mike lisa - winter workshop on nuclear dynamics -12 april 2008 1 how interesting is momentum...

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

SSulfur32.066

16 286 U

Uranium238.02891

183221

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

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

Spectra

Flow-dominated “Blast-wave”toy models capture main characteristicse.g. PRC70 044907 (2004)

mT (GeV/c)

STAR PRL 91 262301 (2003)

space-momentum substructure mapped in detail

p+p: A clear reference system?

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?

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

{ } −1 ⎛ ⎝ ⎜

⎞ ⎠ ⎟

⎣ ⎢ ⎤

⎦ ⎥

typical “Gaussian” fitting function

The essence of CMB at a glance - decomposing WMAP survey

al,m ≡ dΩ ⋅T θ ,φ( ) ⋅Yl ,m* θ ,φ( )∫

ClTT ≡ al ,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

QLONG Q

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)

r Q ( ) =

ΔcosθΔφ

4πYl ,m

* θ i ,φi( )Cr Q , cosθ i ,φi( )

∑nucl-ex/0505009 & arXiv:0803.0022 [nucl-th]

QLONG Q

• Al,m coefficients encode strength and order of

angular oscillations

simulated events

r Q ( ) =

ΔcosθΔφ

4πYl ,m

angular oscillations• ... for each |Q| !

simulated events

simulated eventsEMCICs only

r Q ( ) =

ΔcosθΔφ

4πYl ,m

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]

r Q ( ) =

ΔcosθΔφ

4πYl ,m

simulated eventsEMCICs only

C(Qout)

C(Qside)

C(Qlong)

Cr q ( ) = N ⋅ 1+ λ ⋅ Kcoul

r q ( ) ⋅ 1+ e

− qo2Ro

2 +qs2Rs

2 +ql2Rl

{ } −1 ⎛ ⎝ ⎜

⎞ ⎠ ⎟

⎣ ⎢ ⎤

⎦ ⎥

C(Qout)

C(Qside)

C(Qlong)

For femtoscopic correlations

Cr q ;

r q → ∞( ) = C

r q → ∞( )

⇒ Al ≠0m r

q → ∞( ) = 0

• 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

{ } −1 ⎛ ⎝ ⎜

⎞ ⎠ ⎟

⎣ ⎢ ⎤

⎦ ⎥

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 ( )

C r P ab r

q ( ) |r q |→∞ ⏐ → ⏐ ⏐ Konst.

STAR preliminary d+Au peripheral collisions

Gaussian fit

For femtoscopic correlations

Cr q ;

r q → ∞( ) = C

r q → ∞( )

⇒ Al ≠0m r

q → ∞( ) = 0

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

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

energy-momentum conservation in n-body states

f α( ) =d

2⋅Rn( )

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

∑ ⎛

⎝ ⎜ ⎜

⎠ ⎟ ⎟ δ pi

2 − mi2

( )d4pi

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

4pi =r p 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

∑ ⎛

⎝ ⎜ ⎜

⎠ ⎟ ⎟

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

→ Probevent α ∝d3n

• 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

Correlations arising from conservation laws (PS constraints)

˜ f ( pi) = 2E i f ( pi) = 2E i

single-particle distributionw/o P.S. restriction

˜ f c(p1,...,pk ) ≡ ˜ f (pi)i=1

∏ ⎛ ⎝ ⎜ ⎞

⎠ ⎟⋅

˜ f (pi)i= k +1

∏ ⎛

⎝ ⎜

⎠ ⎟∫ δ 4 pi

∑ − P ⎛

⎝ ⎜

⎠ ⎟

˜ f (pi)i=1

∏ ⎛

⎝ ⎜

⎠ ⎟∫ δ 4 pi

∑ − P ⎛

⎝ ⎜

⎠ ⎟

= ˜ f (pi)i=1

∏ ⎛ ⎝ ⎜ ⎞

⎠ ⎟⋅

d4piδ(pi2 − mi

2)˜ f (pi)i= k +1

∏ ⎛ ⎝ ⎜ ⎞

⎠ ⎟∫ δ 4 pi

∑ − P ⎛

⎝ ⎜

⎠ ⎟

d4piδ(pi2 − mi

2)˜ f (pi)i=1

∏ ⎛ ⎝ ⎜ ⎞

⎠ ⎟∫ δ 4 pi

∑ − P ⎛

⎝ ⎜

⎠ ⎟

k-particle distribution (k<N) with P.S. restriction

no othercorrelations

what wemeasure

Using central limit theorem (“large N-k”)

˜ f c(p1,...,pk ) = ˜ f (pi)i=1

∏ ⎛ ⎝ ⎜ ⎞

⎠ ⎟ N

N − k

⎝ ⎜

⎠ ⎟2

exp −

pi,μ − pμ( )i=1

∑ ⎛

⎝ ⎜

⎠ ⎟

2(N − k)σ μ2

μ = 0

⎜ ⎜ ⎜ ⎜ ⎜

⎟ ⎟ ⎟ ⎟ ⎟

σ μ2 = pμ

2 − pμ

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

Using central limit theorem (“large N-k”)

˜ f c(p1,...,pk ) = ˜ f (pi)i=1

∏ ⎛ ⎝ ⎜ ⎞

⎠ ⎟ N

N − k

⎝ ⎜

⎠ ⎟2

exp −

pi,μ − pμ( )i=1

∑ ⎛

⎝ ⎜

⎠ ⎟

2(N − k)σ μ2

μ = 0

⎜ ⎜ ⎜ ⎜ ⎜

⎟ ⎟ ⎟ ⎟ ⎟

σ μ2 = pμ

2 − pμ

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

∏ ⎛ ⎝ ⎜ ⎞

⎠ ⎟⋅

d4 piδ(pi2 − mi

2) ˜ f (pi)i= k +1

∏ ⎛ ⎝ ⎜ ⎞

⎠ ⎟∫ δ 4 pi

∑ − P ⎛

⎝ ⎜

⎠ ⎟

d4 piδ(pi2 − mi

2) ˜ f (pi)i=1

∏ ⎛ ⎝ ⎜ ⎞

⎠ ⎟∫ δ 4 pi

∑ − 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)

Effects on single-particle distribution

˜ f c(pi) = ˜ f (pi)N

N −1

⎝ ⎜

⎠ ⎟2

exp −pi,μ − pμ( )

2(N −1)σ μ2

μ = 0

∑ ⎛

⎜ ⎜

⎟ ⎟

= ˜ f (pi)N

N −1

⎝ ⎜

⎠ ⎟2

exp −1

2(N −1)

+E i − E( )

E 2 − E2

⎜ ⎜

⎟ ⎟

⎜ ⎜

⎟ ⎟

in this case, the index i is only keepingtrack of particle type, really

k-particle correlation function

C(p1,...,pk ) ≡˜ f c(p1,...,pk )

˜ f c(p1)....̃ f c(pk )

N − k

⎝ ⎜

⎠ ⎟2

N −1

⎝ ⎜

⎠ ⎟2k

exp −1

2(N − k)

px,ii=1

∑ ⎛ ⎝ ⎜ ⎞

⎠ ⎟2

+py,ii=1

∑ ⎛ ⎝ ⎜ ⎞

⎠ ⎟2

+pz,ii=1

∑ ⎛ ⎝ ⎜ ⎞

⎠ ⎟2

+E i − E( )

∑ ⎛ ⎝ ⎜ ⎞

⎠ ⎟2

E 2 − E2

⎜ ⎜ ⎜

⎟ ⎟ ⎟i=1

⎜ ⎜ ⎜

⎟ ⎟ ⎟

exp −1

2(N −1)

+E i − E( )

E 2 − E2

⎜ ⎜

⎟ ⎟

∑ ⎛

⎜ ⎜

⎟ ⎟

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

r p T,1 ⋅

r p T,2

+pz,1 ⋅pz,2

+E1 − E( ) ⋅ E 2 − E( )

E 2 − E2

⎝ ⎜ ⎜

⎠ ⎟ ⎟

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

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

femtoscopy in p+p @ STAR

DELPHI

Z0 decay @ LEP

m, mT (GeV)

hep-ph/0108194

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”...)

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?

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 remember!

˜ f c( pi ) = ˜ f (pi )N

N −1

⎝ ⎜

⎠ ⎟2

exp −1

2(N −1)

2 pT ,i2

+pz ,i

+Ei − E( )

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 −1

⎝ ⎜

⎠ ⎟2

exp −1

2(N −1)

2 pT ,i2

+Ei − E( )

E2 − E2

⎝ ⎜ ⎜

⎠ ⎟ ⎟

⎜ ⎜

⎟ ⎟

where N is for minbias p + p, and N A+A ≈ ∞

Then we would measure:

Multiplicity evolution of spectra - p+p to A+A (soft sector)

˜ f cp+ p pT ,i( )

˜ f cA+A pT ,i( )

N −1

⎝ ⎜

⎠ ⎟3/2

exp −1

2(N −1)

2 pT ,i2

+Ei − E( )

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

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

⎝ ⎜

⎠ ⎟

2 N2 −1( )−

2 N1 −1( )

⎝ ⎜

⎠ ⎟2 pT ,i

+Ei − E( )

E2 − E2

⎝ ⎜ ⎜

⎠ ⎟ ⎟

⎜ ⎜

⎟ ⎟

Then we would measure:

pion mass assumed

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

⎝ ⎜

⎠ ⎟

2 N2 −1( )−

2 N1 −1( )

⎝ ⎜

⎠ ⎟2 pT ,i

+Ei − E( )

E2 − E2

⎝ ⎜ ⎜

⎠ ⎟ ⎟

⎜ ⎜

⎟ ⎟

pion 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)

˜ f cN1 pT ,i( )

˜ f cN 2 pT ,i( )

=N2 −1( )N1

N1 −1( )N2

⎝ ⎜

⎠ ⎟

2 N2 −1( )−

2 N1 −1( )

⎝ ⎜

⎠ ⎟2 pT ,i

+Ei − E( )

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

⎝ ⎜

⎠ ⎟

2 N2 −1( )−

2 N1 −1( )

⎝ ⎜

⎠ ⎟2 pT ,i

+Ei − E( )

E2 − E2

⎝ ⎜ ⎜

⎠ ⎟ ⎟

⎜ ⎜

⎟ ⎟

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?!

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

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

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

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

THEEND

mike lisa - winter workshop on nuclear dynamics -12 april 2008 1 how interesting is momentum...

mike lisa winter workshop

nuclear dynamics

pp r aa

p p reference

pion femtoscopy slide

aa coincidental

momentum conservation

intense study slide

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