wounded nucleons, wounded quarks, and relativistic ion collisions

11Zakopane, June 06, HBZakopane, June 06, HB

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

CollisionsCollisionsHelena BiałkowskaHelena Białkowska

Institute for Nuclear StudiesInstitute for Nuclear Studies

WarsawWarsaw

Zakopane, June 06, HBZakopane, June 06, HB 22

What is a wounded nucleon?What is a wounded nucleon?• Classic definition,

given by Białas, Błeszyński & Czyż in 1976:

It is a nucleon that underwent at least one inelastic collision


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

observation:observation:• 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

ddn /

hAhpA /


21 hphAA nnR /

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

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


The Model:The Model:

Particle production in a nuclear collision -a superposition of independent contributionsfrom the wounded nucleons in the projectileand the target

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


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

qBqA

ABABR


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


Pre-history: 1980Pre-history: 1980

2.06.3 dTa

CTa

P,d,,C on Ta, 4.2 GeV/NJINR DUBNA

Model: 3.0

1.07.1 dTa

Ta Model 1.6

AQM


First real high energy nuclear beams:200 GeV/c O and S from SPSK. Kadija et al., ZPhysC66,393(1995) consistent parametrization of production rates of negatives – proportional to the No of wounded nucleonsand of kaons – proportional to wounded quarks

More history: NA35


WNAB works

for negatives

… and it does not for K0s


For kaons - need Wq


Now for RHIC A – A data:

Notice: AuAuscaled by ppat twice the energy!

s2

(to account for ‘leading baryon’)

PHOBOSWhite Paper


Here it looks better

but… read the fine print!

AuAu normalizedto e+e-

Almost the same plot


Look more closely at total multiplicity per Npart

Proportionality,but higher than for ppat the same energy

pp systematically lower

WNM does not work

for Au - Au


Still, the scaling with NStill, the scaling with Npartpart

is surprisingis surprising

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/dPHOBOS

and not only for total multiplicities ::


Cu+Cupreliminary

Au+Au

dydp/NdN

dydp/NdR

Tpp2

coll

TAA2

AA

PHOBOS Au+Au PRL 94,082304(2005) PLB578,297(2004) Cu+Cu PRL(2006) accepted

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

(courtesy ofBarbara Wosiek)


A very specific come-back of A very specific come-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

The model requires )()( yFyF AB

And the first consequence is

)(2

1)0( BAAB wwyR

(F is a contribution from a singlewounded nucleon)


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

PHOBOSdAu 200 GeV


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

d

dN

d

dNG

)()()(

And compare to data:


Symmetric and antisymmetric part Symmetric and antisymmetric part for several centralities dAu:for several centralities dAu:

ddN

ce

ntr

alit

y


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))

Interpretation by the authors:

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


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

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

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


Try NTry Nq-partq-part instead of N instead of NNpartNpart

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


Calculating NCalculating Nn-partn-part and N and Nq-partq-part

partnN partqN

fm53.0d

fm)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

)zb(dzn)b(T 22A

30

q0 fm51.0n3n

9/inelNNqq

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.


Compare NCompare NNN, N, Nqq

two versions of qq


Eremin & Voloshin

Scale bynucleon participants

Scale byquark participants

increase

perhaps slight decrease

(full vs empty: different


How does it work at SPS?

Netrakanti & Mohanty, PRC70(2004)027901

look at WA98 data 158 GeV/n Pb-Pb

Nucleon participants

Quark participants


Same trick at RHIC:


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

Noticelog scale…

nucleons

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 data by the number of quark participants for ‘most central’ pp collisions

Is this a correct procedue?


p+p 200 GeV

(Nq-part)inclusive 2.4 (Nq-part)central 3.5

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


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

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

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

looks intriguing

Wounded quarks - perhaps better scaling?


DisclaimerDisclaimer

• I am fully aware that A-A collisions at high energy produce something that can not be fully described in terms of simple hadronic degrees of freedom and/or nuclear geometry

wounded nucleons, wounded quarks, and relativistic ion collisions

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