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PHYSICAL REVIEW C 68, 061901(R) (2003) Strange Pentaquark Hadrons in Statistical Hadronization Jean Letessier Laboratoire de Physique Théorique et Hautes Energies Université Paris 7, 2 place Jussieu, F–75251 Cedex 05. Giorgio Torrieri, Steve Steinke, Johann Rafelski Department of Physics, University of Arizona, Tucson, Arizona, 85721, USA 4 0 (Dated: October15, 2003, Published December 22, 2003) 0 2 Westudy,withinthestatisticalhadronizationmodel,theinfluenceofnarrowstrangenesscarrying n baryon resonances (pentaquarks) on the understanding of particle production in relativistic heavy a ion collisions. Thereis agreat variation of expectedyieldsasfunction of heavyion collision energy J duetorapidlyevolvingchemicalconditionsatparticlechemicalfreeze-out. Atrelativelylowcollision 7 energies, these new states lead toimprovement of statistical hadronization fits. 2 PACSnumbers: 24.10.Pa,25.75.-q,13.60.Rj,12.38.Mh v 8 8 Enhancedproductionofstrangehadronsinrelativistic ouranalysis,wedonotdependontheunknownmassesof 1 heavy ion collisions is well established [1, 2]. The avail- I =1/2,andI =1states. However,theinterpretationof 0 ability of a high abundance of strangeness favors pro- thenewlydiscoverednarrowstatesaspentaquarksenters 1 duction of strange hadron resonances, a topic of current our considerations decisively. The pentaquark valance 3 intense experimental interest in the field of relativistic quarkcontententerstheassignedchemicalfugacitiesand 0 heavy ion collisions [3, 4, 5, 6, 7, 8, 9]. The discovery by phasespaceoccupancies. Theyieldisproportionaltothe h/ the NA49 collaboration [10]of a new Ξ−−(1862) I =3/2 presumed spin degeneracyof the new states, taken to be p narrow Γ < 5 MeV resonance in their pp background, two for a spin 1/2 anti decuplet. - p rather than in the AA foreground data at projectile en- Inourapproach[2,17,18],asinotherrecentwork[19], e ergy 158 GeV (√sNN =17.2 GeV) poses the question in the chemical equilibrium and non-equilibrium is consid- h which conditions one should look in heavy ion collisions ered. Accordingly,weallowquarkpairphasespaceoccu- v: for such new resonances. pancies, for light quarks γq = 1, and/or strange quarks 6 i This newly discovered hadron resonance has, given γs = 1 [20]. Since we study at SPS the total particle X 6 the mass and charge, an exceedingly narrow width. multiplicities, and at RHIC the central yields which can r This feature is common with Θ+(1540), another re- be considered produced by rapidity-localized fireballs of a cently reported resonance [11, 12, 13, 14], which de- matter, we require in our fits balance in the strange and cays into the channel with quark content uudds¯ and antistrange quark content [21]. I = 0. This is believed to be the predicted [15], low- There aretwoindependent fitparameterswhenweas- ∗ est mass, pentaquark state [16]. The Ξ (1862) can be sumecompletechemicalequilibrium,thechemicalfreeze- interpreted as its most massive isospin quartet member out temperature T and the light quark fugacity λ = q ssddu¯, ssudu¯, ssudd¯, ssuud¯with electrical charge vary- √λ λ = eµb/(3T). The baryochemical potential µ u d b ing, respectively, from 2 to +1, in units of e. is the physical parameter controlling baryon density. − | | Appearance of these new resonances can have many Strangeness conservation fixes the strange quark fugac- consequences in the field of heavy ion collisions. We ity λ (equivalently, strangeness chemical potential, for s at first explore how the introduction into the fam- moredetailssee,e.g.,[2]). Addingthepossibilitythatthe ily of hadronic particles of these two new resonances, number ofstrangequarkpairs is notinchemicalequilib- Θ+(1540) and Ξ∗(1862), influence the results of statis- rium, γ = 1, we have 3 parameters, and allowing also s 6 tical hadronization fit to relativistic heavy ion hadron that light quark pair number is not in chemical equilib- production experimental results. We use the same data rium, we have 4 parameters. These three alternatives set as has been employed in Ref [2, 17, 18] and obtain will be coded as open triangles, open squares and filled predictions of how the relative abundances of these new squares,respectively,inallresultswepresentgraphically. resonantstatesvaryasfunctionoftheheavyioncollision We find that the new resonance Θ+(1540) influences energy. significantly the statistical hadronization fit to particle Importantly,onlythetwoalreadyidentifiedstateswith production at the lowest SPS energies. In a baryon rich I = 0, and I = 3/2 of the anti decuplet, which also environment the introduction into the fit of Θ+(1540), includesthe I =1/2,andI =1statesareofrelevancein a b = 1 baryon with ‘wrong’ strangeness influences the the study of the statistical hadronization fits. Thus, in strangeness balance condition, and thus indirectly the 2 TABLE I: The chemical freeze-out statistical parameters found for nonequilibrium (left) and semi equilibrium (right) fits to SPS results. We show √sNN, the temperature T, light quark fugacity λq, strange quark fugacity λs, the quark occupancy parameters γ and γ /γ . Bottom line presents the statistical significance of the fit. The star (*) indicates for λ that it is q s q s a value resulting from strangeness conservation constraint. For γ that there is an upper limit to which the value converged, q γ2<emπ/T (on left), or that the valueof γ =1 is set (on right). q q √sNN[GeV] 17.2 12.3 8.75 17.2 12.3 8.75 T[MeV] 135 3 135 3 133 2 157 4 156 4 154 3 ± ± ± ± ± ± λ 1.69(5) 1.98(6) 2.56(6) 1.74(5) 2.03(7) 2.69(8) q λ 1.23∗ 1.27∗ 1.31∗ 1.20∗ 1.24∗ 1.24∗ s ∗ ∗ ∗ ∗ ∗ ∗ γ 1.68 1.68 1.69 1 1 1 q γ /γ 0.91(6) 0.83(4) 0.85(6) 0.66(4) 0.60(4) 0.67(5) s q χ2/dof 11.4/6 4.3/2 2.3/4 23/7 8.9/3 4.0/5 TABLE II: The chemical freeze-out statistical parameters found for nonequilibrium (left) and semi equilibrium (right) fits to RHIC results. We show √sNN, the temperature T, light quark fugacity λ , strange quark fugacity λ ,the quark q s occupancy parameters γ and γ /γ . Bottom line presents q s q thestatisticalsignificanceofthefit. Thestar(*)indicatesfor λ that it is a value resulting from strangeness conservation s constraint. For γ that there is an upper limit to which the q value converged, γ2 < emπ/T (on left), or that the value of q γ =1 is set (on right). q √sNN[GeV] 200 130 200 130 T[MeV] 142 5 143 3 159 6 159 2 ± ± ± ± λ 1.051(9) 1.069(8) 1.052(9) 1.067(8) q ∗ ∗ ∗ ∗ λ 1.018 1.023 1.018 1.023 s ∗ ∗ ∗ ∗ γ 1.62 1.63 1 1 q γ /γ 1.23(12) 1.32(5) 1.013(6) 1.13(4) FIG. 1: (Color online) χ2/dof for statistical hadronization s q χ2/dof 2.9/6 16.9/20 4.6/7 32.7/21 fits at SPS and RHIC: results are shown for 40, 80, 158A GeV Pb on stationary Pb target collisions and at RHIC for 65+65 and 100+100A GeV Au–Auhead on interactions. individual yields of all strange hadrons. This leads to a Θ+(1540)assuresthatthestatisticalhadronizationworks reductioninthe statisticalfiterrorforourhadronization well down to the lowest SPS energies. To compare with study of the 40A GeV Pb–Pb reactions where we see a earlier results on χ2/dof, obtained prior to the discovery significant change in the relative yield of kaons and Λ. of these new resonances, see Ref. [17], figure 16. We also find changes in the details of the statistical fit parameters. In comparison to [17], aside of the intro- Aninterestingpoint,seeninfigure1,isthatthechem- duction of the new resonances, we also have harmonized ical equilibrium fit γ = 1, γ = 1 is rendered unac- s q our hadron decay table with those used by the Kraków ceptable at all SPS energies in presence of the new reso- group [22]. The improvement of the particle yield fit is nances. The semi-equilibrium fit, which allowsa varying both,atheoreticalconfirmationofthevalidityofthesta- strangeness saturation, but assumes light quark equilib- tistical hadronization model of particle production, and rium is generallyresulting in twice as largeχ2 compared its applicability at low SPS energies. to the full non-equilibrium approach. In a study of χ2 profile as function of γ we find a clear and strong mini- We show how the fit errorevolves in figure 1, which is q alsopresentedinthebottomlinesoftablesIandIIalong mum for γq →γqmax ≡e−mπ/(2T). Acquisition by the fit with the number of data points and resulting degrees of ofthis limitingvalueimpliesthatthereisnofitting error freedom. Considering the small number of degrees of in the γq presented below. freedomatSPS,weneedχ2/dof<1tohavegoodsignif- The chemical freeze-out parameters of the fits consid- icance of the fit. The errors seen in figure 1 are, for the ered play a very important role in predicting the (rela- chemicalnonequilibriumcase(filledsquares),sufficiently tive) yield of hadronic particles, and this dependence is small to allow us to conclude that the introduction of even stronger for many pentaquark states, due to their 3 FIG. 2: (Color online) Yield of Θ+(1540) in relativistic FIG. 3: (Color online) Relative yields Ξ−−(1862)/Ξ− and − heavy ion collisions, based on statistical hadronization fit to Σ (1786)/Λ are shown from bottom to top, see figure 2 for hadronizationparametersatSPSandRHIC40,80,158AGeV further details. PbonstationaryPbtargetcollisions andatRHICfor65+65 and 100+100A GeV Au–Au head on interactions. Relative yields with K , Λ, and Λ(1520) are shown from bottom to include 50% weak interaction cascade from Ξ. s top. The reason that the chemical nonequilibrium is lead- ing to greater than equilibrium yields is that the lower hadronization temperature is overcompensated unusual quantum numbers. These fit parameters for by the chemical factors, e.g., Θ+(1540)/Λ(1520) RHIC are shownin table II, andfor SPSin table I along ≃ 1/2γ2(λ /λ )2 ignoring the small mass difference. The withthefreeze-outtemperature. Wenotethatforthefull q q s factor1/2isduetothedifferenceinspindegeneracy. The chemical non-equilibrium, the freeze-out temperature is actuallyobservedyieldratioΘ+(1540)/Λ(1520)couldbe found to be smaller than for semi-equilibrium case. This still greatersince Λ(1520)is seenat 50%of the expected reduction is over-compensated in pentaquark yields by statistical hadronization yield in heavy ion collisions. In the significantly increased value of γ . q figure 2, we also recognize that the reason that there is We now consider the relative yields of the new reso- suchasignificantimpactatlowSPSenergiesofΘ+(1540) nances in figures 2 and 3. These yields vary strongly is thatit is producedatthe levelof+10–20%ofΛin fits withcollisionenergyforthecaseofΘ+(1540)infigure2, at 40A GeV. This is due to the large prevailing bary- but are rather constant in figure 3. Certainly our result ochemical density. Clearly, this is the environment in differs greatly from expectations arising from an earlier whichonewouldwanttostudythepropertiesofthisnew studyofthestatisticalmodelproductionoftheΘ+(1540) resonanceinmoredetail. However,atallenergiesconsid- resonance[23]wherethedecisivevariationoftheparticle ered,we find thatΘ+(1540)is moreabundantcompared yield with chemical potentials was not explored. More- toΛ(1520)andthusthisnewresonancecouldbecomean over, the hadron yields, presented in [23], did not in- important probe of the hadronization dynamics. clude the contributions from decay of short lived hadron The observation of the pattern of relative yield of resonances. We checked that the relative particle yields Θ+(1540), seen in figure 2, would firmly confirm the 4- shown in [23] for zero chemical potentials and varying quark,oneantiquarkcontentofthisstate. Namely,were temperature are mathematically correct, also as a cross forexampletheΘ+(1540)anothertri-quarkbaryonstate, check of our program. theyieldratiowith(strange)baryonswouldbequiteflat In figure 2, we show (from top to bottom) the relative as function of collision energy. We further note that the yields Θ+(1540)/Λ(1520),Θ+(1540)/Λ,Θ+(1540)/K absolute magnitude of the relative yield, seen in figure s for chemical nonequilibrium (solid lines), semi- 2, will be of help in establishing the degree of chemical equilibrium (γ = 1, dashed lines) and chemical equilibration. q equilibrium (dotted lines). The yields of Λ used here In figure 3, we show at the bottom the expected rel- 4 −− − ative yield of the Ξ (1862)[ssddu¯] relative to Ξ [ssd]. of relative yields seen in figure 3 is primarily due to the ∗ The Ξ (1862) adds at the percentile level to the yield of hadron mass, and degeneracy. observedΞandthus itis lessinfluentialinthe statistical Wehaveshownthatinclusionofthepentaquarkstates hadronizationapproach. The absence of variation of the inthestudyofparticleproductioninheavyioncollisions relative yield with collision energy is due to cancellation improvesthequalityofourfitstoexperimentaldata. We ofchemicalfactors. Thisrelativelysmallrelativeyieldat find that Θ+(1540) state influences the low energy SPS all collision energies here considered shows that indeed particleyieldfitresults. Itcanbeexpectedthatitwillbe the pp environment, where it has been identified by the detectable, in particular at low heavy ion collision ener- NA49 collaboration, is most suitable. The dotted lines, gies, and thus should become a new probe of hadroniza- in figure 3, are visibly breaking the trend in some of the tiondynamics. Theotherpentaquarkstateswillbehard results,indicatingthatthelargeχ2 chemicalequilibrium to observe in heavy ion collisions. fit generates unreliable statistical model parameters. We also show, in figure 3 on the top, the yield of the pentaquark state Σ(1776)[sdduu¯] which for purpose of Work supported in part by a grant from the U.S. this study is assumed at the mass indicated. Again due Department of Energy, DE-FG03-95ER40937. 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