1 Zakopane, June 06, HB Wounded Nucleons, Wounded Quarks, and Relativistic Ion Collisions Helena Białkowska Institute for Nuclear Studies Warsaw

Zakopane, June 06, HB2 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

Zakopane, June 06, HB3 The WNM (1976!) – as usual – started from experimental 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

Zakopane, June 06, HB4 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

Zakopane, June 06, HB5 The Model: Particle production in a nuclear collision - a superposition of independent contributions from the wounded nucleons in the projectile and the target Thus you can: 1 just measure NN 2 count the participants in h - A 3 and you have particle multiplicity in h – A!

Zakopane, June 06, HB6 For p-A: works surprisingly well. from AGS energies up to RHIC! Notice: we check here both N part scaling and pp scaling

Zakopane, June 06, HB7 New idea: not wounded nucleons but wounded quarks Andrzej Białas et al., 1977, Vladimir Anisovitch et al., 1978

Zakopane, June 06, HB8 Additive Quark Model 1982 Białas et al.: Specific predictions for nuclear collisions on the basis of the Additive Quark Model - with particle production from three sources: Breaking of the color strings between quarks from the projectile and the target Fragmentation of wounded quarks Fragmentation of spectator quarks

Zakopane, June 06, HB9 Pre-history: 1980 P,d, ,C on Ta, 4.2 GeV/N JINR DUBNA Model: 3.0 Model 1.6 AQM

Zakopane, June 06, HB10 First real high energy nuclear beams: 200 GeV/c O and S from SPS K. Kadija et al., ZPhysC66,393(1995) consistent parametrization of production rates of negatives – proportional to the No of wounded nucleons and of kaons – proportional to wounded quarks More history: NA35

Zakopane, June 06, HB11 W N AB works for negatives … and it does not for K 0s

Zakopane, June 06, HB12 For kaons - need W q

Zakopane, June 06, HB13 Now for RHIC A – A data: Notice: AuAu scaled by pp at twice the energy! (to account for ‘leading baryon’) PHOBOS White Paper

Zakopane, June 06, HB14 Here it looks better but… read the fine print! AuAu normalized to e + e - Almost the same plot

Zakopane, June 06, HB15 Look more closely at total multiplicity per N part Proportionality, but higher than for pp at the same energy pp systematically lower WNM does not work for Au - Au

Zakopane, June 06, HB16 Still, the scaling with N part is surprising Au+Au 35-40%,N part = 98 Cu+Cu Preliminary 3-6%, N part = GeV Cu+Cu Preliminary 3-6%, N part = GeV Au+Au 35-40%, N part = 99 PHOBOS dN/d  PHOBOS and not only for total multiplicities : :

Zakopane, June 06, HB17 Cu+Cu preliminary Au+Au PHOBOS Au+Au PRL 94,082304(2005) PLB578,297(2004) Cu+Cu PRL(2006) accepted This ‘geometric’ scaling with N part works not only for soft (low pt) data! (courtesy of Barbara Wosiek)

Zakopane, June 06, HB18 A very specific come-back of WNM 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 contributions from WN in the projectile and the target Applies not only to the total charged multiplicity but longitudinal spectra also

Zakopane, June 06, HB19 Density of particles in A – B collision: The model requires And the first consequence is (F is a contribution from a single wounded nucleon)

Zakopane, June 06, HB20 A. Białas, W. Czyż, Acta Phys. Pol. B36, 905(2005) PHOBOS dAu 200 GeV

Zakopane, June 06, HB21 For full (pseudo)rapidity range: construct symmetric and antisymmetric component And compare to data:

Zakopane, June 06, HB22 Symmetric and antisymmetric part for several centralities dAu: centrality

Zakopane, June 06, HB23 Two step particle production: 1.Multiple color exchanges between partons from projectile and target 2.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 nucleon extends over full rapidity range There is a big difference between its symmetric and antisymmetric part

Zakopane, June 06, HB24 Revival of wounded quarks concept for A - A S. Eremin & S.Voloshin, Phys.Rev.C67, (2003) As Recall: at midrapidity – increase of dN/d  per participant with N part

Zakopane, June 06, HB25 Try N q-part instead of N Npart 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 

Zakopane, June 06, HB26 Calculating N n-part and N q-part Mass numbers of colliding nuclei are 3 times larger, but their size is the same. For pp the same procedure with A=B=3, hard sphere R=0.8fm.

Zakopane, June 06, HB27 Compare N N, N q two versions of

Zakopane, June 06, HB28

Zakopane, June 06, HB29 Eremin & Voloshin Scale by nucleon participants Scale by quark participants increase perhaps slight decrease (full vs empty: different 

Zakopane, June 06, HB30 How does it work at SPS? Netrakanti & Mohanty, PRC70(2004) look at WA98 data 158 GeV/n Pb-Pb Nucleon participants Quark participants

Zakopane, June 06, HB31 Same trick at RHIC:

Zakopane, June 06, HB32 Bhaskar De & S.Bhattacharyya PRC 71(2005) look at NA49 data (SPS) Notice log scale… nucleons quarks

Zakopane, June 06, HB33 Caveat: D & B write about ‘integrated yields’ in figure caption, but show integrated yields for p, K and midrapidity values for pbar, d (plots to be re-done by NA49)

Zakopane, June 06, HB34 Moreover... When you put together light and heavy nuclei, you see that Npart is not a good scaling variable for strange particles

Zakopane, June 06, HB35 Now for the energy dependence: R.Nouicer, nucl-ex/051244,2005 One step further: energy dependence R.Nouicer nucl-ex/ Midrapidity charged particle density normalized to: Nucleon participants Quark participants

Zakopane, June 06, HB36 Again: Caveat The author normalizes pp data by the number of quark participants for ‘most central’ pp collisions Is this a correct procedue?

Zakopane, June 06, HB37 p+p 200 GeV (N q-part ) inclusive  2.4 (N q-part ) central  3.5 ( plot stolen from Barbara Wosiek, who noticed the problem)

Zakopane, June 06, HB38 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?

Zakopane, June 06, HB39 Disclaimer 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