GeV

1800 GeV31-62 GeVSTAR preliminary

200 GeV


RRGG/R/RBB(N, √s) - world systematics(N, √s) - world systematics21.7 GeV

1800 GeV200-900 GeV200 GeV

53-126 GeV

STAR preliminary

UA1

Femtoscopy in STAR vs world systematics

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