zbigniew chaj ę cki, mike lisa ohio state university
DESCRIPTION
Z. Ch. & M. Lisa, PRC 78 064903 (2008) Z. Ch. & M. Lisa, PRC 79 034908 (2009) Z. Ch., arXiv:0901.4078 [nucl-ex] Z. Ch. & M. Lisa, to be published. Do p+p Collisions Flow at RHIC? Understanding One- and Two-particle Distributions, Multiplicity Evolution, and Conservation Laws. - PowerPoint PPT PresentationTRANSCRIPT
Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009 1
Zbigniew Chajęcki,
Mike Lisa
Ohio State University
Do p+p Collisions Flow at Do p+p Collisions Flow at RHIC?RHIC? Understanding One- and Two-particle Understanding One- and Two-particle
Distributions, Multiplicity Evolution, and Conservation Distributions, Multiplicity Evolution, and Conservation LawsLaws
Z. Ch. & M. Lisa, PRC 78 064903 (2008)Z. Ch. & M. Lisa, PRC 79 034908 (2009)Z. Ch., arXiv:0901.4078 [nucl-ex]Z. Ch. & M. Lisa, to be published
Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009 2
Outline & MotivationOutline & Motivation p+p as a reference to heavy ion collisions
Effect of the phase-space constraints due to energy and momentum conservation
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
[hard sector]
Heavy ion collisions as a reference to p+p?
Summary
[soft sector]
Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009 3
Small vs BigSmall vs BigLarge system (Au+Au)Small system (p+p)
STAR, PRL93 (2004) 252301
Hard sector : p+p apparently different than Au+Au Soft sector : Is p+p a clear reference to Au+Au?
STAR PRL 92 112301 (2004)
p+p
Au+Au
Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009 4
Phase-Space varies with Phase-Space varies with multiplicitymultiplicity
Phase-space constraints
Extreme 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
Phase-space factor: Hagedorn/FermiPhase-space factor: Hagedorn/Fermi
€
Sn - dynamics
Rn - kinematics
Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009 5
Correlations arising (only) from Correlations arising (only) from conservation laws (PS constraints)conservation laws (PS constraints)
€
˜ f ( pi) = 2E i
dN
d3 pi
single-particle “parent” distributionw/o P.S. restriction
%fc (p1,..., pk ) : %f (pi )i=1
k∏( )⋅ d4 piδ(pi2 −mi
2 ) %f (pi )i=k+1
N∏( )∫ δ 4 pii=1
N
∑ −P⎛⎝⎜
⎞⎠⎟
≅ %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
∑
⎛
⎝
⎜⎜⎜⎜
⎞
⎠
⎟⎟⎟⎟
k-particle distribution (k<N)
no othercorrelations
what wemeasure
with P.S. restriction
CLT approximation works best for N>10 & Ei < 23<E>
Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009 6
Phase-space effect on k-particle Phase-space effect on k-particle distributiondistribution
%fc (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 (in CMS frame)
pμ2 ≡ d3p⋅pμ
2 ⋅ %f p( )unmeasuredparent distrib
{∫ ≠ d3p⋅pμ2 ⋅%fc p( )
measured{∫
–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)
“distortion” due to PS constraints
Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009 7
N=5
N=40
Z.C
h, M.Lisa, P
RC
79 034908 (2009)
1-particle PS effect1-particle PS effect
Phase-space effect on kinematic Phase-space effect on kinematic observablesobservables
%fc (pi ) =%f (pi )×
×N
N −1⎛⎝⎜
⎞⎠⎟
2
exp −1
2(N −1)2pT ,i
2
pT2
+pz,i2
pz2
+Ei − E( )
2
E2 − E 2
⎛
⎝⎜
⎞
⎠⎟
⎛
⎝⎜⎜
⎞
⎠⎟⎟
Finite-particle constrains
C(p1, p2 ) ≅1−1N
2rpT ,1 ⋅
rpT ,2
pT2
+pz,1 ⋅pz,2
pz2
+E1 − E( )⋅E2 − E( )
E2 − E 2
⎛
⎝⎜
⎞
⎠⎟
NA49 pions Borghini et al, PRC 66 014901 (2002)- also, Danielewicz, PLBB157:146 (1985)
2-particle PS effect2-particle PS effect
CF (GenBod)
EMCICs
Z. Ch, M. Lisa, PRC 78 064903 (2008)
N. Borghini, PRC75:021904 (2007)
3-particle PS effect3-particle PS effect
C(p1,..., pk ) ≡%fc(p1,..., pk)
%fc(p1)....%fc(pk)
=
NN −k
⎛⎝⎜
⎞⎠⎟2
NN −1
⎛⎝⎜
⎞⎠⎟2k
exp −1
2(N −k)
px,ii=1
k∑( )2
px2 +
py,ii=1
k∑( )2
py2
+pz,ii=1
k∑( )2
pz2 +
Ei − E( )i=1
k∑( )2
E2 − E 2
⎛
⎝
⎜⎜⎜
⎞
⎠
⎟⎟⎟i=1
k
∑⎛
⎝
⎜⎜⎜
⎞
⎠
⎟⎟⎟
exp −1
2(N −1)px,i2
px2 +
py,i2
py2
+pz,i2
pz2 +
Ei − E( )2
E2 − E 2
⎛
⎝⎜
⎞
⎠⎟
i=1
k
∑⎛
⎝⎜⎜
⎞
⎠⎟⎟
Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009 8
1-particle phase-space 1-particle phase-space effect effect
€
˜ f c( pi ) = ˜ f (pi )N
N −1
⎛
⎝ ⎜
⎞
⎠ ⎟2
exp −1
2(N −1)
2 pT ,i2
pT2
+pz ,i
2
pz2
+Ei − E( )
2
E2 − E2
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
⎛
⎝
⎜ ⎜
⎞
⎠
⎟ ⎟
“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
exp1
2 NAA −1( )−
1
2 N pp −1( )
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟2pT ,i
2
pT2
+E i − E( )
2
E 2 − E2
⎛
⎝
⎜ ⎜
⎞
⎠
⎟ ⎟
⎛
⎝
⎜ ⎜
⎞
⎠
⎟ ⎟
Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009 9
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
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( )
∝ exp1
2 NAA −1( )−
1
2 N pp −1( )
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟2 pT ,i
2
pT2
+E i − E( )
2
E 2 − E2
⎛
⎝
⎜ ⎜
⎞
⎠
⎟ ⎟
⎛
⎝
⎜ ⎜
⎞
⎠
⎟ ⎟
STAR PRL 92 112301 (2004)
Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009 10
Kinematic scales of “the Kinematic scales of “the system”system”
postulate of same parent consistent with all spectra• magnitude• pT dependence (shape)
• mass dependence
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, …
Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009 11
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.
Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009 12
Blast-wave in p+p@200GeV: Blast-wave in p+p@200GeV: simultaneous description of spectra, simultaneous description of spectra,
HBTHBT
€
T =105.5 MeV
ρ 0 = 0.934 β = 0.535( )
R = 2.19 fm
τ = 2.25 fm/c
Δτ ~ 0.15
determined entirelyby spectra
STAR PreliminarySee M. Lisa’s poster (STAR)
Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009 13
Fits to pion CF in p+p by STARFits to pion CF in p+p by STAR
C(p1, p2 ) =a 1+ λ ⋅ Kcoul (Qinv) 1+ exp −Rout2 Qout
2 −Rside2 Qside
2 −Rlong2 Qlong
2( )( )−1⎡⎣
⎤⎦{ } ×
1−2⋅
rp1,T ⋅
rp2,T
N pT2
−p1,Z ⋅p2,Z
N pz2
−E1 − E( )⋅E2 − E( )
N E2 − E 2( )
⎡
⎣
⎢⎢
⎤
⎦
⎥⎥
N =14
pT2 =0.17 (GeV / c)2
pz2 =0.32 (GeV / c)2
E =0.68 GeV
E2 =0.50 GeV2HBT
exp CF
HBT+ “conservation”
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(pi )N
N −1⎛⎝⎜
⎞⎠⎟
2
exp −1
2(N −1)2pT ,i
2
pT2
+pz,i2
pz2
+Ei − E( )
2
E2 − E 2
⎛
⎝⎜
⎞
⎠⎟
⎛
⎝⎜⎜
⎞
⎠⎟⎟
STAR PreliminarySee M. Lisa’s poster (STAR)
Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009 14
Combined fit: consistent flow-based Combined fit: consistent flow-based descriptiondescription
Blast-Wave Model: F. Retiere, M. Lisa, PRC70:044907,2004.
€
T =106 ± 3 MeV
β = 0.48 ± 0.03
R = 2.09 ± 0.04 fm
τ 0 = 2.25 ± 0.05 fm/c
Δτ = 0.1± 0.2 fm/c
STAR PreliminarySee M. Lisa’s poster (STAR)
Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009 15
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 flow signals as A+A collisions
p+p collisions show same flow signals as A+A collisions
Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009 16
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
• Has A+A become the reference system for p+p in non-perturbative sector???
?
HBT
exp CF
HBT+ “conservation”
STAR PRL 92 112301 (2004)
STAR Preliminary
Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009 17
““the system”… a nontrivial the system”… a nontrivial conceptconcept
€
N, E , E 2 , pT2 , pZ
2
Characteristic scales of relevant system in which limited energy-momentum is shared
• Not known a priori• should track measured quantities, but not be identical to them
1. N includes all primary particles (including unmeasured γ’s etc)
2. secondary decay (resonances, fragmentation) smears connection b/t <E2> and measured one
3. <E2> etc: averages of the parent distribution
4. “relevant system” almost certainly not the “whole” (4π) system• e.g. beam fragmentation probably not relevant to system emitting at midrapidity
• characteristic physical processes (strings etc): Δy ~ 1÷2
• jets: “of the system” ??• or just stealing energy from “the system?”
1.if “relevant system” ≠ “whole system”, then total energy-momentum will fluctuate e-by-e
€
pμ2 ≡ d3p ⋅pμ
2 ⋅ ˜ f p( )unmeasuredparent distrib
{∫ ≠ d3p ⋅pμ2 ⋅ ˜ f c p( )
measured{∫
Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009 18
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 d3N
d3 p~ e−E /T
non - rel ultra - rel if T = .15 ÷ .35
pT2 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
Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009 19
Spectra
v2
HBT
€
mT ≈ T + mβ flow2
Heavy Ion Collisions : Explosive flow revealed through Heavy Ion Collisions : Explosive flow revealed through specific fingerprints specific fingerprints on soft-sector observableson soft-sector observables
calculable in hydrodynamics or toy “blast wave” models
slow
fast
Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009 20
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
Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009 21
Implication: A+A is just a collection Implication: A+A is just a collection of flowing p+p?of flowing p+p?
• No! Quite the opposite.– femtoscopically
• A+A looks like a big BlastWave• not superposition of small
BlastWaves• A+A has thermalized globally
–spectra• superposition of spectra from p+p
has same shape as a spectrum from p+p!
• relaxation of P.S. constraints indicates A+A has thermalized globally
• rather, p+p looks like a “little A+A”
Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009 22
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. - QM 2009, Knoxville, Tennessee, Mar 31, 2009 23
Average matrix element - Average matrix element - factorizationfactorization
W ′p1( )d3 ′p1 ∝ d3 ′p1 L δ ′p12 −m2( )dp01 δ ′pi
2 −m2( )d4 ′pii=2
n
∏ ×∫∫
δ 4 ′pj −p1 −p2j=1
n
∑⎛
⎝⎜⎞
⎠⎟S ′p1K ′pn |p1, p2( )
≡d3 ′p1 ⋅Sn ′p1( )RF
Probability for an n-particle final state:
Single-particle spectrum
R. Hagedorn, Relativistic Kinematics 1963
dynamics kinematics
Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009 24
……STAR PRC 2007
Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009 25
World Systematics : R(pWorld Systematics : R(pTT/m/mTT) in small ) in small systemssystems
**
€
pT = 2 / 3 ⋅r p
STAR preliminary
€
*RT ≈ RO ≈ RSfrom STAR talk at WWND 2009non-STAR data taken from Z. Ch. arXiv:0901.4078 [nucl-ex]
STAR preliminary
Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009 26
Non-femto correlationsNon-femto correlations
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. - QM 2009, Knoxville, Tennessee, Mar 31, 2009 27
Significant non-femto correlations, but little effect on Significant non-femto correlations, but little effect on “message”“message”
STAR preliminary Ratio of (AuAu, CuCu, dAu) HBT radii by pp
rather, “suggestion”: explosive flow in p+p?
Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009 28arXiv:0810.4979 submitted
looks to me like the spectrum evolves…arXiv:0809.4737
PLB 612 (2005) 181 99 (2007) 112301
folks use this onefor p+p data
… and this onefor Au+Au data(looks better than the one to the left!)
these ones arerecently submittedpapers that replotthe data from the above
these ones arerecently submittedpapers that replotthe data from the above
jetty starting ~ mT-m=1.5 pT=2.3
STAR ϕ spectra
Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009 29
phi agrees as well/poorly phi agrees as well/poorly as pi/K/p from our paperas pi/K/p from our paper
Z. Chajecki & M. Lisa PRC 79 034908 (2009)
as discussed in our paper, EMCICsalone is not enough to explain behaviorbeyond ~ 1GeV/c
using same parameters as in our paper,multiplicity-dependence of phi is described,as well, and up to same pT, as pi/k/p
Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009 30
Phase-space effects in Phase-space effects in PYTHIAPYTHIA
correlation function from PYTHIA
It’s likely that there are also other correlations in PYTHIA than just due to E&M correlations
Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009 31
b