In ultra-relativistic heavy ion collisions, early stage multiple scatterings may lead to an increase of the color electric field strength. Consequently, particle production - especially heavy quark (and di-quark) production - is greatly enhanced according to the Schwinger mechanism. We test this idea via the Ultra-relativistic Quantum Molecular Dynamics model (UrQMD) for Au+Au collisions at the full RHIC energy (ps = 200 AGeV). Relative to p+p collisions, a factor of 60, 20 and 7 enhancement respectively, for (sss), (ss), and , (s) is predicted for a model with increased color electric field strength

Bleicher, Marcus

Greiner, Walter

Stöcker, Horst

Xu, Nu

English

Hochschulschriftenserver - Universität Frankfurt am Main

arXiv:hep-ph/0007215 v1   19 Jul 2000Strangeness enhancement from strong color ﬁelds at RHICM. Bleichera,ξ∗, W. Greinerb, H. St¨ ockerb, N. Xuaa Nuclear Science Division, Lawrence Berkeley Laboratory, Berkeley, CA 94720, U.S.A.bInstitut f¨ ur Theoretische Physik, Goethe-Universit¨ at, 60054 Frankfurt am Main, GermanyIn ultra-relativistic heavy ion collisions, early stage mul-tiple scatterings may lead to an increase of the color elec-tric ﬁeld strength. Consequently, particle production - espe-cially heavy quark (and di-quark) production - is greatly en-hanced according to the Schwinger mechanism. We test thisidea via the Ultra-relativistic Quantum Molecular Dynamicsmodel (UrQMD) for Au+Au collisions at the full RHIC en-ergy (√s = 200 AGeV). Relative to p+p collisions, a factorof 60, 20 and 7 enhancement respectively, for Ω (sss), Ξ (ss),and Λ, Σ (s) is predicted for a model with increased colorelectric ﬁeld strength.LBNL-preprint: LBNL-46167One of the major goals of the relativistic heavy ioncollider (RHIC) at Brookhaven National Laboratory is toexplore the phase diagram of hot and dense matter nearthe quark gluon plasma (QGP) phase transition. TheQGP is a state in which the individual hadrons dissolveinto a gas of free (or almost free) quarks and gluons instrongly compressed and hot matter (for recent reviewson the topic, we refer to [1,2]). The achievable energy-and baryon densities depend on the extend to which thenuclei are stopped during penetration, thus on centralityand bombarding energy.Strange particles, especially multi-strange baryons(which have more than one strange quark) carry vitalinformation about the collision dynamics [3–10]. Rela-tive strangeness abundancies have been proposed as apowerful tool for searching the transition from hadronicmatter to partonic matter in high energy nuclear col-lisions [3–5]. Indeed, strangeness enhancement has beobserved in heavy ion collisions at all collision energieswith diﬀerent colliding systems.Recently, measurements by the WA97 and the NA49collaborations clearly demonstrated the relative enhance-ment of the (anti-)hyperon yields (Λ, Ξ, Ω) in Pb-Pbcollisions as compared to p-Pb collisions [11–16]. Theobserved enhancement increases with the strangenesscontent (|S| = 1,2,3) of the probe under investigation∗Feodor Lynen Fellow of the Alexander v. Humboldt Foun-dation, E -mail: bleicher@nta2.lbl.gov[11–16]. For the (Ω−+Ω−)-yield the enhancement factoris as large as 15.A number of diﬀerent mechanisms are under debate tounderstand this strong increase in strangeness productionwith centrality and beam energy:• Equilibrated (gluon rich) plasma phase: Chemi-cal and ﬂavour equilibration times are predicted tobe shorter in a plasma phase than in a thermallyequilibrated hadronic ﬁreball of T ∼ 160MeV[3]. Thus, a dominant production mechanism forstrangeness in an equilibrated gluon rich plasmaphase (Hot glue scenario [17]), might be the produc-tion of ss pairs via gluon fusion (gg → ss) [3]. Thismight allow for strangeness equilibration within thelifetime of the QGP, resulting in strong strangenessenhancement compared to hadronic scenarios.• Baryon-junctions: A baryon junction exchangemechanism was proposed to explain valence baryonnumber transport in nuclear collisions. Recently itwas extended to study midrapidity (anti-)hyperonproduction [18]. It was found that Baryon junction-anti-junction (J anti-J) loops can indeed enhanceanti-Lambda, anti-Xi, anti-Omega yields at SPSenergies. While this mechanism leads to a reason-able description of central interactions, it can notexplain the enhancement in the measured hyperonto anti-hyperon ratios with increasing centrality.• Diquark breaking and sea-diquarks: A new versionof the dual parton model, featuring an improved di-quark breaking mechanism has been applied to ex-plain the observed strangeness enhancement at thefull SPS energy [19]. Here, the strange- and anti-baryon production invokes strings originating fromdiquark-antidiquark pairs in the nucleon sea to re-produces the observed yields of p and Lambda andtheir antiparticles. However cascades are underes-timated by 50% and Omega’s are underestimatedby a factor ﬁve. Agreement with measured datacan only be achieved in this model if additional ﬁ-nal state interactions among hadrons are taken intoaccount.• Strong color ﬁelds: Another kind of string-hadronicmodels employs the Schwinger mechanism [20] of afragmenting color ﬁeld (string) directly. However,in central high energy heavy ion collisions the stringdensity can be so high that the color ﬂux tubesoverlap [21,22]. Consequently, the superposition ofthe color electric ﬁelds yields an enhanced particle1production [21,22]. In particular, the heavy ﬂavorsand diquarks are dramatically enhanced due to ahigher eﬀective string tension [22–24]. Note thatthe strong color ﬁeld leads to the enhancement notonly of the heavy ﬂavors and diquarks but also en-hances the high pt tail of the transverse momentumdistribution of all created particles. However, thechanges in the ﬁnal pt are rather moderate in AAcollisions due to ﬁnal state interactions [22]. A con-sistent enhancement of hyperons and anti-protonsis necessary to support this scenario. In fact, ithas been shown that this approach is consistentwith the measured anti-proton and hyperon yieldsat SPS energies, if rescattering eﬀects are taken intoaccount [25,26].As a tool for our investigation of heavy ion reactionsat RHIC the Ultra-relativistic Quantum Molecular Dy-namics model (UrQMD 1.2) is applied [27]. UrQMD isa microscopic transport approach based on the covari-ant propagation of constituent quarks and diquarks ac-companied by mesonic and baryonic degrees of freedom.It simulates multiple interactions of ingoing and newlyproduced particles, the excitation and fragmentation ofcolor strings and the formation and decay of hadronicresonances. At RHIC energies, the treatment of sub-hadronic degrees of freedom is of major importance. Inthe UrQMD model, these degrees of freedom enter via theintroduction of a formation time for hadrons produced inthe fragmentation of strings [28–30]. The leading hadronsof the fragmenting strings contain the valence-quarks ofthe original excited hadron. In UrQMD they are allowedto interact even during their formation time, with a re-duced cross section deﬁned by the additive quark model,thus accounting for the original valence quarks containedin that hadron [27]. Those leading hadrons therefore rep-resent a simpliﬁed picture of the leading (di)quarks ofthe fragmenting string. Newly produced (di)quarks do,in the present model, not interact until they have co-alesced into hadrons – however, they contribute to theenergy density of the system. For further details aboutthe UrQMD model, the reader is referred to Ref. [27].In the following two diﬀerent scenarios will be exploredin order to study the speculation of a string tension in-crease in heavy ion collision at RHIC energies: UrQMDcalculations with the standard color ﬂux tube break-upmechanism (i.e. a string tension κ = 1 GeV/fm) will becontrasted by UrQMD simulations with an in-medium κincreased to 3 GeV/fm. According to the implementedSchwinger mechanism for the string fragmentation (mdenoting the ((di-)quark masses)γX =P(XX)P(q¯ q)= exp −π(m2X − m2q)κ!, (1)this results in an enhancement of the strangeness anddiquark production probabilities to γs = 0.72 and γqq =0.46 (for κ = 3 GeV/fm) compared to γs = 0.37 andγqq = 0.093 for κ = 1 GeV/fm. Note that a decrease ofthe (di-)quark masses due to chiral symmetry restorationmay lead to a similar enhancement as the κ = 3 GeV/fmscenario.Fig. 1 depicts the particle rapidity distributions (a, b)and ratios from Au+Au (b = 2 fm) to p+p collisions (c,d) at the RHIC full energy√s = 200AGeV. The symbolsdenote: Ω− + Ω− (full circles), Ξ− + Ξ− (full triangles),Σ0 + Σ0 (reversed triangle), Λ0 + Λ0 (full square) andanti-protons (open circles). (a) shows the rapidity dis-tributions with string tension κ = 1GeV/fm; (b) showsthe same as (a) with κ = 3GeV/fm. (c) depicts the ratioR(y) =dNdyAu(y)/ApartdNdypp(y)/2 of the particle yields per partic-ipant from central AA collisions over that of the p+pcollisions with κ = 1GeV/fm; (d) same as (c), howeverwith κ = 3GeV/fm for Au+Au.0102030405060(a) k = 1 GeV/fm (b) k = 3 GeV/fm110102-6 -4 -2 0(c) k = 1 GeV/fm0 2 4 6(d) k = 3 GeV/fmRapidityR(y)dN/dyFIG. 1. Particle rapidity distributions and ratios fromAu+Au (b = 2 fm) and p+p collisions at the RHIC full energy √s = 200AGeV. (a) Rapidity distributions with string energydensity κ = 1GeV/fm3; (b) same as (a) with κ = 3GeV/fm3;(c) ratio R(y) =dNdyAu(y)/ApartdNdypp(y)/2 of the particle yields perparticipant from central nuclear collisions over that of thep+p collisions with κ = 1GeV/fm; (d) same as (c) withκ = 3GeV/fm. Ω− + Ω− (full circles), Ξ− + Ξ− (full tri-angles), Σ0 + Σ0 (reversed triangles), Λ0 + Λ0 (full squares)and anti-protons (open circles).A strong enhancement of the (anti-)hyperon produc-tion compared to scaled pp interactions is predicted(cf. (c)). This enhancement is purely due to rescatter-ing between constituent (di-)quarks and hadrons in themedium. If strong color ﬁelds, similar to Pb+Pb at SPS[25,26], are present, the model predicts a dramatic en-2hancement in the multi-strange hadron production, upto a factor of 100 (in case of the Omega) at midrapidity.The enhancement of the hyperon yields is strongly de-pendent on the centrality of the events as shown in Fig.2: (a) shows the particle yields with string tension κ =1GeV/fm, while (b) is same as (a) with κ = 3GeV/fm.Fig. 2(c) shows the ratio R =NAu(Apart)/ApartNpp/2 of theparticle yields per participant1 from central AA colli-sions over that of the inelastic p+p collisions with κ =1GeV/fm. (d) depicts the same as (c) with κ = 3GeV/fmfor Au+Au collisions. The symbols are: Ω− + Ω− (fullcircles), Ξ−+Ξ− (full triangles), Σ0+Σ0 (reversed trian-gle), Λ0+Λ0 (full square) and anti-protons (open circles).10-210-1110102(a) k = 1 GeV/fm (b) k = 3 GeV/fm1101020 100 200 300(c) k = 1 GeV/fm0 100 200 300(d) k = 3 GeV/fmNumber of ParticipantsYieldRFIG. 2. Particle 4π yields and ratios as a function of num-ber of participants from Au+Au and inelastic p+p collisionsat the RHIC full energy√s = 200AGeV. (a) yields withstring energy density κ = 1GeV/fm3; (b) same as (a) withκ = 3GeV/fm3; (c) ratio R =NAu(Apart)/ApartNpp/2 of the particleyields per participant from central AA collisions over that ofthe p+p collisions with κ = 1GeV/fm3; (d) same as (c) withκ = 3GeV/fm3 for the Au+Au interactions. Ω− + Ω− (fullcircles), Ξ−+Ξ− (full triangles), Σ0+Σ0 (reversed triangles),Λ0 + Λ0 (full squares) and anti-protons (open circles).The 4π yields and ratios as a function of number ofparticipants from Au+Au at the RHIC full energy√s =1The number of participating nucleons in this paper is de-ﬁned as:Apart = A1 + A2 − Σ(Nucleons with pT ≤ 270 MeV). Thisprescription yields a reasonable parametrization of the exper-imental data on Apart.200AGeV increase rapidly with centrality (a, b) by twoorders of magnitude when going from peripheral (Apart ≈25) to central collision. The enhancement itself is mostpronounced when scaled with the number of participatingnucleons Apart and compared to p+p collisions at theRHIC full energy (c, d).Finally, Fig. 3 depicts an inside view into a cen-tral (b=2 fm) Au+Au collision at the full RHIC en-ergy. Open circles show the mass distribution of excitedstrings. Filled circles and squares represent the probabil-ities of a [3]−[3] string of a given mass to decay into Ωswith κ = 1 and 3 GeV/fm, respectively. The increase ofthe string tension to κ = 3 GeV/fm leads to a strong in-crease of the Omega production over all inspected stringmasses (compare full circle with full squares). However,the probability to excite a string with a large mass isstrongly suppressed, as can been seen by the exponen-tial decrease of probabilities above excitation energies of2 GeV. Therefore, most of the Ω’s are produced fromrather low mass strings. This is in contrast to the expec-tations that early (high energetic) collisions lead to highmass excitations and give the major contribution to themulti-strange hyperon yield.10-510-410-310-210-111 10 102dN(string)/dmString Mass (GeV)ProbabilitiesString→W  (k=3)String→W  (k=1)FIG. 3. Probability distributions of strings (open circles).Filled circles and squares represent the probabilities of stringsto decay into Ωs with κ = 1 and 3 GeV/fm, respectively.In conclusion, the UrQMD model has been appliedto Au+Au reactions at RHIC energies. This modeltreats the dynamics of the hot and dense system byconstituent (di-)quark and hadronic degrees of freedom.(Anti-)Hyperon yields in central Au+Au collisions at thefull RHIC energy (√s = 200 AGeV) strongly enhanced incomparison to inelastic pp interactions at√s = 200 GeV3or peripheral Au+Au collisions. This enhancement growsdramatically with the strangeness content of the hyperon.The present model predicts that strangeness enhance-ment occurs as a threshold eﬀect already at rather smallnumber of participants (≈ 25) due to rescattering. In-creasing the string tension, similar to SPS energies (orreducing the eﬀective masses of the constituent quarksto the current quark mass values yields large additionalenhancement, which grows with the strangeness contenteven stronger: Λ’s are enhancement by a factor of 7, whileΩ’s are enhanced by a factor of 60 compared to pp.ACKNOWLEDGEMENTSThis research used resources of the National EnergyResearch Scientiﬁc Computing Center (NERSC). 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Strangeness enhancement from strong color fields at RHIC

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