wounded nucleons wounded quarks and relativistic ion ... · wounded nucleons, wounded quarks, and...

11Kraków, 18/05/2007, HBKraków, 18/05/2007, HB

Wounded Nucleons,Wounded Nucleons,Wounded Quarks,Wounded Quarks,and Relativistic Ion and Relativistic Ion

CollisionsCollisionsHelena BiałkowskaHelena Białkowska

Sołtan Institute for Nuclear StudiesSołtan Institute for Nuclear StudiesWarsawWarsaw

Kraków, 18/05/2007, HBKraków, 18/05/2007, HB 22

The Founding Fathers:The Founding Fathers:


What is a wounded nucleon?What is a wounded nucleon?

• A.Białas, M.Błeszyński, W.CzyżNucl.Phys.B111, 461 (1976)

`It is a nucleon that underwent at least one inelastic collision’


The WNM (1976!) The WNM (1976!) –– as usual as usual ––started from experimental started from experimental

observationobservationss::• Series of Fermilab expt`s

on h-A• also European NA5• and lots of emulsion data• Average multiplicity and

increases more slowly than the number of collisions

ηddn /

hAhpA σσ=ν /


Observation: ratio of multiplicities (hA/hp) behaves as

21 ν+=><>=< hphAA nnR /

And this is just the ratio of participants in p-A(1 from p and ν from nucleus A) and in p-p (2 protons)


The Model:The Model:

Particle production in a nuclear collision -a superposition of independent contributionsfrom the wounded nucleons in the projectileand the targetThus you can:

1 just measure NN2 count the participants in h - A3 and you have particle multiplicity in h – A!


0 2 4 6 8 10 12 14 160

2

4

6

8

E178b)

partN21

= A R

chp

p/N

ch=N

AR

⟩ part N⟨

200 GeV d + Au

200 GeV d + Au Min-Bias

+ Pb+ K

+ Pb+π p + C

p + Cu

p + Pb

For p-A:works surprisingly well.from AGS energiesup to RHIC!

Notice:we check here both Npart scalingand pp scaling


New idea: not wounded New idea: not wounded nucleons but wounded quarksnucleons but wounded quarks

Andrzej Białas et al., 1977, Vladimir Anisovitch et al., 1978


Additive Quark ModelAdditive Quark Model

1982 Białas et al.:Specific predictions for nuclear collisions on the basis ofthe Additive Quark Model - with particle production fromthree sources:Breaking of the color strings between quarks fromthe projectile and the targetFragmentation of wounded quarks Fragmentation of spectator quarks


Thus for the central region

Ratio of multiplicities in A-B to that in pp given by

ABqq

qBqABARσσσσ

=),(


PrePre--history: 1980history: 1980

AQM

2.06.3 ±=dTaCTa Model: 3.0

1.07.1 ±=dTaTaα Model 1.6

P,d,α,C on Ta, 4.2 GeV/NJINR DUBNA


First real high energy nuclearbeams:200 GeV/c O and Sfrom SPS

More history: NA35

K. Kadija et al., ZPhysC66,393(1995)consistent parametrization of production rates ofnegatives – proportional to the number ofwounded nucleonsand of kaons – proportional to wounded quarks


WNAB works

for negatives

… andit does not

for K0s


For kaons- need Wq


Now for RHIC A – A data: PHOBOSWhite Paper

Notice: AuAuscaled by ppat twicethe energy!(to account for ‘leading baryon’)

s2


Almost the same plot

Here it looks better

but…read the fine print!

AuAu normalizedto e+e-


Intriguing scaling/universality for multiplicity/participant

ee

pp

AA central

Energy dependence


Look more closely at total multiplicity per Npart

for Au - Au

Proportionality,but higher than for ppat the same energy

pp systematically lower

WNM does not work


Still, the scaling withStill, the scaling with NNpartpartis surprisingis surprising

and not only for total multiplicities ::

Au+Au35-40%,Npart = 98

Cu+CuPreliminary

3-6%, Npart = 96

62.4 GeV

Cu+CuPreliminary

3-6%, Npart = 100

200 GeV

Au+Au35-40%, Npart = 99

PHOBOS

dN/dηPHOBOS


PHOBOS Au+Au PRL 94,082304(2005)PLB578,297(2004)

Cu+Cu PRL96:212301(2006)

This ‘geometric’ scaling with Npart worksnot only for soft (low pt) data!

Cu+Cupreliminary

Au+Au

dydp/NdNdydp/NdR

Tpp2

coll

TAA2

AA =


Still new data:Still new data:

also scaleswith Npart

Net baryon density at midrapidity

PHOBOS, PhysRev C75:024910,2007


A very specific comeA very specific come--back of back of WNMWNM

A.Białas & W.Czyż, first presented in Zakopane in 2004:a two-component WNM to describe d-Au at 200 GeV/c

Basic assumption:Superposition of independent contributionsfrom WN in the projectile and the targetApplies not only to the total charged multiplicitybut longitudinal spectra also


Density of particles in A – B collision:

)()( yFwyFwdy

dNBBAA

AB +=

)()( yFyF AB −=The model requires

(F is a contribution from a singlewounded nucleon)

And the first consequence is

)(21)0( BAAB wwyR +==


R (y = 0)Au-d

8

7

6

5

4

3

2

1

W +W

2Au d

W +W

2Au d

1 2 3 4 5 6 7 8 9

PHOBOSdAu 200 GeV

A. Białas, W. Czyż, Acta Phys. Pol. B36, 905(2005)


For full (pseudo)rapidity range: construct symmetric and antisymmetric component

ηη

ηηη

ddN

ddNG )()()( −

±=

aa )(2

)( ηη ++ Φ+

= dAu wwG )(2

)( ηη ++ Φ+

= dAu wwG

The Model predicts:

where

2/][)()( c

dcAuc

cc

wwG

+ΣΣ

=Φ+

+ ηη(c– centrality}


Symmetric andSymmetric and antisymmetricantisymmetric part part of the inclusiveof the inclusive xsectionxsection for several for several

centralitiescentralities dAudAu::ηddN

cent

ralit

yη

Comparison Model vs data (PHOBOS)for several centralities


Next step: Next step:

)()0()( ppddNRdAu

ddN

dAu ηη−

Model looks OK for d hemispherenot so good for Au

Next step: determine contribution from a single wounded nucleon


The contribution from one wounded nucleonextends over (almost) full rapidity rangeThere is a big difference between its symmetricand antisymmetric part

Authors interpretation:

Two step particle production:1. Multiple color exchanges between partons from projectile

and target2. Particle emission from color sources created in step 1

(AB+Marek Jeżabek, Phys.Lett.B590,233 (2004))


Revival of wounded quarks Revival of wounded quarks concept for A concept for A -- AA

S. Eremin & S.Voloshin, Phys.Rev.C67, 064905 (2003)

As Recall:at midrapidity –increase of dN/dηper participantwith Npart


TryTry NNqq--partpart instead ofinstead of NNNpartNpart

To calculate: use same Nuclear Overlap Calculation(K.J.Eskola et al.,Nucl.Phys.B323,37(1989))as for N-N, but change density and σ


CalculatingCalculating NNnn--partpart andand NNqq--partpart

partnN −

fm53.0dfm)A86.0A12.1(R

fm17.0n]d/)Rrexp[(1

n)r(n

3/13/1

30

0A

=−=

=

−+=

−

−

}]A

)s(T1[1){bs(sTd

}]B

)bs(T1[1){s(sTd|N

AAinelNN

B2

BBinelNN

A2

ABpartn

rrr

rrr

σ−−−+

−σ−−=

∫

∫−

)zb(dzn)b(T 22A∫

+∞

∞−+=

partqN −

30

q0 fm51.0n3n −==

9/inelNNqq σ=σ

Mass numbers of collidingnuclei are 3 times larger,but their size is the same.

For pp the same procedurewith A=B=3, hard sphere R=0.8fm.


0 2 4 6 8 10 12 14 16 180

200

400

600

800

1000

1200

par

tN

Impact parameter b (fm)

Nucleon

a)

Constituent Quarks

: Au+Au at 200 GeVn-part

N

: Au+Au at 130 GeVn-part

N

: Au+Au at 62.4 GeVn-part

N

: Au+Au at 19.6 GeVn-part

N

: Au+Au at 200 GeVq-part

N

: Au+Au at 130 GeVq-part

N

: Au+Au at 62.4 GeVq-part

N

: Au+Au at 19.6 GeVq-part

N0 1 2 3 4 5

350

355

360

365

370

375

380

par

tN

Impact parameter

Nucleon


Compare NCompare NNN,, NNqqtwo versions of qqσ

0

200

400

600

800

1000

1200

0 2 4 6 8 10 12 14 16b (fm)

NN-part

Quark participantsNucleon participants

(a)

0

0.5

1

1.5

2

2.5

0 50 100 150 200 250 300 350 400NN-part

Nq-part/NN-part

(b)


Eremin & Voloshin

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 50 100 150 200 250 300 350NN-part

(dNch/d

η)/(

<Npart>/2)

- √s=200 GeV

- √s=130 GeV

Scale bynucleon participants

increase

Scale byquark participants

perhaps slight decrease

(full vs empty: different σ)


How does it work at SPS?Nucleon participants

0.6

0.8

1

1.2

1.4

chγET

((dN

,dE

T)/

dη)/

NN

-par

t

0

0.2

0.4

0.6

0.8

1

0 50 100 150 200 250 300 350 400NN-part

((dN

,dE

T)/

dη)/

Nq-

part

Netrakanti & Mohanty, PRC70(2004)027901

look at WA98 data 158 GeV/n Pb-Pb

Quark participants


Bhaskar De & S.Bhattacharyya PRC 71(2005) 024903look at NA49 data (SPS)

nucleons

Noticelog scale…

quarks


Caveat:

D & B write about ‘integrated yields’ in figure caption,

but show integrated yields for p, Kand midrapidity values for pbar, d

(plots to be re-done by NA49)


Moreover...

When you put together light and heavy nuclei,you see that Npart is not a good scaling variablefor strange particles


Now for the energy Now for the energy dependence:dependence:

R.Nouicer, nucl-ex/051244,2005

One step further: energy dependenceR.Nouicer nucl-ex/0512044

Midrapidity charged particle density normalized to:

Nucleon participants Quark participants


Again: Caveat

The author normalizes pp databy the number of quark participantsfor ‘most central’ pp collisions

Is this the correct procedure?


1 10 210 3100

1

2

3

4

5

-0.02 + 0.27 ln (s)

/2)

⟩p

art

N⟨/(η

/dch

dN

(GeV)NN s

) + p p p(

A + A

)n-partAuAu (norm. N) n-partCuCu (norm. N n-partPbPb (norm. N

)n-part

p (norm. Np)n-partpp (norm. N

)q-partAuAu (norm. N) q-partCuCu (norm. N q-partPbPb (norm. N

)q-part

p (norm. Np)q-partpp (norm. N

p+p 200 GeV(Nq-part)inclusive ≈2.4

(Nq-part)central ≈3.5

(plot stolen from Barbara Wosiek,who noticed the problem)


SpinSpin--off/extensions:off/extensions:

• `Used nucleon model’• `Wounded quarks and diquarks’

• `Dissipating energy participants’(E.Sarkisyan, A.Sakharov)

A. Bzdak, A.Białas (next talk)


For pp: ‘practically’ only single quark contributesFor central AA: ‘practically’ all 3 quarks from each nucleon contribute

(Sarkisyan&Sakharov)

Note differentenergy scale:


An attempt at a summary:An attempt at a summary:

Wounded nucleons remarkably successful in parameterization of global characteristics of particle production

Nobody expects everything to be just a multiplication of N-N but the proportionalitylooks intriguing

Wounded quarks - perhaps better scaling?

wounded nucleons wounded quarks and relativistic ion ... · wounded nucleons, wounded quarks, and...

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