mike lisa - winter workshop on nuclear dynamics -12 april 2008 1 how interesting is momentum...
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mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 1
How interesting is momentum conservation?
(How important is it?)Mike Lisa & Zbigniew Chajecki
OOxygen15.9994
8 26
SSulfur32.066
16 286 U
Uranium238.02891
92 28
183221
92
mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 2
Outline• Touchstones in R.H.I.C. at RHIC
• Crucial: apples::apples reference to p+p collisions (little/no collectivity?)• femtoscopy (similarity to AA “coincidental”?)
– importance of conservation laws (EMCICs *)
•soft-sector spectra (differences: “trivial” or physics?)– importance of conservation laws (EMCICs *)
•hard-sector spectra (RAA)
• clear signal of physical quenching AA versus pp
• RAA versus Rpp
– importance of conservation laws (EMCICs *)
• “Conclusions”
EMCICs: Energy and Momentum Conservation Induced Correlations
mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 4
Perfect Press Releases
• Perfect or not, creation of a bulk system at RHIC is established - flow
• This system is very color dense and largely opaque to partons traversing it - RAA
? Are these statements unique to A+A collisions?
blah blahthe quick brown/..fox...jumped..ove... th lazydog /// whatever one wants to say here s.....is just fine with mw. It’s not mattering at all. This is just a bunch of squiglly, unreadable text on this sllide I hope nobody can read itanyways since it is all nonsense. Not like that distinguishes it very much from much of my other writing, of course. But what the hell... OKlet’s just finish this lnbe and we’re done
ature of EoS unde estigation ; agreement widata might be accidental ;
viscous hydrodynamics under development ; assumption
of thermalization in questionsensitivity to modeling of
initial state, underintense study
mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 5
Spectra
v2
HBT
Flow-dominated “Blast-wave”toy models capture main characteristicse.g. PRC70 044907 (2004)
K
R (
fm)
mT (GeV/c)
STAR PRL 91 262301 (2003)
space-momentum substructure mapped in detail
mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 7
p+p: A clear reference system?
mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 8
STAR, nucl-ex/0305015
high pTsuppression
pQCD + Shadowing + Cronin
pQCD + Shadowing + Cronin + Energy Loss
Importance of a p+p reference : “jet quenching” in hard sector
Deduced initial gluon density at = 0.2 fm/c dNglue/dy ≈ 800-1200
≈ 15 GeV/fm3 (e.g. X.N. Wang nucl-th/0307036)
RAA: the 2nd “crucial result” @ RHIC
what about soft sector comparisons?
mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 9
Au+Au: central collisions
C(Qout)
C(Qside)
C(Qlong)
Obtaining 3D radii from 3D correlation functions
• Au+Au: “Gaussian” radii capture bulk scales• (but c.f. talk of R. Lacey)
• R(pT) consistent with explosive flow
€
Cr q ( ) = N ⋅ 1+ λ ⋅ Kcoul
r q ( ) ⋅ 1+ e
− qo2Ro
2 +qs2Rs
2 +ql2Rl
2( )
{ } −1 ⎛ ⎝ ⎜
⎞ ⎠ ⎟
⎡
⎣ ⎢ ⎤
⎦ ⎥
typical “Gaussian” fitting function
mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 10
The essence of CMB at a glance - decomposing WMAP survey
€
al,m ≡ dΩ ⋅T θ ,φ( ) ⋅Yl ,m* θ ,φ( )∫
ClTT ≡ al ,m
2
m
(average over m no “special” direction)
mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 11also: Danielewicz,Pratt: nucl-th/0501003
The essence of the 3D correlation function at a glance: SH decomposition
QOUT
QSIDE
QLONG Q
Au+Au: central collisions
C(Qout)
C(Qside)
C(Qlong)
3 “radii” by using3-D vector q
• extract 3D information from 3D CF• but typically view projections (“set of zero measure”)
identical treatment as CMB decomposition,except now direction matters (keep m)
€
Al,m
r Q ( ) =
ΔcosθΔφ
4πYl ,m
* θ i ,φi( )Cr Q , cosθ i ,φi( )
i
bins
∑nucl-ex/0505009 & arXiv:0803.0022 [nucl-th]
mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 12also: Danielewicz,Pratt: nucl-th/0501003
The essence of the 3D correlation function at a glance: SH decomposition
QOUT
QSIDE
QLONG Q
• Al,m coefficients encode strength and order of
angular oscillations
simulated events
€
Al,m
r Q ( ) =
ΔcosθΔφ
4πYl ,m
* θ i ,φi( )Cr Q , cosθ i ,φi( )
i
bins
∑nucl-ex/0505009 & arXiv:0803.0022 [nucl-th]
mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 13also: Danielewicz,Pratt: nucl-th/0501003
The essence of the 3D correlation function at a glance: SH decomposition
• Al,m coefficients encode strength and order of
angular oscillations• ... for each |Q| !
simulated events
simulated eventsEMCICs only
€
Al,m
r Q ( ) =
ΔcosθΔφ
4πYl ,m
* θ i ,φi( )Cr Q , cosθ i ,φi( )
i
bins
∑nucl-ex/0505009 & arXiv:0803.0022 [nucl-th]
mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 14also: Danielewicz,Pratt: nucl-th/0501003
The essence of the 3D correlation function at a glance: SH decomposition
• Al,m coefficients encode strength and order of
angular oscillations• ... for each |Q| !
“full” 3D structure at a glance
• We have many values of Q, but only a few (l,m) combos
• CMB: have only one “Q-bin” but ~1000 relevant l values!
• --> similar data volume
simulated eventsEMCICs only[Genbod; F. James 1968]
€
Al,m
r Q ( ) =
ΔcosθΔφ
4πYl ,m
* θ i ,φi( )Cr Q , cosθ i ,φi( )
i
bins
∑nucl-ex/0505009 & arXiv:0803.0022 [nucl-th]
simulated eventsEMCICs only
mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 15
Au+Au: central collisions
C(Qout)
C(Qside)
C(Qlong)
Obtaining 3D radii from 3D correlation functions
• Au+Au: “Gaussian” radii capture bulk scales• (but c.f. talk of R. Lacey)
• R(pT) consistent with explosive flow
€
Cr q ( ) = N ⋅ 1+ λ ⋅ Kcoul
r q ( ) ⋅ 1+ e
− qo2Ro
2 +qs2Rs
2 +ql2Rl
2( )
{ } −1 ⎛ ⎝ ⎜
⎞ ⎠ ⎟
⎡
⎣ ⎢ ⎤
⎦ ⎥
typical “Gaussian” fitting function
mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 16
Au+Au: central collisions
C(Qout)
C(Qside)
C(Qlong)
Obtaining 3D radii from 3D correlation functions
€
For femtoscopic correlations
Cr q ;
r q → ∞( ) = C
r q → ∞( )
⇒ Al ≠0m r
q → ∞( ) = 0
mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 17
Obtaining 3D radii from 3D correlation functions
• Au+Au: “Gaussian” radii capture bulk scales• (but c.f. talk of R. Lacey)
• R(pT) consistent with explosive flow
• p+p (d+A): strong non-femtoscopic correlations• not a “normalization” problem• not a “non-Gaussian effect”
€
Cr q ( ) = N ⋅ 1+ λ ⋅ Kcoul
r q ( ) ⋅ 1+ e
− qo2Ro
2 +qs2Rs
2 +ql2Rl
2( )
{ } −1 ⎛ ⎝ ⎜
⎞ ⎠ ⎟
⎡
⎣ ⎢ ⎤
⎦ ⎥
typical “Gaussian” fitting function
STAR preliminary d+Au peripheral collisions
Gaussian fit
€
C r P ab r
q ( ) = d 3 ′ r r ⋅S r
P ab ′
r r ( )∫ ⋅φ
r ′ q ,
r ′ r ( )
2
C r P ab r
q ( ) |r q |→∞ ⏐ → ⏐ ⏐ Konst.
mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 18
Obtaining 3D radii from 3D correlation functions
STAR preliminary d+Au peripheral collisions
Gaussian fit
€
For femtoscopic correlations
Cr q ;
r q → ∞( ) = C
r q → ∞( )
⇒ Al ≠0m r
q → ∞( ) = 0
mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 19
We are not alone...
mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 20
We are not alone...
Non-femto correlations in B-E analysis through the years:
CLEO PRD32 (1985) 2294
NA22, Z. Phys. C71 (1996) 405
Qx<0.04 GeV/cOPAL, CERN-PH-EP/2007-025(submitted to Eur. Phys. J. C.)
Qx<0.2 GeV/c
mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 21
non-femto “large-Q” behaviour - various approaches
• ignore it
• various ad-hoc parameterizations
• divide by +- (only semi-successful, and only semi-justified)
• divide by MonteCarlo PYTHIA, tuning until tail is matched (similar to ad-hoc)
• Can we understand it in terms of simplest-possible effect- correlations induced by conservation laws?•Z. Chajecki & MAL, arXiv:0803.0022 [nucl-th], sub PRC
mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 22
energy-momentum conservation in n-body states
€
f α( ) =d
dαM
2⋅Rn( )
where
M = matrix element describing interaction
(M =1 → all spectra given by phasespace)
spectrum of kinematic quantity (angle, momentum) given by
€
Rn = δ 4 P − p j
j=1
n
∑ ⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟ δ pi
2 − mi2
( )d4pi
i=1
n
∏4n
∫
where
P = total 4 - momentum of n - particle system
pi = 4 - momentum of particle i
mi = mass of particle i
n-body Phasespace factor Rn
€
δ pi2 − mi
2( )d
4pi =r p i
2
E i
dr p i ⋅d cosθ i( ) ⋅dφi
statistics: “density of states”
larger particle momentum more available states
P conservation
€
δ 4 P − p j
j=1
n
∑ ⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
Induces “trivial” correlations(i.e. even for M=1)
mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 23
Example of use of total phase space integral
• In absence of “physics” in M : (i.e. phase-space dominated)
€
Γ pp → πππ( )Γ pp → ππππ( )
=R3 1.876;π ,π ,π( )
R4 1.876;π ,π ,π ,π( )
€
In limit where "α "="event" = collection of momenta r p i
"spectrum of events" = f α( ) =d
dαRn
→ Probevent α ∝d3n
dpi3
i=1
n
∏Rn
• single-particle spectrum (e.g. pT):
• “spectrum of events”:
F. James, CERN REPORT 68-15 (1968)
€
W pi( ) = d 3 pi ⋅S n pi( )Rn
Hagedorn
mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 24
Correlations arising from conservation laws (PS constraints)
€
˜ 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
no othercorrelations
what wemeasure
mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 25
Using central limit theorem (“large N-k”)
€
˜ 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 ミ 385, (2003)–Chajecki & MAL, arXiv:0803.0022 [nucl-th], sub PRC
mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 26
Using central limit theorem (“large N-k”)
€
˜ 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 ミ 385, (2003)–Chajecki & MAL, arXiv:0803.0022 [nucl-th], sub PRC
€
˜ f c (p1,..., pk ) = ˜ f ( pi)i=1
k
∏ ⎛ ⎝ ⎜ ⎞
⎠ ⎟⋅
d4 piδ(pi2 − mi
2) ˜ f (pi)i= k +1
N
∏ ⎛ ⎝ ⎜ ⎞
⎠ ⎟∫ δ 4 pi
i=1
N
∑ − P ⎛
⎝ ⎜
⎞
⎠ ⎟
d4 piδ(pi2 − mi
2) ˜ f (pi)i=1
N
∏ ⎛ ⎝ ⎜ ⎞
⎠ ⎟∫ δ 4 pi
i=1
N
∑ − P ⎛
⎝ ⎜
⎞
⎠ ⎟
exact expression:• calculable numerically (iteratively)• correpondence with CLT discussed in detail in arXiv:0803.0022 [nucl-th]
• (for “femtoscopic” correlations -others need individual study)
mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 27
Effects on single-particle distribution
€
˜ f c(pi) = ˜ f (pi)N
N −1
⎛
⎝ ⎜
⎞
⎠ ⎟2
exp −pi,μ − pμ( )
2
2(N −1)σ μ2
μ = 0
3
∑ ⎛
⎝
⎜ ⎜
⎞
⎠
⎟ ⎟
= ˜ f (pi)N
N −1
⎛
⎝ ⎜
⎞
⎠ ⎟2
exp −1
2(N −1)
px,i2
px2
+py,i
2
py2
+pz,i
2
pz2
+E i − E( )
2
E 2 − E2
⎛
⎝
⎜ ⎜
⎞
⎠
⎟ ⎟
⎛
⎝
⎜ ⎜
⎞
⎠
⎟ ⎟
in this case, the index i is only keepingtrack of particle type, really
mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 28
k-particle correlation function
€
C(p1,...,pk ) ≡˜ f c(p1,...,pk )
˜ f c(p1)....̃ f c(pk )
=
N
N − k
⎛
⎝ ⎜
⎞
⎠ ⎟2
N
N −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
+E i − E( )
i=1
k
∑ ⎛ ⎝ ⎜ ⎞
⎠ ⎟2
E 2 − E2
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟i=1
k
∑
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟
exp −1
2(N −1)
px,i2
px2
+py,i
2
py2
+pz,i
2
pz2
+E i − E( )
2
E 2 − E2
⎛
⎝
⎜ ⎜
⎞
⎠
⎟ ⎟
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) ≅1−1
N2
r p T,1 ⋅
r p T,2
pT2
+pz,1 ⋅pz,2
pz2
+E1 − E( ) ⋅ E 2 − E( )
E 2 − E2
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 30
p+p minbias
€
N ≈15
pT2 , pZ
2 , E , E 2 poorly constrained but right magnitude
RO = 0.98 fm RS = 0.94 fm RL =1.46 fm
mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 31
Improved fit with non-femto correlations included
minbias p+p collisions
fem + non-fem
fit method Rout [fm] Rside [fm] Rlong [fm]
standard 0.65 +/- 0.01 0.85 +/- 0.01 1.42 +/- 0.02
"NA22" 1.18 +/- 0.02 1.05 +/- 0.02 1.75 +/- 0.03
"zeta-beta" 1.01 +/- 0.03 0.79 +/- 0.03 1.52 +/- 0.05
EMCICs (constr.) 1.05 +/- 0.02 1.06 +/- 0.02 1.66 +/- 0.03
EMCICs(free) 1.06 +/- 0.02
1.08 +/- 0.02 1.69 +/- 0.03
•several treatments of non-femto tried
•understood (still in progress) as due to conservation laws
•worth it! - key probe of dynamics
mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 32
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 will be significantly different effect than for Au+Au
Zbigniew Chajecki QM05
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?
mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 33pp, dAu, CuCu - STAR preliminary
Ratio of (AuAu, CuCu, dAu) 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”...)
mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 34
Significant non-femto correlations, but little effect on Significant non-femto correlations, but little effect on “message”“message”
Ratio of (AuAu, CuCu, dAu) HBT radii by pp
Fit w/o baseline parameterization NEW fit w/ baseline parameterization
STAR preliminary
alternate non-femto
rather, “suggestion”: explosive flow in p+p?
mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 36
pT spectra in soft sector: evidence against flow in p+p?
STAR PRL 92 112301 (2004)
minbias p+p
70-80% Au+Au
0-5% Au+Au
sNN = 200 GeV
Blast-wave fit to spectra:• much less explosive flow in p+p collisions
BUT!
mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 37
But remember!
€
˜ 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
€
˜ f cp+ p pi( )
˜ f cA+A pi( )
=N
N −1
⎛
⎝ ⎜
⎞
⎠ ⎟2
exp −1
2(N −1)
2 pT ,i2
pT2
+pz,i
2
pz2
+Ei − E( )
2
E2 − E2
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
⎛
⎝
⎜ ⎜
⎞
⎠
⎟ ⎟
where N is for minbias p + p, and N A+A ≈ ∞
Then we would measure:
mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 38
Multiplicity evolution of spectra - p+p to A+A (soft sector)
€
˜ f cp+ p pT ,i( )
˜ f cA+A pT ,i( )
=N
N −1
⎛
⎝ ⎜
⎞
⎠ ⎟3/2
exp −1
2(N −1)
2 pT ,i2
pT2
+Ei − E( )
2
E2 − E2
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
⎛
⎝
⎜ ⎜
⎞
⎠
⎟ ⎟
N evolution of spectra dominated by PS “distortion”
p+p system samples same parent distribution, but under stronger PS constraints
5% central Au+Au
minbias p+p
“corrected” minbias p+p
“corrected” minbias p+p scaled
mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 39
Multiplicity evolution of spectra - within p+p (soft sector)
STAR, PRD74 032006 (2006)
What if the only difference betweenmultiplicity-selected p+p collisions was N?
€
same ˜ f p( ) , pT2 , E , E2
€
˜ f cN1 pT ,i( )
˜ f cN 2 pT ,i( )
=N2 −1( )N1
N1 −1( )N2
⎛
⎝ ⎜
⎞
⎠ ⎟
3/2
exp1
2 N2 −1( )−
1
2 N1 −1( )
⎛
⎝ ⎜
⎞
⎠ ⎟2 pT ,i
2
pT2
+Ei − E( )
2
E2 − E2
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
⎛
⎝
⎜ ⎜
⎞
⎠
⎟ ⎟
Then we would measure:
pion mass assumed
mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 40
Multiplicity evolution of spectra - within p+p (soft sector)
soft sector: N evolution of spectra dominated by PS “distortion”
STAR, PRD74 032006 (2006)
€
˜ f cN1 pT ,i( )
˜ f cN 2 pT ,i( )
=N2 −1( )N1
N1 −1( )N2
⎛
⎝ ⎜
⎞
⎠ ⎟
3/2
exp1
2 N2 −1( )−
1
2 N1 −1( )
⎛
⎝ ⎜
⎞
⎠ ⎟2 pT ,i
2
pT2
+Ei − E( )
2
E2 − E2
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
⎛
⎝
⎜ ⎜
⎞
⎠
⎟ ⎟
pion mass assumed
mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 41
Multiplicity evolution of spectra - within p+p (hard sector)
hard sector: N evolution of spectra NOT explained by PS “distortion”
STAR, PRD74 032006 (2006)
€
˜ f cN1 pT ,i( )
˜ f cN 2 pT ,i( )
=N2 −1( )N1
N1 −1( )N2
⎛
⎝ ⎜
⎞
⎠ ⎟
3/2
exp1
2 N2 −1( )−
1
2 N1 −1( )
⎛
⎝ ⎜
⎞
⎠ ⎟2 pT ,i
2
pT2
+Ei − E( )
2
E2 − E2
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
⎛
⎝
⎜ ⎜
⎞
⎠
⎟ ⎟
pion mass assumed
mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 42pion mass assumed
Multiplicity evolution of spectra - within p+p (hard sector)
hard sector: N evolution of spectra NOT explained by PS “distortion”
STAR, PRD74 032006 (2006)
“Rpp” after dividingout EMCIC effects
In fact, suggests high-pT tail in high multiplicity collisions is suppressedrelative to low-multiplicity (like AA)
€
˜ f cN1 pT ,i( )
˜ f cN 2 pT ,i( )
=N2 −1( )N1
N1 −1( )N2
⎛
⎝ ⎜
⎞
⎠ ⎟
3/2
exp1
2 N2 −1( )−
1
2 N1 −1( )
⎛
⎝ ⎜
⎞
⎠ ⎟2 pT ,i
2
pT2
+Ei − E( )
2
E2 − E2
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
⎛
⎝
⎜ ⎜
⎞
⎠
⎟ ⎟
mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 43
So you are saying that...
• There may be a bulk, collective system created in p+p, as A+A??•soft-sector signals: femtoscopy, spectra•obscured if one ignores PS
• This bulk medium might suppress jets, similar to in A+A??• though P.S. effects make it appear opposite to A+A
• Whoever heard of such a stupid idea?!
mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 44
So you are saying that...
• There may be a bulk, collective system created in p+p, as A+A??•soft-sector signals: femtoscopy, spectra•obscured if one ignores PS
• This bulk medium might suppress jets, similar to in A+A??• though P.S. effects make it appear opposite to A+A
• Whoever heard of such a stupid idea?!
Fig. 3
mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 45
Does this maybe suggest...• ...that the flow in A+A is nothing more than
the individual p+p collisions flowing?(i.e. A+A is superposition of 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
mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 46
Does this maybe suggest...• ...that the flow in A+A is nothing more than
the individual p+p collisions flowing?(i.e. A+A is superposition of 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• anisotropic flow
• A+A shows increased signal over superposition of p+p
• is the p+p signal “flow” ??
• ... that p+p looks like a “little A+A”?• yes
mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 47
Summary• Collective motion: critical observable of bulk sector at RHIC
• bulk matter, “perfect liquid,” etc.
• evidence in AA from spectra, anisotropic flow, id and non-id femtoscopy
• apples::apples A+A::p+p• invaluable to identify onset of bulk (or “new”) behaviour
• conservation laws can distort p+p, generating potentially misleading results
• p+p collisions may be more similar to A+A than usually thought• collective flow?
• Rpp behaves “similar” to RAA?
• Danger of confusing “trivial” (?) effectswith physics
mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 48
THEEND