ma lisa - femtoscopy in small systems & emcics - kent state university - january 20071...

ma lisa - Femtoscopy in small systems & EMCICs - Kent State University - January 2007 1

Conservation laws & femtoscopy of small systems

Zbigniew Chajeçki & Mike Lisa

Ohio State University

nucl-th/0612080


Outline

• Introduction– RHI, femtoscopy, & collectivity in bulk matter– including: new representation of correlation functions

• the p+p “reference”– intriguing features pp versus AA– non-femtoscopic effects

• Global conservation effects (EMCICs)– Restricted phasespace calculations: GenBod (FOWL)– Analytic EMCIC calculations– Experimentalists’ recipe:– Fitting correlation functions [in progress]

• Summary


RHIC BRAHMSPHOBOS

PHENIXSTAR

AGS

TANDEMS

Nuclear Particle


Why heavy ion collisions?

Nuclear Particle

STAR ~500 Collaborators


2 types (?) of collisions...

looks like fun...

looks like a mess...


A dynamical but crude view of the collision

QuickTime™ and aYUV420 codec decompressor

are needed to see this picture.

In this model, insufficient re-interactionsc/o UrQMD Collaboration, Frankfurt


A dynamical but crude view of the collision

In this model, insufficient re-interactions


R.H.I.C. defined...

• collision of nuclei sufficiently large that nuclear details unimportant– distinct from nuclear or particle physics– “Geranium on Linoleum”

• sufficiently large for meaningful bulk & thermodynamic quantities

• non-trivial spatial scales & geometry drive bulk dynamics (e.g. flow)

• how big is “sufficient” ?– important reference issue


phase structure of bulk system:

• driving symmetries

• long-range collective behaviour

• “new” physics [superfluidity in l-He]

• relevance of meaningful EoS


Generating a deconfined state

Nuclear Matter(confined)

Hadronic Matter(confined)

Quark Gluon Plasmadeconfined !

Present understanding of Quantum Chromodynamics (QCD)• heating• compression deconfined color matter !


Expectations from Lattice QCD

/T4 ~ # degrees of freedom

confined:few d.o.f.

deconfined:many d.o.f.

TC ≈ 173 MeV ≈ 21012 K ≈ 130,000T[Sun’s core]


The four elements from 400 BC to 2000AD

400 BC : all creation

Earth Fire

Air Water

?


QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

RHIC energies: the first quantitative success of hydro• direct access to EoS (phase transitions, lattice, etc.)

EoS: P versus versus n(Heinz et al)


Microexplosions Femtoexplosions

1017 J/m3 5 GeV/fm3 = 1036 J/m3

s 0.1 J 1 J

T 106 K 200 MeV = 1012 K

rate 1018 K/sec 1035 K/s

• energy quickly deposited• enter plasma phase• expand hydrodynamically• cool back to original phase• do geometric “postmortem” & infer momentum


Microexplosions Femtoexplosions

s 0.1 J 1 J

1017 J/m3 5 GeV/fm3 = 1036 J/m3

T 106 K 200 MeV = 1012 K

rate 1018 K/sec 1035 K/s

• energy quickly deposited• enter plasma phase• expand hydrodynamically• cool back to original phase• do geometric “postmortem” & infer momentum


Impact parameter & Reaction plane

b = 0 “central collision”many particles produced

“peripheral collision”fewer particles produced

br


Impact parameter & Reaction plane

b = 0 “central collision”many particles produced

“peripheral collision”fewer particles produced

br br

Reaction plane:

spanned by beam direction and br


How do semi-central collisions evolve?

br

1) Superposition of independent p+p:momenta pointed at randomrelative to reaction plane



br

1) Superposition of independent p+p:

2) Evolution as a bulk system

momenta pointed at randomrelative to reaction plane

highdensity / pressure

at center

“zero” pressurein surrounding vacuum

Pressure gradients (larger in-plane) push bulk “out” “flow”

more, faster particles seen in-plane



1) Superposition of independent p+p:

2) Evolution as a bulk system

momenta pointed at randomrelative to reaction plane

Pressure gradients (larger in-plane) push bulk “out” “flow”

more, faster particles seen in-plane

N

-RP (rad)0 /2 /4 3/4

N

-RP (rad)0 /2 /4 3/4


Azimuthal distributions at RHIC

STAR, PRL90 032301 (2003)

b ≈ 4 fm

“central” collisions

b ≈ 6.5 fm

midcentral collisions


Azimuthal distributions at RHIC

STAR, PRL90 032301 (2003)

b ≈ 4 fmb ≈ 6.5 fmb ≈ 10 fm

peripheral collisions


Beyond press releases

Nature of EoS under investigation ; agreement with

data may be accidental ; viscous hydro under

development ; assumptionof thermalization in question

sensitive to modeling ofinitial state,

presently under study

The detailed work now underway is what can probe & constrain sQGP properties

It is probably not press-release material......but, hey, you’ve already got your coffee mug


Beyond press releases:Access to the dynamically-generated geometric substructure?

The feature of collectivity:

space

is globally correlated with

momentum


222111 p)xr(i22

p)xr(i11T e)p,x(Ue)p,x(U

rrrrrr rrrr ⋅−⋅−=ψ

probing source geometry through interferometry

12 ppqrrr −=

2

21

2121 )q(~1

)p(P)p(P)p,p(P

)p,p(C ρ+== C (Qinv)

Qinv (GeV/c)

1

2

0.05 0.10

Width ~ 1/R

Measurable! F.T. of pion source

( ))xx(iq2

*21

*1T

*T

21e1UUUU −⋅+⋅⋅=ψψ

Creation probability ρ(x,p) = U*U5 fm

1 m sourceρ(x)

r1

r2

x1

x2

{2

1

}e)p,x(Ue)p,x(U 212121 p)xr(i21

p)xr(i12

rrrrrr rrrr ⋅−⋅−+

p1

p2

The Bottom line…if a pion is emitted, it is more likely to emit another

pion with very similar momentum if the source is small

experimentally measuring this enhanced probability: quite challenging


Correlation functions for different colliding systemsC

2(Q

inv)

Qinv (GeV/c)

STAR preliminary p+pR ~ 1 fm

d+AuR ~ 2 fm

Au+AuR ~ 6 fm

Different colliding systems studied at RHIC

Interferometry probes the smallest scales ever measured !

Au+Au: central collisions

C(Qout)

C(Qside)

C(Qlong)

3 “radii” by using3-D vector q


Femtoscopic information

€

C r P

ab(r q ) = d3 ′

r r ⋅Sr

P

ab( ′ r r )∫ ⋅ φ(

r ′ q ,r ′ r )

2

xaxb

pa

pbxa

xb

pa

pb

€

Sr P

ab( ′ r r ) =

r x a -

r x b( ) distribution

φ(r ′ q ,r ′ r ) = (a,b) relative wavefctn

• femtoscopic correlation at low |q|• must vanish at high |q|. [indep “direction”]


C(Qout)

C(Qside)

C(Qlong)



Femtoscopic information - Spherical harmonic representation



C(Qout)

C(Qside)

C(Qlong)


QOUT

QSIDE

QLONG Q

∑→→ ΔΔ

=binsall

iiiiimlml QCYQA

.

,

cos

, ),cos|,(|),(|)(| φθφθπ

φθ

4

This new method of analysis represents a real breakthrough. ...(should) become a standard tool in all experiments.

- A. Bialas, ISMD 2005

nucl-ex/0505009


Femtoscopic information - Spherical harmonic representation


•ALM(Q) = L,0


C(Qout)

C(Qside)

C(Qlong)


∑→→ ΔΔ

=binsall

iiiiimlml QCYQA

.

,

cos

, ),cos|,(|),(|)(| φθφθπ

φθ

4

L=0

L=2M=0

L=2M=2

nucl-ex/0505009


Why do the radii fallwith increasing momentum ??

€

(3 "radii" corresponding to the three components of r q )


It’s collective flow !!

Direct geometrical/dynamical evidencefor bulk behaviour!!!

Amount of flow consistent with p-space nucl-th/0312024

Huge, diverse systematics consistent with this substructurenucl-ex/0505014

Why do the radii fallwith increasing momentum ??


p+p: A clear reference system?


STAR preliminary

mT (GeV) mT (GeV)

Z. Chajecki QM05nucl-ex/0510014femtoscopy in p+p @ STAR

• Decades of femtoscopy in p+p and in A+A, but...

• for the first time: femtoscopy in p+p and A+A in same experiment, same analysis definitions...

• unique opportunity to compare physics

• ~ 1 fm makes sense, but...

• pT-dependence in p+p?

• (same cause as in A+A?)


Surprising („puzzling”) scaling

HBT radii scale with pp

Scary coincidence or something deeper?

On the face: same geometric substructure

pp, dAu, CuCu - STAR preliminary

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

A. Bialasz (ISMD05):I personally feel that its solution may provide new insight into the hadronization process of QCD


BUT... Clear BUT... Clear interpretationinterpretation clouded by clouded by datadata features features

STAR preliminary d+Au peripheral collisions

Gaussian fitNon-femtoscopic q-anisotropicbehaviour at large |q|

does this structure affect femtoscopic region as well?


STAR preliminary d+Au peripheral collisions

Gaussian fit

∑→→ ΔΔ

=binsall

iiiiimlml QCYQA

.

,cos

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

|)(| φθφθπ

φθ

Decomposition of CF onto Spherical Harmonics

Z.Ch., Gutierrez, MAL, Lopez-Noriega, nucl-ex/0505009

non-femtoscopic structure(not just “non-Gaussian”)


Just push on....?

• ... no!– Irresponsible to ad-hoc fit (often the practice) or ignore (!!) & interpret

without understanding data– no particular reason to expect non-femtoscopic effect to be limited to

non-femtoscopic (large-q) region• not-understood or -controlled contaminating correlated effects

at low q ?

• A possibility: energy-momentum conservation?– must be there somewhere!– but how to calculate / model ?

(Upon consideration, non-trivial...)


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

€

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

€

4 P − p j

j=1

n

∑ ⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

Induces “trivial” correlations(i.e. even for M=1)


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 of :

€

f α( ) =d

dαRn

• “spectrum of events”:

F. James, CERN REPORT 68-15 (1968)


Genbod:phasespace sampling w/ P-conservation

• F. James, Monte Carlo Phase Space CERN REPORT 68-15 (1 May 1968)

• Sampling a parent phasespace, conserves energy & momentum explicitly

– no other correlations between particles

Events generated randomly, buteach has an Event Weight

€

WT =1

Mm

M i+1R2 M i+1;M i,mi+1( ){ }i=1

n−1

∏

WT ~ probability of event to occur

ALL EVENTS ARE

EQUAL, BUT SOME EVENTS ARE

MORE EQUAL THAN OTHERS


“Rounder” events: higher WT

ALL EVENTS ARE




€

Rn = δ 4 P − p j

j=1

n

∑ ⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟ δ pi

2 − mi2

( )d4pi

i=1

n

∏4n

∫

δ pi2 − mi

2( )d

4pi =r p i

2

E i


6 particles


“Rounder” events: higher WT

ALL EVENTS ARE




€

Rn = δ 4 P − p j

j=1

n

∑ ⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟ δ pi

2 − mi2

( )d4pi

i=1

n

∏4n

∫

δ pi2 − mi

2( )d

4pi =r p i

2

E i


30 particles


Genbod:phasespace sampling w/ P-conservation

€

WT =1

Mm

M i+1R2 M i+1;M i,mi+1( ){ }i=1

n−1

∏

• Treat identical to measured events

• use WT directly• MC sample WT

• Form CF and SHD


Effect of varying frame & kinematic cuts

Watch the green squares --


N=18 <K>=0.9 GeV; LabCMS Frame - no cuts

Watch the green squares


N=18 <K>=0.9 GeV; LabCMS Frame - ||<0.5

kinematic cuts have strong effect!



N=18 <K>=0.9 GeV, LCMS - no cuts


as does choice of frame!



N=18 <K>=0.9 GeV; LCMS - ||<0.5





N=18 <K>=0.9 GeV; PRF - no cuts





N=18 <K>=0.9 GeV; PRF - ||<0.5





Effect of varying multiplicity & total energy

Watch the green squares --


GenBod : 6 pions, <K>=0.5 GeV/c


GenBod : 9 pions, <K>=0.5 GeV/cincreasing mult reduces P.S. constraint



increasing s reduces P.S. constraint


So...

• Energy & Momentum Conservation Induced Correlations (EMCICs) “resemble” our data

• So... on the right track...

• But what to do with that?– Sensitivity to s, Mult of particles of interest and other particles

– will depend on p1 and p2 of particles forming pairs in |Q| bins

risky to “correct” data with Genbod...

• Solution: calculate EMCICs using data!!– Danielewicz et al, PRC38 120 (1988)– Borghini, Dinh, & Ollitraut PRC62 034902 (2000)

– Chajecki & MAL, nucl-th/0612080 - generalization of the above


Distributions w/ phasespace constraints

€

˜ f ( pi) = 2E i f ( pi) = 2E i

dN

d3 pi

single-particle distributionw/o P.S. restriction


Distributions w/ phasespace 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


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

(*) 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-particle distribution in N-particle system

€

pμ2 ≡ d3p ⋅pμ

2 ⋅ ˜ f p( )unmeasuredparent distrib

{∫ ≠ d3p ⋅pμ2 ⋅ ˜ f c p( )

measured{∫N.B.

relevant later


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

⎛

⎝

⎜ ⎜

⎞

⎠

⎟ ⎟

⎛

⎝

⎜ ⎜

⎞

⎠

⎟ ⎟


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

⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟

⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟

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

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟


€

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

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

2-particle correlation function (1st term in 1/N expansion)

“The pT term” “The pZ term” “The E term”

Names used in the following plots


Effect of varying multiplicity & total energy

Same plots as before, but now we look at:

• pT (), pz () and E () first-order terms

• full () versus first-order () calculation

• simulation () versus first-order () calculation


Findings

• first-order and full calculations agree well for N>9– will be important for “experimentalist’s recipe”

• Non-trivial competition/cooperation between pT, pz, E terms

– all three important

• pT1•pT2 term does affect “out-versus-side” (A22)

• pz term has finite contribution to A22 (“out-versus-side”)

• calculations come close to reproducing simulation for reasonable (N-2) and energy, but don’t nail it. Why?– neither (N-k) nor s is infinite– however, probably more important... [next slide]...


Remember...

€

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

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

€

pμ2 ≡ d3p ⋅pμ

2 ⋅ ˜ f p( )unmeasuredparent distrib

{∫ ≠ pμ2

c≡ d3p ⋅pμ

2 ⋅ ˜ f c p( )measured{∫

relevant quantities are average over the (unmeasured) “parent” distribution,not the physical distribution

€

expect pμ2

c< pμ

2

of course, the experimentalist never measures all particles(including neutrinos) or <pT

2> anyway, so maybe not a big loss


€

C(p1,p2) ≅ 1−2

N pT2

NEW PARAM 11 2 3

⋅r p 1,T ⋅

r p 2,T{ } −

1

N pZ2

NEW PARAM 21 2 3

⋅ p1,z ⋅p2,z{ }

−1

N E 2 − E2

( )

NEW PARAM 31 2 4 4 3 4 4

⋅ E1 ⋅E 2{ } +E

N E 2 − E2

( )

NEW PARAM 41 2 4 4 3 4 4

⋅ E1 + E 2{ } +E

2

N E 2 − E2

( )

UNIMPORTANT"NORMALIZED AWAY"

1 2 4 4 3 4 4

where

X{ } denotes the average of X over the (p1,p2) bin. (or r q - bin or whatever we are binning in)

I.e. it is just another histogram which the experimentalist makes, from the data

momenta and energy are measured in the lab frame.

The experimentalist’s recipeTreat the not-precisely-known factors as fit parameters (4 of them)• values determined mostly by large-|Q|; should not cause “fitting hell”• look, you will either ignore it or fit it ad-hoc anyway (both wrong)• this recipe provides physically meaningful, justified form


18 pions, <K>=0.9 GeV


Highly correlatedEMCIC parameters


€

C(p1,p2) = Norm 1− M1 ⋅r p 1,T ⋅

r p 2,T{ } − M2 ⋅ p1,z ⋅p2,z{ } − M3 ⋅ E1 ⋅E 2{ } + M4 ⋅ E1 + E 2{ }+"λ ⋅e

− Rα2 qα

2

α =o,s,l

∑"

⎡

⎣ ⎢ ⎢

⎤

⎦ ⎥ ⎥

The COMPLETE experimentalist’s recipe

€

C(q) + M1 ⋅r p 1,T ⋅

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

femtoscopicfunction ofchoicefit this...

...or image this...


Summary• H.I.C raison d’etre & distinction from p+p

– bulk, thermalized, collective matter

• Momentum-space and femtoscopic probes support bulk collectivity

• The p+p “reference” - [femtoscopic apples-to-apples for the first time]– is it understood?– is it really different than a “small A+A” ?– full understanding must be high priority


Famous picture from famous article by famous guy

Energy loss of energetic partons in quark-gluon plasma:Possible extinction of high pT jets in hadron-hadron collisions

J.D. Bjorken, 1982b


Summary• H.I.C raison d’etre & distinction from p+p

– bulk, thermalized, collective matter

• Momentum-space and femtoscopic probes support bulk collectivity

• The p+p “reference” - [femtoscopic apples-to-apples for the first time]– is it understood?– is it really different than a “small A+A” ?– full understanding must be high priority

• Interpretation complicated by non-femtoscopic correlations

• May be largely due to P.S. restrictions (EMCICs)– numerical studies track data– analytic formulation of EMCIC projection onto femtoscopic analysis

presented– highly non-trivial interplay between cuts, frames, and conserved

components (pz, pT, E)– first-order expansion --> experimentalists’ formula– application to STAR underway

• Hotter spotlight due to impending LHC (December 2007!!)


Thanks to...

• Alexy Stavinsky & Konstantin Mikhaylov (Moscow) [suggestion to use Genbod]

• Jean-Yves Ollitrault (Saclay) & Nicolas Borghini (Bielefeld)[original correlation formula]

• Adam Kisiel (Warsaw) [don’t forget energy conservation]

• Ulrich Heinz (Columbus)[validating energy constraint in CLT]

ma lisa - femtoscopy in small systems & emcics - kent state university - january 20071...

Documents

ma lisa femtoscopy

frankfurt slide

heavy ions bulk matter

progress summary slide

tsuns core slide

phase structure of bulk

insufficient reinteractions

nuclearparticle star