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 33
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’
Kraków, 18/05/2007, HBKraków, 18/05/2007, HB 44
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 /
Kraków, 18/05/2007, HBKraków, 18/05/2007, HB 55
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)
Kraków, 18/05/2007, HBKraków, 18/05/2007, HB 66
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!
Kraków, 18/05/2007, HBKraków, 18/05/2007, HB 77
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
Kraków, 18/05/2007, HBKraków, 18/05/2007, HB 88
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
Kraków, 18/05/2007, HBKraków, 18/05/2007, HB 99
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
Kraków, 18/05/2007, HBKraków, 18/05/2007, HB 1010
Thus for the central region
Ratio of multiplicities in A-B to that in pp given by
ABqq
qBqABARσσσσ
=),(
Kraków, 18/05/2007, HBKraków, 18/05/2007, HB 1111
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
Kraków, 18/05/2007, HBKraków, 18/05/2007, HB 1212
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
Kraków, 18/05/2007, HBKraków, 18/05/2007, HB 1515
Now for RHIC A – A data: PHOBOSWhite Paper
Notice: AuAuscaled by ppat twicethe energy!(to account for ‘leading baryon’)
s2
Kraków, 18/05/2007, HBKraków, 18/05/2007, HB 1616
Almost the same plot
Here it looks better
but…read the fine print!
AuAu normalizedto e+e-
Kraków, 18/05/2007, HBKraków, 18/05/2007, HB 1717
Intriguing scaling/universality for multiplicity/participant
ee
pp
AA central
Energy dependence
Kraków, 18/05/2007, HBKraków, 18/05/2007, HB 1818
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
Kraków, 18/05/2007, HBKraków, 18/05/2007, HB 1919
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
Kraków, 18/05/2007, HBKraków, 18/05/2007, HB 2020
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 =
Kraków, 18/05/2007, HBKraków, 18/05/2007, HB 2121
Still new data:Still new data:
also scaleswith Npart
Net baryon density at midrapidity
PHOBOS, PhysRev C75:024910,2007
Kraków, 18/05/2007, HBKraków, 18/05/2007, HB 2222
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
Kraków, 18/05/2007, HBKraków, 18/05/2007, HB 2323
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 +==
Kraków, 18/05/2007, HBKraków, 18/05/2007, HB 2424
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)
Kraków, 18/05/2007, HBKraków, 18/05/2007, HB 2525
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}
Kraków, 18/05/2007, HBKraków, 18/05/2007, HB 2626
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
Kraków, 18/05/2007, HBKraków, 18/05/2007, HB 2727
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
Kraków, 18/05/2007, HBKraków, 18/05/2007, HB 2828
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))
Kraków, 18/05/2007, HBKraków, 18/05/2007, HB 2929
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
Kraków, 18/05/2007, HBKraków, 18/05/2007, HB 3030
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
Kraków, 18/05/2007, HBKraków, 18/05/2007, HB 3131
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.
Kraków, 18/05/2007, HBKraków, 18/05/2007, HB 3232
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
Kraków, 18/05/2007, HBKraków, 18/05/2007, HB 3333
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)
Kraków, 18/05/2007, HBKraków, 18/05/2007, HB 3434
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)
Kraków, 18/05/2007, HBKraków, 18/05/2007, HB 3535
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
Kraków, 18/05/2007, HBKraków, 18/05/2007, HB 3636
Bhaskar De & S.Bhattacharyya PRC 71(2005) 024903look at NA49 data (SPS)
nucleons
Noticelog scale…
quarks
Kraków, 18/05/2007, HBKraków, 18/05/2007, HB 3737
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)
Kraków, 18/05/2007, HBKraków, 18/05/2007, HB 3838
Moreover...
When you put together light and heavy nuclei,you see that Npart is not a good scaling variablefor strange particles
Kraków, 18/05/2007, HBKraków, 18/05/2007, HB 3939
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
Kraków, 18/05/2007, HBKraków, 18/05/2007, HB 4040
Again: Caveat
The author normalizes pp databy the number of quark participantsfor ‘most central’ pp collisions
Is this the correct procedure?
Kraków, 18/05/2007, HBKraków, 18/05/2007, HB 4141
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)
Kraków, 18/05/2007, HBKraków, 18/05/2007, HB 4242
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)
Kraków, 18/05/2007, HBKraków, 18/05/2007, HB 4343
For pp: ‘practically’ only single quark contributesFor central AA: ‘practically’ all 3 quarks from each nucleon contribute
(Sarkisyan&Sakharov)
Note differentenergy scale:
Kraków, 18/05/2007, HBKraków, 18/05/2007, HB 4444
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?