Table Of Content

Directed Flow of Λ-Hyperons in 2 - 6 AGeV Au + Au Collisions P. Chung(1), N. N. Ajitanand(1), J. M. Alexander(1), M. Anderson(5), D. Best(3),F.P. Brady(5), T. Case(3), W. Caskey(5), D. Cebra(5),J.L. Chance(5), B. Cole(10), K. Crowe(3), A. Das(2), J.E. Draper(5), M.L. Gilkes(1), S. Gushue(1,8), M. Heffner(5),A.S. Hirsch(6), E.L. Hjort(6), L. Huo(12), M. Justice(4), M. Kaplan(7), D. Keane(4), J.C. Kintner(11), J. Klay(5),D. Krofcheck(9),R. A. Lacey(1), J. Lauret(1), M.A. Lisa(2),H. Liu(4), Y.M. Liu(12), R. McGrath(1), Z. Milosevich(7),G. Odyniec(3), D.L. Olson(3),S. Y. Panitkin(4), C. Pinkenburg(1), N.T. Porile(6),G. Rai(3), H.G. Ritter(3), J.L. Romero(5), R. Scharenberg(6), L. Schroeder(3),B. Srivastava(6), N.T.B Stone(3), T.J.M. Symons(3), T. Wienold(3), R. Witt(4) J. Whitfield(7), L. Wood(5), and W.N. Zhang(12) (E895 Collaboration) (1)Depts. of Chemistry and Physics, SUNY Stony Brook, New York 11794-3400 (2)Ohio State University, Columbus, Ohio 43210 (3)Lawrence Berkeley National Laboratory,Berkeley, California, 94720 (4)Kent State University, Kent, Ohio 44242 1 (5)University of California, Davis, California, 95616 0 (6)Purdue University, West Lafayette, Indiana, 47907-1396 0 (7)Carnegie Mellon University, Pittsburgh, Pennsylvania 15213 2 (8)Brookhaven National Laboratory, Upton, New York 11973 n (9)University of Auckland, Auckland, New Zealand a (10)Columbia University, New York, New York 10027 J (11)St. Mary’s College, Moraga, California 94575 6 (12)Harbin Institute of Technology, Harbin, 150001 P. R. China (February 8, 2008) 1 v 2 fluence of the vector component of the in-medium kaon- 0 0 nucleon potential [16–18]. The propagation of Λ’s [in DirectedflowmeasurementsforΛ-hyperonsarepresented 1 nuclear matter] is predicted to differ from that of kaons and compared to those for protons produced in the same 0 due to these different interactions. For example, at rela- Au+Aucollisions(2,4,and6AGeV;b<5−6fm). Themea- 1 tively lowenergiesthe Λ-nucleonscatteringcrosssection 0 surementsindicatethatΛ- hyperonsflowconsistently in the ismuchlargerthanthekaon-nucleoncrosssection. More / samedirectionandwithsmallermagnitudesthanthoseofpro- x importantly, the kaon potential is thought to be weakly tons. Such a strong positive flow [for Λs] has been predicted e repulsive while that for Λ-hyperons is believed to be at- in calculations which include the influence of the Λ-nucleon - tractive for the conditions expected in 1-10AGeV heavy l potential. The experimental flow ratio Λ/p is in qualitative uc agreement with expectations (∼ 2/3) from the quark count- ion collisions [12]. One of the possible manifestations of these differences is a predicted pattern for directed flow n ing rule at 2 AGeV but is found to decrease with increasing : beam energy. of Λ’s which is distinguishable from that for kaons and v protons[9,12,13]. Theoreticalstudiesofthedirectedflow i X PACS 25.70.+r, 25.70.Pq ofΛ’sshowthattheΛflowisrelativelyinsensitivetothe magnitudeoftheΛ-nucleoncrosssection,buthasgreater r a sensitivity to the Λ-nucleon potential [9,12]. Thus, it is A pervasive theme of current relativistic heavy ion re- important to obtain a set of Λ flow measurements in the searchisthecreationandstudyofnuclearmatterathigh 1-10 AGeV beam energy range and to test its utility as energy densities [1–4]. Centralto these studies are ques- an important constraint for the Λ-nucleon potential. tionsrelatedtohowhadronicpropertiesmaybemodified In this letter, we present the first experimental flow in a hot and dense nuclear medium [5,6]. Modifications excitation function for Λ - hyperons at AGS energies, to the properties of Λ’s and kaons which influence their andcompareit to thatforprotonsproducedinthe same production and propagationare of particular current in- Au + Au collisions. These measurements are important terest [5,7–13]. This is because they have not only been because they provide a unique opportunity for probing linked to a chirally restored phase of nuclear matter [5], the Λ-nucleon potential in collisions which are predicted butalsotothedetailedcharacteristicsofthehighdensity to produce the highest baryon densities [19]. Such an nuclear material existing in neutron stars [14,15]. opportunity is not affordedby hypernucleistudies which Recent theoretical studies of the propagation of Λ’s allow the investigation of the Λ-nucleon potential at or and kaons, in hot and dense nuclear matter, have identi- below normal nuclear matter density. Knowledge of the fed characteristic flow patterns for these particles which Λ - nucleon potential at high baryon densities is crucial could serve as an important probe for their respective for accurate predictions of the amount of strangeness- in-medium potentials [9,10,12,13]. Subsequently, results bearing matter in the interior of neutron stars [20] fromkaon measurementshave been attributed to the in- Measurements have been performed with the E895 1 detector system at the Alternating Gradient Syn- exponentialfittothedistributionoveraregionforwhich chrotron at the Brookhaven National Laboratory. De- thedetectionefficiencyisconstant(∼22−38cm),yields tails on the detector and its setup have been reported a cτ value of 7.9±0.1 cm (χ2 ∼0.9). This value is close earlier [18,22,23]. Suffice it to say, the data presented to the expected value of 7.8 cm. here benefit from the excellent coverage,continuous 3D- A better appreciationof the TPC coveragecan be ob- tracking, and particle identification capabilities of the tainedfromtheP vsrapidityplot(cfFig.2)obtainedfor t TPC.Thesefeaturesarecrucialfortheefficientdetection 4 AGeV Λ’s. One can identify 2 areas of low acceptance and reconstruction of Λ’s and for accurate flow determi- : (1) P < 100 MeV , due to the high track density in a T nations. conearoundthebeam,(2)rapidity<-0.6,duetothefi- The Λ-hyperons have been reconstructed from the nitevolumeoftheTPC.Thesetwotypesoflossesexhibit − daughters of their charged particle decay, Λ −→ p+π different trends with beam energy. The first one is least (branchingratio∼64%)followingtheprocedureoutlined prominent at 2 AGeV and becomes graduallyworse at 6 in Refs. [18] and [24]. All TPC tracks in an event were AGeVduetothehighertrackdensity. Thesecondoneis reconstructed followed by the calculation of an overall worstat2AGeV butimprovesgraduallywith increasing − event vertex. Thereafter, each pπ pair was considered beamenergyasaresultoftheincreasingnucleon-nucleon and its point of closest approach obtained. Pairs whose c.m. rapidity with beam energy. trajectoriesintersect(withfairlyloosecriteriasuchasde- The method for analysis of the sideward flow of pro- caydistancefromeventvertex>0.5cm)atapointother tons has been discussed in a prior publication [28]. Here thanthemaineventvertexwereassignedasΛcandidates we focus only on the procedure employed for Λ’s. The and evaluated to yield an invariant mass and associated hatchedareacenteredontheinvariantmasspeaksshown momentum. These Λ candidates were then passed to a inFigs.1a-1c(1.11≤m ≤1.122)representsthemass inv fully connected feedforwardmultilayered neural network gatesusedfortheflowanalysis. Thesegatesensurearel- [26]trainedtoseparate“true”Λ’sfromthecombinatoric ativelypuresampleofΛ’s(∼90%)forallbeamenergies. background. Thenetworkwastrainedfromasetconsist- On the other hand, this sample may include secondary ing of “true” Λ’s and a set consisting of a combinatoric Λ’swhichresultfromthedecayofΣ0’s. Thesesecondary background. “True” Λ’s were generated by tagging and Λ’sareexperimentallyindistinguishable[viaouranalysis] embeddingsimulatedΛ’sinrawdataeventsinadetailed fromthe primaryonesbutitisbelievedthattheydonot GEANT simulationofthe TPC.The combinatoricback- constitute the bulk ofthe detected Λ’s. Results fromthe ground or “fake” Λ’s were generated via a mixed event RelativisticQuantumMolecularDynamicsmodel[29]in- procedureinwhichthedaughterparticlesoftheΛ(pπ−) dicate; (a) a maximum ratio Σ0/Λ, of ∼0.3 for the 2 - 6 were chosen from different data events. AGeV Au + Au collisions relevant to our analysis and TheinvariantmassdistributionsforΛ’sobtainedfrom (b) a Σ0 flow magnitude which is similar to that for Λ’s. the neural network are shown in Figs. 1a - 1c for 2, 4, The reaction plane was determined via the standard and 6 AGeV Au + Au collisions respectively [27]. It is transverse momentum analysis method of Danielewicz noteworthythatwehaveverifiedthattheprocedureused and Odyniec [30] as described in detail in Ref. [23]. We totrainthe neuralnetworkdoesnotleadtothe spurious noteherethatthedaughterprotonsofΛcandidateswere “creation” of Λ’s (see Ref. [18]). That is, combinatoric excluded fromthe protonsample usedfor reactionplane background processed through the neural network does determination. Such a procedure eliminates any auto- not leadto Λ peaks in the invariant-massdistribution as correlation. Deficiencies in the acceptance of the TPC demonstrated for 6 AGeV data in Fig. 1d. resultinanon-uniformreactionplanedistributionforall The distributions shown in Fig. 1 have been obtained beam energies. We account for such non-uniformities by for central and mid-central events in which one or more applying rapidityandmultiplicity dependent corrections Λ’s have been detected. Using the charged particle mul- [23] which serve to flatten the reaction plane distribu- tiplicity of an event as a measure of its centrality, we tion. The dispersionof the reactionplane was estimated estimatethattheseeventsareassociatedwithanimpact- for 2,4 and 6 AGeV via the the sub-event method [30]; parameterrangeb<∼5−6fm. Thedistributionsshownin valuesofthedispersioncorrectionare1.08,1.20and1.44 Figs.1a-1cshowrelativelynarrowinvariantmasspeaks respectively [23]. (Full Width at Half Maximun ∼ 6 MeV) at the charac- Figs. 3a - c show representative results for the mean teristicvalueexpectedfortheΛhyperon(∼1.116GeV). transverse momenta in the reaction plane < px >, vs. The distributions also show an excellent peak to back- thenormalizedc.m. rapidityy ,forprotonsandΛ’spro- 0 groundratiowhichclearlyatteststothereliabilityofthe ducedinthesameevents. y =y /y −1,wherey 0 Lab cm Lab separation from combinatoric background. and y represent the rapidity of the emitted particle in cm Fig. 1e shows a typical decay-length distribution (in the Lab and the rapidity of the c.m respectively. The thec.m. frame)forΛ’sobtainedat6AGeV.Adeficitbe- < px > values shown in Fig. 3 have been corrected for low ct ∼ 20 cm reflects the difficulty of Λ reconstruction reactionplanedispersion[31–33]bytheabovemultiplica- intheregionofhightrackdensityneartothemainevent tive correction factors. The values for the Λ’s also take vertex. Deficiencies above 40 cm reflect inefficiencies as- account of a small correction associated with the ∼ 9% sociatedwith Λ decays close to the edge of the TPC.An combinatoric background at each beam energy. The lat- 2 ter correction was made by evaluating the < px > for takeable deviation from the value 2/3 (indicated by the the experimental combinatoric background [for each of dashed line) with increasing beam energy. Such a devia- severalrapiditybins foreachbeamenergy]followedby a tion suggests that a simple scaling by 2/3 to obtain the weightedsubtractionofthesevaluesfromthe<px >val- Λ-nucleon potential may be an oversimplification. The ues obtained for the invariant mass selections indicated deviationcouldberelatedtorescatteringeffectsortothe in Fig. 1 (The backgroundflow is consistent with expec- detailedcharacteristicsoftheΛ-nucleonpotentialforthe tations for the uncorrelated proton pion pairs). densities producedat 4 and6 A GeV. Moredetailed cal- Figs.3a-cshowtrendswhichclearlyindicatethatΛ’s culations are required to distinguish between these two andprotonsflowconsistentlyinthesamedirection. How- effects. ever, the magnitude of the Λ flow is consistently smaller We have measured directed flow excitation functions than that for protons. These results are consistent with for Λ-hyperons and protons produced in the same mid- prior Λ - flow measurements [16,24] performed for beam central Au+Au collisions. The data show positive flow energies<∼ 2 A GeV.However,they arein starkcontrast for Λ’s and protons for all beam energies. This observa- to the anti-flowpatternrecentlyobservedfor K0 mesons tion is in stark contrast to the prominent anti-flow ob- s at6AGeV[18]. Thiscontrastissuggestiveofdifferences servedforneutralkaonsfromthesamedataset[18]. This in the kaon-nucleon and Λ-nucleon potentials. Namely, contrast is suggestive of the expected differences in the for a similar range of densities and momenta, the pre- kaon-nucleonandΛ-nucleoninteractionsforthedensities dicted kaon-nucleon potential is repulsive while that for attained in 2 - 6 AGeV Au + Au collisions. A compar- the Λ-nucleon is attractive [9,12,13]. ison of the Λ flow excitation function to that obtained In order to quantify the flow magnitude we have eval- fromRQMD,showsconsistentlylargerexperimentalval- uated the slope at mid-rapidity for protons F and Λ’s ues,suggestinganinfluenceoftheΛ-nucleoninteraction. p FΛ (Fp,Λ = d<dpyx0>|(y0∼0)) of the transverse momentum Bbeoatmh Λenaenrdgyp.rHotoowneflvoerw, sthheowfloawderacrteioasFe w/iFth,indcerceraeasisnegs data (cf. Figs. 3) . The results obtained from linear fits Λ p from ∼ 2/3 at 2 AGeV to ∼ 1/3 at 6 AGeV. Such a to these data are summarized in Figs. 4a and 4b. Ex- trend is qualitatively inconsistent with the quark count- perimentalandcalculatedΛflowexcitationfunctionsare ing rule and could be related to the detailed features of showninFig.4a;thedataandtheresultsfromRQMD(v the Λ-nucleon potential. More studies of strange parti- 2.3))[29]calculationsbothindicateacontinuousdecrease cledynamicscanilluminateadditionalpropertiesofhigh in the flow (F) with increasing beam energy. However, densitymatterwhichisthoughttoberichinstrangeness. the results fromthe calculationsystematicallyunderpre- This work was supported in part by the U.S. De- dict the experimentally observed flow magnitude. Since partment of Energy under Grant No. DE-FGO2- rescattering effects are included in the RQMD calcula- 87ER40331.A008and other grants acknowledgedin Ref. tions, it is suggested that the difference may be due to [23]. We acknowledge fruitful discussions with M. theabsenceoftheΛ-nucleonpotentialinRQMD.Itisim- Prakash. portant to point out here that stronger Λ flow has been found in calculations which include the explicit effect of the Λ nucleon potential [9,12,13]. The observed trend of the Λ flow is very similar to that observed for protons co-produced with Λ’s, as well as forprotons inwhichno explicit conditionfor Λ detec- tionwasimposed[28]. ThedecreaseofF withincreasing [1] H.StockerandW.Greiner, Phys.Rep.137, 277,(1987). beamenergyisconsistentwiththenotionthattheflowof [2] Quark Matter ’99, Nucl. Phys.A661 , (1999) primordial Λ’s reflects the collective flow of the baryon- [3] W.Reisdorf,H.Ritter,Ann.Rev.Nuc.Par.Sci.47,663 (1997) baryon and pion-baryon pairs from which they are pro- [4] S. A. Bass et al., J. Phys.G 25:R1 (1999) duced. This trend could also result from a weakening of [5] G. E. Brown et al., Phys.Rev. C43, 1881, (1991). rescattering effects and/or the attractive Λ-nucleon po- [6] P. Senger and H. Stro¨bele, nucl-ex/9810007. tential. Such a weakeningofthe Λ-nucleonpotential has [7] D. B. Kaplan et al., Phys.Lett. B175, 57 (1986). been predicted for relatively large baryon densities [12]. [8] T. Waas et al., Phys.Lett. B379, 34 (1996). The quark counting rule asserts that Λ’s interact [9] G.Q. Li, C.M. Ko Phys.Rev.C54 1897, (1996). with nucleonsonly throughtheir non-strangequarkcon- [10] Bratkovskaya et al., Nucl. Phys.A 622, 593, (1997). stituents [25]. Since a Λ particle has only two such [11] M. Lutz,Phys. Lett. B 426, 12 (1998). quarks,thissuggeststhattheΛpotentialis∼2/3ofthat [12] G. Q.Li et al., Nucl.Phys. A636, 487 (1998). for nucleons [25]. The experimental flow ratio F /F , is [13] Z.S.Wangetal.,Nucl.Phys.A645177,(1999);Erratum- Λ p shownasafunctionofbeamenergyinFig.4b. Thedata ibid. A648 281, (1999). indicate a value of ∼2/3 at 2 AGeV. This value is simi- [14] G. Q.Li et al., Nucl.Phys. A625, 372 (1997). lar to that obtained for the Ni + Cu system [24], and is [15] V. Thorsson et al., Nucl. Phys. A572, 693 (1994). [16] J. Ritman et al., Z Phys. A352, 355, (1995). in qualitative agreement with the suggested ratio of the [17] Y. Shin et al., Phys. Rev.Lett. 81, 1576 (1998). Λ/p potential. On the other hand, there is an unmis- [18] P. Chung et al., Journal of Phys. G., 25, 255 (1999); 3 P.Chung et al., Phys. Rev.Lett 85, 940 (2000). [19] Y.Pang et al., Phys. Rev.Lett.68, 2743 (1992). [20] M.Prakash, J.Lattimer, Nucl.Phys.A639, 433c (1998). 1.4 [21] G. Bauer et al., NIMA386, 249 (1997). [22] G. Rai et al., IEEE Trans. Nucl.Sci. 37, 56 (1990). 15 [23] C. Pinkenburget al., Phys.Rev.Lett. 83, 1295 (1999). 1.2 [24] M. Justice, et al., Phys. Lett. B440, 12, (1998). 30 [25] StevenA. Moszkowski, Phys. Rev.D,1613 (1973) 1 45 [26] M. Justice, NIMPhys. Res. A 400, 463 (1997). 60 [27] Actualbeamenergieswere1.85,3.9and5.9AGeV.Mea- 75 surementswerealso madeat7.9AGeVbuttheseresults V)0.8 90 sufferfrom ratherpoor statistics. e 105 G [28] H.Liu et al., Phys.Rev.Lett. 84, 5488 (2000). (T 120 [29] H.Sorge, Phys.Rev. C52, 3291, (1995). P0.6 135 [30] P.Danielewicz, G.Odyniec,Phys.Lett.B157,146 (1985). [31] P.Danielewicz et al., Phys. Rev.C 38, 120,(1988). 0.4 [32] J.-Y. Ollitrault, nucl-ex/9711003 v2. [33] A.Poskanzer, S.Voloshin, Phys. Rev C58, 1671, (1998). 0.2 0 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 y /y -1 lab c.m. Au+Au → L + X FIG.2. <pT >vsy0 forΛ’sdetectedin4AGeVAu+Au 1400 collisions. Contour levels are indicated. 160 # evnts 91703 (a) # evnts 96756 (b) 140 # L 1089 2 GeV 1200 # L 11539 4 GeV 120 FWHM ≈ 5 MeV 1000 FWHM ≈ 6 MeV 100 Purity 90% 800 Purity 92% L Sideward Flow b < 6fm 80 0.2 60 600 L data (a) p data 40 400 0.1 p reflected 2 GeV s 20 200 nt 0 u 0 Co5000 # evnts 2815.6193 1.12 (c) 1.14 6 G1e.1V (1d0)3 1.12 1.14(e) -0.1 4000 # L 42624 6 GeV 103 L Bkg 6 GeLV FWHM ≈ 6 MeV -00..22 3000 Purity 91% 102 (b) 2000 102 IOnuptuptut eV/c) 0.1 4 GeV 1000 10 c±t 0=. 079.8 c7m x>p (G 0 < -0.1 0 1 1.08 1.1 1.12 1.14 1.1 1.12 1.14 20 40 Inv. Mass (GeV/c2) ct (cm) -00..22 c.m. (c) 0.1 6 GeV FIG.1. Invariant mass distribution for Λ hyperons mea- 0 suredat2,4,6AGeVasindicated(b<6fm). Panel(d)shows input(dashedcurve)andoutput(solid curve)invariantmass -0.1 distributions for combinatoric events. Panel (e) shows the decay length distribution. -0.2 -1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1 y /y -1 lab c.m. FIG. 3. < px > vs y for Λ’s and protons (b < 6fm). 0 Theopencirclesindicatethereflectedvaluesforprotons,and the solid and dashed-curves represent fits to the data. The <px > values are corrected for reaction plane dispersion. 4 0.2 L Sideward Flow Excitation Function ( b < 6fm ) 0.18 (a) 0.16 E895 L V)0.14 RQMD (2.3) L e G0.12 w ( o 0.1 Fl 0.08 0.06 0.04 (b) 0.8 o 0.7 ati w r 0.6 o Fl 0.5 p / L 0.4 0.3 0.2 2 3 4 5 6 7 8 E (GeV) beam FIG. 4. (a) Λ hyperon flow vs beam energy. Filled stars and squares represent data and RQMD results respectively. (b) Λ/p flow ratio vs beam energy for the same im- pact-parameter range. The dashed line indicates a value of 2/3. 5