1. Nuts and bolts of EMCICs: Large & small systems
Mike Lisa
Ohio State University
ma lisa - hot&dense matter - weizmann institute - rehovat, israel - nov 2008

2. Where is Ohio?
ma lisa - hot&dense matter - weizmann institute - rehovat, israel - nov 2008

3. Heavy Ion physics in Ohio
ma lisa - hot&dense matter - weizmann institute - rehovat, israel - nov 2008

4. prelude: EMCIC* effects/phasespace dominance in soft sector
Danger of ignoring EMCICs
3-particle
2-particle (1)
2-particle (2)
1-particle
Analogy: “0” particle
* EMCIC = “Energy and Momentum Induced Correlation”
or “Energy and Momentum Induced Constraint”
ma lisa - hot&dense matter - weizmann institute - rehovat, israel - nov 2008

5. 3-particle EMCIC effects
N. Borghini, PRC75: (2007)
may mimic “conical emission” !
Again, “the system:”
[N] might not be the total event multiplicity, but one could argue that different rapidity slices are decorrelated, so that the constraint from pT conservation would actually be driven by a smaller multiplicity.
Before trying to identify definite structures, which require high-precision measurements, in the recoil region of a high-pT particle, it is important to first determine precisely the reference pattern — including the effects of momentum conservation and anisotropic collective flow — over which they would develop.
ma lisa - hot&dense matter - weizmann institute - rehovat, israel - nov 2008

6. 2 particle EMCIC effects (I): anisotropic flow
Danielewicz, PLBB157:146 (1985)
Borghini et al, PRC66:014901,2002.
Z. Chajecki & MAL, arXiv: [nucl-th]
NA49 pions
more important for heavier particles:
the effect of momentum conservation alone is large enough to reverse the sign of the proton directed flow measured by NA49
Bhorgini et al PRC62:034902,2000.
ma lisa - hot&dense matter - weizmann institute - rehovat, israel - nov 2008

7. 2 particle EMCIC effects (2): femtoscopy
Chajecki & MAL, arXiv: [nucl-th], PRC in press
Z. Chajecki & MAL, PRC in press
arXiv: [nucl-th]
For small systems, non-femtoscopic effects contribute significantly, clouding the
extraction and interpretation of the femtoscopic ones.
ma lisa - hot&dense matter - weizmann institute - rehovat, israel - nov 2008

8. 1 particle EMCIC effects: spectra
Z. Chajecki & MAL, arXiv: [nucl-th]
the multiplicity evolution of the soft portion of the pT spectra at RHIC is dominated by phase- space restrictions. Effects due to actual physics (the parent distribution) are subdominant.
ma lisa - hot&dense matter - weizmann institute - rehovat, israel - nov 2008

9. Outline Once more, quickly but with feeling… flow and femtoscopy
Two-particle correlation functions in detail
SHD representation
Evidence of EMCICs*
“Fermi” approach, phasespace integral, CLT approximation
“the system”
EMCICs** and the multiplicity evolution of spectra
“The system” again: does it hang together?
Implications
* EMCIC = “Energy and Momentum Induced Correlation”
** EMCIC = “Energy and Momentum Induced Constraint”
ma lisa - hot&dense matter - weizmann institute - rehovat, israel - nov 2008

10. space-momentum substructure mapped in detail, well-understood
Flow-dominated “Blast-wave”
toy models capture main characteristics
e.g. PRC (2004)
Spectra v2
HBT
R (fm)
mT (GeV/c)
STAR PRL (2003) 
slow 
OK OK clearly it is flow. We are QUANTITATIVE here! K
fast 
space-momentum substructure mapped in detail, well-understood
ma lisa - hot&dense matter - weizmann institute - rehovat, israel - nov 2008

11. Obtaining 3D radii from 3D correlation functions
typical “Gaussian” fitting function
Au+Au: central collisions
C(Qout)
C(Qside)
C(Qlong)
Au+Au: “Gaussian” radii capture bulk scales
(resonance tails from imaging)
R(pT) consistent with explosive flow
“set of zero measure”
of full 3D correlation fctn
ma lisa - hot&dense matter - weizmann institute - rehovat, israel - nov 2008

12. Spherical harmonic representation of 3D data
(average over m  no “special” direction)
ma lisa - hot&dense matter - weizmann institute - rehovat, israel - nov 2008

13. Spherical harmonic representation of 3D data
Au+Au: central collisions
C(Qout)
C(Qside)
C(Qlong)
Z. Chajecki & MAL,PRC in press, arXiv: [nucl-th]
ma lisa - hot&dense matter - weizmann institute - rehovat, israel - nov 2008 13

14. Spherical harmonic representation of 3D data
d+Au peripheral collisions
Not a “normalization problem”
Not a “non-Gaussian” issue
A real, non-femtoscopic correlation
STAR prelim (QM05)
Z. Chajecki & MAL,PRC in press, arXiv: [nucl-th]
ma lisa - hot&dense matter - weizmann institute - rehovat, israel - nov 2008 14

15. non-femto “large-Q” behaviour - various approaches
ignore it
various ad-hoc parameterizations (e.g. NA22)
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– Energy and Momentum Conservation Induced Correlations (EMCICs)?
Z. Chajecki & MAL, arXiv: [nucl-th], PRC in press
see also
pT conservation effects on v1 [Danielewicz, Ollitrault & Borghini]
pT conservation on 3-particle “conical emission” observables [Borghini]
p and E conservation effects on single particle spectra [Chajecki & MAL]
ma lisa - hot&dense matter - weizmann institute - rehovat, israel - nov 2008

16. energy-momentum conservation in n-body states
spectrum of kinematic quantity  (angle, momentum) given by
statistics: “density of states”
larger particle momentum more available states
n-body Phasespace factor Rn
that first equation is essentially “Fermi’s Golden Rule”
P conservation
Induces “trivial” correlations
(i.e. even for M=1)
ma lisa - hot&dense matter - weizmann institute - rehovat, israel - nov 2008

17. Example of use of total phase space integral
In absence of different “physics” in M : (i.e. phase-space dominated)
single-particle spectrum (e.g. pT):
Hagedorn
“spectrum of events”:
nota: that first equation with pion decay channels actually is missing a numerical factor... See James.
ma lisa - hot&dense matter - weizmann institute - rehovat, israel - nov 2008
F. James, CERN REPORT (1968)

18. Correlations arising (only) from conservation laws (PS constraints)
single-particle “parent” distribution
w/o P.S. restriction
what we
measure
no other
correlations
Note: k<N is just there because if k=N-1 then ALL particle momentum (all N) would be known already since P is conserved. So it just indicates that there is one less 4-vector degree of freedom in the distribution
k-particle distribution (k<N) with P.S. restriction
ma lisa - hot&dense matter - weizmann institute - rehovat, israel - nov 2008

19. Simplification for “large” N-k (1)
Numerator is the probability distribution of a sum of many (N-k) uncorrelated vectors
(i.e. the probability that they will add up to P-Σi=1kpi)
If (N-k) big Multivariate Central Limit Theorem
Note: k<N is just there because if k=N-1 then ALL particle momentum (all N) would be known already since P is conserved. So it just indicates that there is one less 4-vector degree of freedom in the distribution
Denominator is “just” a constant normalization (indep pi)
ma lisa - hot&dense matter - weizmann institute - rehovat, israel - nov 2008

20. Using central limit theorem (“large* N-k”)
k-particle distribution in N-particle system
N.B.
relevant later
(*) For simplicity, I from now on assume identical particles (e.g. pions). I.e. all particles have the same average energy and RMS’s of energy and momentum. Similar results (esp “experimentalist recipe) but more cumbersome notation otherwise
k=1 (spectra) : Z. Chajecki & MAL arXiv: [nucl-th]
k=2 (v1) : Danielewicz et al, PRC (1988); Borghini, et al, PRC (2000)
k=2 (HBT) : Chajecki & MAL, arXiv: [nucl-th], PRC in press
k=3 (conical flow) : N. Borghini, PRC75: (2007)
* “large”: N > ~10
ma lisa - hot&dense matter - weizmann institute - rehovat, israel - nov 2008

21. Effects on single-particle distribution
We will return to this….
note that even single-particle distribution is modified.
I.e. it is not “just” a two-particle effect
in this case, the index i is only keeping
track of particle type, really
ma lisa - hot&dense matter - weizmann institute - rehovat, israel - nov 2008

22. k-particle correlation function
Dependence on “parent” distrib f vanishes,
except for energy/momentum means and RMS
2-particle correlation function (1st term in 1/N expansion)
ma lisa - hot&dense matter - weizmann institute - rehovat, israel - nov 2008

23. How do EMCICs look ? – nontrivial !
Genbod N=18 <K>=0.9 GeV; PRF - ||<0.5
event generator (genbod)
with only EMCICs
O(1/N) term in
CLT approximation
CLT approximation
structure not confined to large Q
kinematic cuts have strong effect
ma lisa - hot&dense matter - weizmann institute - rehovat, israel - nov 2008

24. How do EMCICs look ? – nontrivial !
ma lisa - hot&dense matter - weizmann institute - rehovat, israel - nov 2008

25. “the system”… a nontrivial concept
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
N includes primary particles (including unmeasured γ’s etc)
secondary decay (resonances, fragmentation) smears connection b/t <E2> and measured one
<E2> etc: averages of the parent distribution
“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” ??
sim “leading baryon effect” in microcanonical thermal fits
if “relevant system” ≠ “whole system”, then total energy-momentum will fluctuate event-to-event – see definition above
ma lisa - hot&dense matter - weizmann institute - rehovat, israel - nov 2008

26. “the system”… a nontrivial concept
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
We will treat them as parameters: what to expect?
ma lisa - hot&dense matter - weizmann institute - rehovat, israel - nov 2008

27. “the system”… a nontrivial concept
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
We will treat them as parameters: what to expect?
ma lisa - hot&dense matter - weizmann institute - rehovat, israel - nov 2008 27

28. Obtaining 3D radii from 3D correlation functions
typical “Gaussian” fitting function
p+p collisions minbias
Including Energy and Momentum Conservation
ma lisa - hot&dense matter - weizmann institute - rehovat, israel - nov 2008

29. p+p minbias kT=0.35-0.6 λ 0.46 RO 0.81 fm RS 0.84 fm RL 1.29 fm λ 0.64
Z. Chajecki, WPCF 2008 λ
0.46 RO
0.81 fm RS
0.84 fm RL
1.29 fm λ
0.64 N
12.9 RO
0.96 fm
<pT2>
0.2 (GeV/c)2 RS
0.88 fm
<pZ2>
0.39 (GeV/c)2 RL
1.26 fm
<E>
0.6 GeV
<E2>
0.43 GeV2
ma lisa - hot&dense matter - weizmann institute - rehovat, israel - nov 2008

30. femtoscopy in p+p @ STAR
Zbigniew Chajecki QM05
femtoscopy in STAR
1. Heisenberg uncertainty?
DELPHI
Z0 LEP
m, mT (GeV)
R (fm)
R Z(fm)
hep-ph/  K p 
2. String fragmentation? (Lund)
e.g. G. Alexander
“plausible” in z-direction
unlikely in transvrse
inconsistent with mult-dep
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?
3. Resonance effects?
essentially no quantitative predictions
pT dependence maybe (??)
mass dependence no [Andersson, Moriond 2000]
4. Flow???
e.g. Wiedemann & Heinz ‘97
maybe, but will be significantly different effect than for Au+Au
Increasingly suggested in HEP experiments
STAR preliminary
The Andersson reference is 2000 Recontres de Moriond meeting. It is reference [4] f the cited Alexander paper
Csorgo: fit to star proton-proton coll
Shuryak: check again
Heinz: dependence on the size
More on dAu
More on pp
Rlong
ma lisa - hot&dense matter - weizmann institute - rehovat, israel - nov 2008

31. femtoscopy in p+p @ STAR
Zbigniew Chajecki QM05
OPAL Collaboration, Eur.Phys.J.C52: ,2007; arXiv: [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.
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.
femtoscopy in STAR
1. Heisenberg uncertainty?
DELPHI
Z0 LEP
m, mT (GeV)
R (fm)
R Z(fm)
hep-ph/  K p 
e.g. G. Alexander
“plausible” in z-direction
unlikely in transvrse
2. String fragmentation? (Lund)
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?
3. Resonance effects?
pT dependence maybe (??)
mass dependence probably no [Andersson, Moriond 2000]
4. Flow???
e.g. Wiedemann & Heinz ‘97
maybe, but will be significantly different effect than for Au+Au
E735 Collaboration, PRD (1993)
also PLB 2002
consistent with an expanding shell model.
Increasingly suggested in recent experiments
STAR preliminary
mT (GeV)
The Andersson reference is 2000 Recontres de Moriond meeting. It is reference [4] f the cited Alexander paper
Csorgo: fit to star proton-proton coll
Shuryak: check again
Heinz: dependence on the size
More on dAu
More on pp
Rlong
W. Kittel Acta Phys.Polon. B32 (2001) [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!
ma lisa - hot&dense matter - weizmann institute - rehovat, israel - nov 2008

32. femtoscopy in p+p @ STAR
Zbigniew Chajecki QM05
OPAL Collaboration, Eur.Phys.J.C52: ,2007; arXiv: [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.
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.
Spectra v2
HBT
femtoscopy in STAR
1. Heisenberg uncertainty?
DELPHI
Z0 LEP
m, mT (GeV)
R (fm)
R Z(fm)
hep-ph/  K p 
e.g. G. Alexander
“plausible” in z-direction
unlikely in transvrse
2. String fragmentation? (Lund)
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?
RHIC: “comparison machine”
Vary size. All else fixed. [acceptance, technique…]
spectra
femtoscopy
compare with a system we “know” is flowing
pT dependence maybe (??)
mass dependence probably no [Andersson, Moriond 2000]
3. Resonance effects?
4. Flow???
e.g. Wiedemann & Heinz ‘97
maybe, but will be significantly different effect than for Au+Au
E735 Collaboration, PRD (1993)
also PLB 2002
consistent with an expanding shell model.
Increasingly suggested in recent experiments
STAR preliminary
mT (GeV)
The Andersson reference is 2000 Recontres de Moriond meeting. It is reference [4] f the cited Alexander paper
Csorgo: fit to star proton-proton coll
Shuryak: check again
Heinz: dependence on the size
More on dAu
More on pp
Rlong
W. Kittel Acta Phys.Polon. B32 (2001) [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!
ma lisa - hot&dense matter - weizmann institute - rehovat, israel - nov 2008

33. Significant non-femto correlations, but little effect on “message”
rather, “suggestion”: explosive flow in p+p?
Ratio of (AuAu, CuCu, dAu) HBT radii by pp
STAR preliminary
alternate non-femto
Fit w/o baseline parameterization
NEW fit w/ baseline parameterization
ma lisa - hot&dense matter - weizmann institute - rehovat, israel - nov 2008

34. BUT…..! Au+Au 0-5% Au+Au 60-70% p+p minbias Blast-wave fit to spectra:
STAR PRL (2004)
Au+Au 0-5%
Au+Au 60-70%
p+p minbias
Blast-wave fit to spectra:
much less explosive flow in p+p collisions
ma lisa - hot&dense matter - weizmann institute - rehovat, israel - nov 2008

35. But remember! “distortion” of single-particle spectra measured
“matrix element”
ma lisa - hot&dense matter - weizmann institute - rehovat, israel - nov 2008

36. But remember! “distortion” of single-particle spectra
measured
“distortion” of single-particle spectra
“matrix element”
What if the only difference between p+p and A+A collisions was N?
STAR PRL (2004)
Au+Au 0-5%
Au+Au 60-70%
p+p minbias
ma lisa - hot&dense matter - weizmann institute - rehovat, israel - nov 2008

37. But remember! “distortion” of single-particle spectra
measured
“distortion” of single-particle spectra
“matrix element”
What if the only difference between p+p and A+A collisions was N?
Then we would measure:
ma lisa - hot&dense matter - weizmann institute - rehovat, israel - nov 2008

38. Multiplicity evolution of spectra - p+p to A+A (soft sector)
N evolution of spectra dominated by PS “distortion”
p+p system samples same parent distribution, but under stronger PS constraints
K ~ unity. driven by conservation of discrete quantum #s (strangeness, etc)
ma lisa - hot&dense matter - weizmann institute - rehovat, israel - nov 2008

39. Kinematic scales of “the system”
ma lisa - hot&dense matter - weizmann institute - rehovat, israel - nov 2008

40. Multiplicity evolution of spectra - p+p to A+A (soft sector)
N evolution of spectra dominated by PS “distortion”
p+p system samples same parent distribution, but under stronger PS constraints
K ~ unity. driven by conservation of discrete quantum #s (strangeness, etc)
ma lisa - hot&dense matter - weizmann institute - rehovat, israel - nov 2008

41. By popular demand Almost universal “flow” & “temperature”
parameters in a BlastWave fit
Apparent changes in β, T with dN/dη caused by EMCICs*
* EMCIC = Energy & Momentum Conservation Induced Constraint
ma lisa - hot&dense matter - weizmann institute - rehovat, israel - nov 2008

42. Blast-wave in p+p: simultaneous description of spectra, HBT
determined entirely
by spectra
ma lisa - hot&dense matter - weizmann institute - rehovat, israel - nov 2008

43. Coming back to HBT… p+pbar @ Tevatron p+p, Au+Au @ RHIC EMCICs EMCICs
Wang & Gyulassy 1992
Tevatron
STAR PRL (2004)
p+p, RHIC
EMCICs
EMCICs
more flow
more minijets
Geometric substructure argues against changing flow argument
…and against a pure minijet mechanism (next page)
ma lisa - hot&dense matter - weizmann institute - rehovat, israel - nov 2008

44. A+A is just a collection 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”
ma lisa - hot&dense matter - weizmann institute - rehovat, israel - nov 2008

45. A+A is just a collection 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”
anisotropic flow
A+A shows increased signal over superposition of p+p
is the p+p signal “flow” ??
ma lisa - hot&dense matter - weizmann institute - rehovat, israel - nov 2008

46. Summary
E&M conservation: phasespace constraints w/ explicit N 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”)
2-particle correlations
p+p resembles clear flow signal from A+A
strong EMCICs seen
Soft-sector spectra
mult-dep of pT spectra consistent with EMCIC “distortion” of unchanging parent
is pp/AA physics very similar, or are measurements insensitive to diff physics?
Thermalization, hadronization, very early color dynamics…?
Has AA become the reference system for pp in soft sector???
ma lisa - hot&dense matter - weizmann institute - rehovat, israel - nov 2008