femtoscopy in star vs world systematics
DESCRIPTION
Femtoscopy in STAR vs world systematics. Zbigniew Chaj ę cki, OSU for the Collaboration. Outline. HBT in Heavy-Ion Collisions at RHIC Multiplicity as universal scaling R(m T ) - direct probe of flow scenario Femtoscopy in p+p [reminder] - PowerPoint PPT PresentationTRANSCRIPT
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
Z. Ch. for STAR - WWND 2009, Big Sky, MT, Feb. 1-8, 2009 2
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?
Z. Ch. for STAR - WWND 2009, Big Sky, MT, Feb. 1-8, 2009 3
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?
Z. Ch. for STAR - WWND 2009, Big Sky, MT, Feb. 1-8, 2009 4
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
Z. Ch. for STAR - WWND 2009, Big Sky, MT, Feb. 1-8, 2009 5
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
Z. Ch. for STAR - WWND 2009, Big Sky, MT, Feb. 1-8, 2009 6
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
Z. Ch. for STAR - WWND 2009, Big Sky, MT, Feb. 1-8, 2009 7
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
Z. Ch. for STAR - WWND 2009, Big Sky, MT, Feb. 1-8, 2009 8
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. for STAR - WWND 2009, Big Sky, MT, Feb. 1-8, 2009 9
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
Z. Ch. for STAR - WWND 2009, Big Sky, MT, Feb. 1-8, 2009 10
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
Z. Ch. for STAR - WWND 2009, Big Sky, MT, Feb. 1-8, 2009 11
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
Z. Ch. for STAR - WWND 2009, Big Sky, MT, Feb. 1-8, 2009 12
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
Z. Ch. for STAR - WWND 2009, Big Sky, MT, Feb. 1-8, 2009 13
€
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|
Z. Ch. for STAR - WWND 2009, Big Sky, MT, Feb. 1-8, 2009 14
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
Z. Ch. for STAR - WWND 2009, Big Sky, MT, Feb. 1-8, 2009 15
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
Z. Ch. for STAR - WWND 2009, Big Sky, MT, Feb. 1-8, 2009 16
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 ⎛
⎝ ⎜
⎞ ⎠ ⎟
Z. Ch. for STAR - WWND 2009, Big Sky, MT, Feb. 1-8, 2009 17
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
Z. Ch. for STAR - WWND 2009, Big Sky, MT, Feb. 1-8, 2009 18
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
⎡
⎣
⎢ ⎢
⎤
⎦
⎥ ⎥
Z. Ch. for STAR - WWND 2009, Big Sky, MT, Feb. 1-8, 2009 19
Various fits to STAR p+p dataVarious fits to STAR p+p data
STAR preliminary
STAR preliminary
Z. Ch. for STAR - WWND 2009, Big Sky, MT, Feb. 1-8, 2009 20
mmTT scaling of HBT radii scaling of HBT radii
Various fits give different radii but mT scaling of HBT radii still holds
STAR preliminary
Z. Ch. for STAR - WWND 2009, Big Sky, MT, Feb. 1-8, 2009 21
Multiplicity dependence in p+pMultiplicity dependence in p+p
200 GeV
Rin
v [
fm]
STAR preliminary
Z. Ch. for STAR - WWND 2009, Big Sky, MT, Feb. 1-8, 2009 22
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
Z. Ch. for STAR - WWND 2009, Big Sky, MT, Feb. 1-8, 2009 24
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
€
C = 1+ λ exp −Rinv2 Qinv
2( )[ ] 1+ δ ⋅Qinv( )
€
C = 1+ λ exp −Rinv2 Qinv
2( )[ ] 1+ δ ⋅Qinv
2( )
€
C = 1+ λ exp −RG2 QG
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
( )
€
C = 1+ λ exp −Rinv2 Qinv
2( )[ ] 1+ ε ⋅Qinv + δ ⋅Qinv
2( )
€
C = 1+ λ2J1 qT RB( )
qT RB
⎡
⎣ ⎢ ⎢
⎤
⎦ ⎥ ⎥
2
1+ qocτ( )2 ⎛
⎝ ⎜
⎞ ⎠ ⎟−1
€
C = 1+ λ exp −Rinv2 Qinv
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?
Z. Ch. for STAR - WWND 2009, Big Sky, MT, Feb. 1-8, 2009 25
Parameterizations of 1D CF used in Parameterizations of 1D CF used in comparision b/w experimentscomparision b/w experiments
€
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
€
⎫
⎬
⎪ ⎪ ⎪
⎭
⎪ ⎪ ⎪
RB≈2·RG
Z. Ch. for STAR - WWND 2009, Big Sky, MT, Feb. 1-8, 2009 26
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
Z. Ch. for STAR - WWND 2009, Big Sky, MT, Feb. 1-8, 2009 27
1D R(p1D R(pTT))
*
**
€
pT = 2 / 3 ⋅r p
STAR preliminary
Z. Ch. for STAR - WWND 2009, Big Sky, MT, Feb. 1-8, 2009 28
3D R(m3D R(mTT))
€
*RT ≈ RO ≈ RS
Leptonic results included!
STAR preliminary
Z. Ch. for STAR - WWND 2009, Big Sky, MT, Feb. 1-8, 2009 29
• 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
Z. Ch. for STAR - WWND 2009, Big Sky, MT, Feb. 1-8, 2009 30
RRinvinv(N,√s) - world systematics(N,√s) - world systematics7.21 GeV 21.7 GeV 27.4 GeV
1800 GeV31-62 GeVSTAR preliminary
200 GeV
Z. Ch. for STAR - WWND 2009, Big Sky, MT, Feb. 1-8, 2009 31
RRGG/R/RBB(N, √s) - world systematics(N, √s) - world systematics21.7 GeV
1800 GeV200-900 GeV200 GeV
53-126 GeV
STAR preliminary
UA1