The ΛΛ Correlation Function in Au+Au collisions at√sNN = 200 GeV

L. Adamczyk1, J. K. Adkins23, G. Agakishiev21, M. M. Aggarwal35, Z. Ahammed53, I. Alekseev19, J. Alford22,

C. D. Anson32, A. Aparin21, D. Arkhipkin4, E. C. Aschenauer4, G. S. Averichev21, A. Banerjee53, D. R. Beavis4,

R. Bellwied49, A. Bhasin20, A. K. Bhati35, P. Bhattarai48, H. Bichsel55, J. Bielcik13, J. Bielcikova14, L. C. Bland4,

I. G. Bordyuzhin19, W. Borowski45, J. Bouchet22, A. V. Brandin30, S. G. Brovko6, S. Bultmann33, I. Bunzarov21,

T. P. Burton4, J. Butterworth41, H. Caines57, M. Calderon de la Barca Sanchez6, J. M. Campbell32, D. Cebra6,

R. Cendejas36, M. C. Cervantes47, P. Chaloupka13, Z. Chang47, S. Chattopadhyay53, H. F. Chen42, J. H. Chen44,

L. Chen9, J. Cheng50, M. Cherney12, A. Chikanian57, W. Christie4, J. Chwastowski11, M. J. M. Codrington48,

G. Contin26, J. G. Cramer55, H. J. Crawford5, X. Cui42, S. Das16, A. Davila Leyva48, L. C. De Silva12, R. R. Debbe4,

T. G. Dedovich21, J. Deng43, A. A. Derevschikov37, R. Derradi de Souza8, B. di Ruzza4, L. Didenko4, C. Dilks36,

F. Ding6, P. Djawotho47, X. Dong26, J. L. Drachenberg52, J. E. Draper6, C. M. Du25, L. E. Dunkelberger7,

J. C. Dunlop4, L. G. Efimov21, J. Engelage5, K. S. Engle51, G. Eppley41, L. Eun26, O. Evdokimov10, O. Eyser4,

R. Fatemi23, S. Fazio4, J. Fedorisin21, P. Filip21, Y. Fisyak4, C. E. Flores6, C. A. Gagliardi47, D. R. Gangadharan32,

D. Garand38, F. Geurts41, A. Gibson52, M. Girard54, S. Gliske2, L. Greiner26, D. Grosnick52, D. S. Gunarathne46,

Y. Guo42, A. Gupta20, S. Gupta20, W. Guryn4, B. Haag6, A. Hamed47, L.-X. Han44, R. Haque31, J. W. Harris57,

S. Heppelmann36, A. Hirsch38, G. W. Hoffmann48, D. J. Hofman10, S. Horvat57, B. Huang4, H. Z. Huang7,

X. Huang50, P. Huck9, T. J. Humanic32, G. Igo7, W. W. Jacobs18, H. Jang24, E. G. Judd5, S. Kabana45,

D. Kalinkin19, K. Kang50, K. Kauder10, H. W. Ke4, D. Keane22, A. Kechechyan21, A. Kesich6, Z. H. Khan10,

D. P. Kikola54, I. Kisel15, A. Kisiel54, D. D. Koetke52, T. Kollegger15, J. Konzer38, I. Koralt33, L. K. Kosarzewski54,

L. Kotchenda30, A. F. Kraishan46, P. Kravtsov30, K. Krueger2, I. Kulakov15, L. Kumar31, R. A. Kycia11,

M. A. C. Lamont4, J. M. Landgraf4, K. D. Landry7, J. Lauret4, A. Lebedev4, R. Lednicky21, J. H. Lee4, C. Li42,

W. Li44, X. Li38, X. Li46, Y. Li50, Z. M. Li9, M. A. Lisa32, F. Liu9, T. Ljubicic4, W. J. Llope41, M. Lomnitz22,

R. S. Longacre4, X. Luo9, G. L. Ma44, Y. G. Ma44, D. P. Mahapatra16, R. Majka57, S. Margetis22, C. Markert48,

H. Masui26, H. S. Matis26, D. McDonald49, T. S. McShane12, N. G. Minaev37, S. Mioduszewski47, B. Mohanty31,

M. M. Mondal47, D. A. Morozov37, M. K. Mustafa26, B. K. Nandi17, Md. Nasim31, T. K. Nayak53, J. M. Nelson3,

G. Nigmatkulov30, L. V. Nogach37, S. Y. Noh24, J. Novak29, S. B. Nurushev37, G. Odyniec26, A. Ogawa4,

K. Oh39, A. Ohlson57, V. Okorokov30, E. W. Oldag48, D. L. Olvitt Jr.46, B. S. Page18, Y. X. Pan7, Y. Pandit10,

Y. Panebratsev21, T. Pawlak54, B. Pawlik34, H. Pei9, C. Perkins5, P. Pile4, M. Planinic58, J. Pluta54, N. Poljak58,

K. Poniatowska54, J. Porter26, A. M. Poskanzer26, N. K. Pruthi35, M. Przybycien1, J. Putschke56, H. Qiu26,

A. Quintero22, S. Ramachandran23, R. Raniwala40, S. Raniwala40, R. L. Ray48, C. K. Riley57, H. G. Ritter26,

J. B. Roberts41, O. V. Rogachevskiy21, J. L. Romero6, J. F. Ross12, A. Roy53, L. Ruan4, J. Rusnak14,

O. Rusnakova13, N. R. Sahoo47, P. K. Sahu16, I. Sakrejda26, S. Salur26, J. Sandweiss57, E. Sangaline6, A. Sarkar17,

J. Schambach48, R. P. Scharenberg38, A. M. Schmah26, W. B. Schmidke4, N. Schmitz28, J. Seger12, P. Seyboth28,

N. Shah7, E. Shahaliev21, P. V. Shanmuganathan22, M. Shao42, B. Sharma35, W. Q. Shen44, S. S. Shi26,

Q. Y. Shou44, E. P. Sichtermann26, M. Simko13, M. J. Skoby18, D. Smirnov4, N. Smirnov57, D. Solanki40,

P. Sorensen4, H. M. Spinka2, B. Srivastava38, T. D. S. Stanislaus52, J. R. Stevens27, R. Stock15, M. Strikhanov30,

B. Stringfellow38, M. Sumbera14, X. Sun26, X. M. Sun26, Y. Sun42, Z. Sun25, B. Surrow46, D. N. Svirida19,

T. J. M. Symons26, M. A. Szelezniak26, J. Takahashi8, A. H. Tang4, Z. Tang42, T. Tarnowsky29, J. H. Thomas26,

A. R. Timmins49, D. Tlusty14, M. Tokarev21, S. Trentalange7, R. E. Tribble47, P. Tribedy53, B. A. Trzeciak13,

O. D. Tsai7, J. Turnau34, T. Ullrich4, D. G. Underwood2, G. Van Buren4, G. van Nieuwenhuizen27,

M. Vandenbroucke46, J. A. Vanfossen, Jr.22, R. Varma17, G. M. S. Vasconcelos8, A. N. Vasiliev37, R. Vertesi14,

F. Videbæk4, Y. P. Viyogi53, S. Vokal21, A. Vossen18, M. Wada48, F. Wang38, G. Wang7, H. Wang4,

J. S. Wang25, X. L. Wang42, Y. Wang50, Y. Wang10, G. Webb4, J. C. Webb4, G. D. Westfall29, H. Wieman26,

S. W. Wissink18, R. Witt51, Y. F. Wu9, Z. Xiao50, W. Xie38, K. Xin41, H. Xu25, J. Xu9, N. Xu26, Q. H. Xu43,

Y. Xu42, Z. Xu4, W. Yan50, C. Yang42, Y. Yang25, Y. Yang9, Z. Ye10, P. Yepes41, L. Yi38, K. Yip4, I.-K. Yoo39,

N. Yu9, H. Zbroszczyk54, W. Zha42, J. B. Zhang9, J. L. Zhang43, S. Zhang44, X. P. Zhang50, Y. Zhang42,

Z. P. Zhang42, F. Zhao7, J. Zhao9, C. Zhong44, X. Zhu50, Y. H. Zhu44, Y. Zoulkarneeva21, M. Zyzak15

1AGH University of Science and Technology, Cracow, Poland2Argonne National Laboratory, Argonne, Illinois 60439, USA3University of Birmingham, Birmingham, United Kingdom

4Brookhaven National Laboratory, Upton, New York 11973, USA5University of California, Berkeley, California 94720, USA6University of California, Davis, California 95616, USA

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7University of California, Los Angeles, California 90095, USA8Universidade Estadual de Campinas, Sao Paulo, Brazil

9Central China Normal University (HZNU), Wuhan 430079, China10University of Illinois at Chicago, Chicago, Illinois 60607, USA

11Cracow University of Technology, Cracow, Poland12Creighton University, Omaha, Nebraska 68178, USA

13Czech Technical University in Prague, FNSPE, Prague, 115 19, Czech Republic14Nuclear Physics Institute AS CR, 250 68 Rez/Prague, Czech Republic

15Frankfurt Institute for Advanced Studies FIAS, Germany16Institute of Physics, Bhubaneswar 751005, India17Indian Institute of Technology, Mumbai, India

18Indiana University, Bloomington, Indiana 47408, USA19Alikhanov Institute for Theoretical and Experimental Physics, Moscow, Russia

20University of Jammu, Jammu 180001, India21Joint Institute for Nuclear Research, Dubna, 141 980, Russia

22Kent State University, Kent, Ohio 44242, USA23University of Kentucky, Lexington, Kentucky, 40506-0055, USA

24Korea Institute of Science and Technology Information, Daejeon, Korea25Institute of Modern Physics, Lanzhou, China

26Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA27Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307, USA

28Max-Planck-Institut fur Physik, Munich, Germany29Michigan State University, East Lansing, Michigan 48824, USA

30Moscow Engineering Physics Institute, Moscow Russia31National Institute of Science Education and Research, Bhubaneswar 751005, India

32Ohio State University, Columbus, Ohio 43210, USA33Old Dominion University, Norfolk, Virginia 23529, USA

34Institute of Nuclear Physics PAN, Cracow, Poland35Panjab University, Chandigarh 160014, India

36Pennsylvania State University, University Park, Pennsylvania 16802, USA37Institute of High Energy Physics, Protvino, Russia

38Purdue University, West Lafayette, Indiana 47907, USA39Pusan National University, Pusan, Republic of Korea

40University of Rajasthan, Jaipur 302004, India41Rice University, Houston, Texas 77251, USA

42University of Science and Technology of China, Hefei 230026, China43Shandong University, Jinan, Shandong 250100, China

44Shanghai Institute of Applied Physics, Shanghai 201800, China45SUBATECH, Nantes, France

46Temple University, Philadelphia, Pennsylvania 19122, USA47Texas A&M University, College Station, Texas 77843, USA

48University of Texas, Austin, Texas 78712, USA49University of Houston, Houston, Texas 77204, USA

50Tsinghua University, Beijing 100084, China51United States Naval Academy, Annapolis, Maryland, 21402, USA

52Valparaiso University, Valparaiso, Indiana 46383, USA53Variable Energy Cyclotron Centre, Kolkata 700064, India

54Warsaw University of Technology, Warsaw, Poland55University of Washington, Seattle, Washington 98195, USA

56Wayne State University, Detroit, Michigan 48201, USA57Yale University, New Haven, Connecticut 06520, USA and

58University of Zagreb, Zagreb, HR-10002, Croatia

(STAR Collaboration)(Dated: December 9, 2014)

We present ΛΛ correlation measurements in heavy-ion collisions for Au+Au collisions at√sNN =

200 GeV using the STAR experiment at the Relativistic Heavy-Ion Collider (RHIC). The Lednicky-Lyuboshitz analytical model has been used to fit the data to obtain a source size, a scatteringlength and an effective range. Implications of the measurement of the ΛΛ correlation function andinteraction parameters for di-hyperon searches are discussed.

PACS numbers: 25.75.-q

Measurements of the correlation function for a pair of particles with small relative momenta have been used

3

to obtain insight into the geometry and lifetime of theparticle-emitting source in relativistic heavy-ion colli-sions [1]. The two-particle correlation function is not onlysensitive to the distribution of the separation of emis-sion points, but also to the effects from Quantum Statis-tics (QS) and to the Final-State Interactions (FSI). Fortwo-particle systems where the final-state interactions arewell known, information about both temporal and spatialseparation distributions can be obtained using the two-particle correlation function [1, 2]. If one has an idea ofthe source size, one could use it to determine the FSIbetween two particles for which the correlation functionis measured. In this paper we have used ΛΛ correlationmeasurements to determine FSI between ΛΛ which is notwell known experimentally.

The ΛΛ correlation function is also relevant for search-ing for the H-dibaryon, a six-quark state predicted byJaffe [3]. Recent lattice QCD calculations from theHAL [4] and NPLQCD [5] collaborations indicate thepossible existence of a bound H-dibaryon, where the cal-culations assumed a pion mass above the physical mass.The production rate for the hypothesized H-dibaryon de-pends on the collision evolution dynamics as well as onits internal structure. It is believed that the most prob-able formation mechanism for the H-dibaryon would bethrough coalescence of ΛΛ and/or ΞN at a late stage ofthe collision process, or through coalescence of six quarksat an earlier stage of the collision [6]. A measurement ofthe ΛΛ interaction is important for understanding theequation of state of neutron stars [7]. Moreover at highdensities, an attractive ΛΛ interaction could lead to for-mation of H-matter or strangelets in the core of moder-ately dense neutron stars [8, 9].

At present, the constraint on the binding energy of theH-dibaryon comes from double Λ hypernuclei (NAGARAevent) [10], which allows the possibility of a weakly boundH-dibaryon or a resonance state [11]. The resonancestate is expected to decay into ΛΛ and would be observedas a bump in the ΛΛ invariant mass spectrum or observedas a peak-like structure in two-particle correlations [12].

Dedicated measurements have been performed to lookfor the H-dibaryon signal, but its existence remainsan open question [13–15]. The STAR experiment hassearched for strangelet production close to the beam ra-pidity at RHIC and has reported an upper limit forstrangelets [16]. The NA49 experiment at the SPS at-tempted to measure the ΛΛ correlation function in heavy-ion collisions, but their statistics were insufficient to drawphysics conclusions [17]. The observed high yield ofmulti-strange hyperons in central nucleus-nucleus colli-sions at RHIC [18] and recent high-statistics data forAu+Au collisions at RHIC provide a unique opportunityto study ΛΛ correlations and search for exotic particleslike the H-dibaryon. In this Letter, we present the firstmeasurement of the ΛΛ correlation function in heavy-ion collisions, for Au+Au collisions at

√sNN = 200 GeV

using the STAR experiment at the RHIC.

STAR is a multi-purpose experiment at RHIC with fullazimuthal coverage. The Time Projection Chamber [19]was used for tracking and particle identification in thepseudorapidity range |η| < 1. Approximately 2.87× 108

events from 2010 and 5.0×108 events from 2011 were an-alyzed. To suppress events from collisions with the beampipe (radius 3.95 cm), the reconstructed primary vertexwas required to lie within a 2 cm radial distance from thecenter of the beam pipe. In addition, the z-position of thevertex was required to lie within ±30 cm of the center ofthe detector. The decay channel Λ→ pπ with branchingratio 63.9±0.5% was used for reconstruction of the Λ [20].The Λ (Λ) candidates were formed from pairs of p (p) andπ− (π+) tracks whose trajectories pointed to a commonsecondary decay vertex which was well separated fromthe primary vertex. The decay length (DL) of a Λ candi-date was required to be more than 5 cm from the primaryvertex. The DL cut did not correspond to a hard cut-offin momentum and it was based on the requirement forhigh purity of the Λ sample as well as reasonable effi-ciency. The distance of closest approach (DCA) to theprimary vertex was required to be within 0.4 cm. Theinvariant mass distribution of the Λ (Λ) candidates at0 − 80% centrality under these conditions as shown inFig. 1 has an excellent signal (S) to background (B) ra-tio of S/(S+B) ∼ 0.97. The solid (dashed) histogram isfor Λ (Λ) candidates. All candidates with invariant massbetween 1.112 and 1.120 GeV/c2 were considered.

FIG. 1. (color online). The invariant mass distribution forΛ and Λ produced in Au+Au collisions at

√sNN = 200 GeV,

for 0−80% centrality. The Λ (Λ) candidates lying in the massrange 1.112 to 1.120 GeV/c2, shown by solid red vertical lines,were selected for the correlation measurement.

The two-particle correlation function is defined as

Cmeasured(Q) =A(Q)

B(Q), (1)

4

where A(Q) is the distribution of the invariant relativemomentum, Q =

√−qµqµ, where qµ = pµ1 − pµ2 , for apair of Λ (Λ) from the same event. B(Q) is the refer-ence distribution generated by mixing particles from dif-ferent events with approximately the same vertex posi-tion along the z-direction. The same single-particle cutswere applied to individual Λs for the mixed-event pairs.Correlations between a real Λ and a false Λ candidatereconstructed from a pair that shares one or two daugh-ters with the real Λ were avoided by removing any Λpair with a common daughter. Possible two-track biasesfrom reconstruction were studied by evaluating correla-tion functions with various cuts on the scalar productof the normal vectors to the decay plane of the Λs andon the radial distance between Λ vertices in a given pair.No significant change in the correlation function has beenobserved due to these tracking effects. Each mixed eventpair was also required to satisfy the same pair-wise cutsapplied to the real pairs from the same event. The ef-ficiency and acceptance effects canceled out in the ratioA(Q)/B(Q). Corrections to the raw correlation functionswere applied according to the expression

C ′(Q) =Cmeasured(Q)− 1

P (Q)+ 1, (2)

where the pair purity, P (Q), was calculated as a productof S/(S+B) for the two Λs of the pair. The pair purity is92% and is constant over the analyzed range of invariantrelative momentum.

The selected sample of Λ candidates also included sec-ondary Λs, i.e. decay products of Σ0, Ξ− and Ξ0, whichwere still correlated because their parents were corre-lated through quantum statistics and emission sources.Toy model simulations have been performed to estimatethe feed-down contribution from Σ0Λ, Σ0Σ0 and Ξ−Ξ−.The Λ, Σ and Ξ spectra have been generated using aBoltzmann fit at midrapidity (T = 335 MeV [18]) andeach pair was assigned a weight according to quantumstatistics. The pair was allowed to decay into daugh-ter particles and the correlation function was obtainedby the mixed-event technique. The estimated feed-downcontribution was around 10% for Σ0Λ, around 5% forΣ0Σ0 and around 4% for Ξ−Ξ−. Thermal model stud-ies have shown that only 45% of the Λs in the sampleare primary [21]. However, one needs to run afterburn-ers to determine the exact contribution to the correla-tion function from feed-down, which requires knowledgeof final-state interactions. The final-state interaction pa-rameters for Σ0Σ0, Σ0Λ and ΞΞ interactions are not wellknown, which makes it difficult to estimate feed-downusing a thermal model [21]. Therefore, to avoid intro-ducing large systematic uncertainties from the unknownfraction of aforementioned residual correlations, the mea-surements presented here are not corrected for residualcorrelations.

The effect of momentum resolution on the correla-

FIG. 2. (color online). The ΛΛ and ΛΛ correlation func-tion in Au+Au collisions at

√sNN = 200 GeV, for 0-80%

centrality. The plotted errors are statistical only.

tion functions has also been investigated using simulatedtracks from Λ decays, with known momenta, embeddedinto real events. Correlation functions have been cor-rected for momentum resolution using the expression

C(Q) =C ′(Q)Cin(Q)

Cres(Q), (3)

where C(Q) represents the corrected correlation function,and Cin(Q)/Cres(Q) is the correction factor. Cin(Q) wascalculated without taking into account the effect of mo-mentum resolution and Cres(Q) included the effect of mo-mentum resolution applied to each Λ candidate. Moredetails can be found in Ref. [22]. The impact of mo-mentum resolution on correlation functions was negligi-ble compared with statistical errors. Figure 2 shows theexperimental ΛΛ and ΛΛ correlation function after cor-rections for pair purity and momentum resolution for 0-80% centrality Au+Au collisions at

√sNN = 200 GeV.

The ΛΛ correlation function is slightly lower than theΛΛ correlation function, although within the systematicerrors. Noting that the correlations C(Q) in Fig. 2 arenearly identical for Λ and Λ, we have chosen to combinethe results for Λ and Λ in order to increase the statisticalsignificance.

The combined ΛΛ and ΛΛ correlation function for 0-80% centrality is shown in Fig. 3. The systematic errorswere estimated by varying the following requirements forthe selection of Λ: DCA, DL and mass range, which affectthe signal-to-background ratio. Systematics from cutson the angular correlation of pairs were also studied thatmay affect correlations at small relative momentum. Thesystematic uncertainties from different sources were thenadded in quadrature. The combined systematic error isshown separately as a shaded band in Fig. 3. If there wereonly antisymmetrization from quantum statistics, a ΛΛcorrelation function of 0.5 would be expected at Q = 0.

5

FIG. 3. (color online). The combined ΛΛ and ΛΛ cor-relation function for 0-80% centrality Au+Au collisions at√sNN = 200 GeV. Curves correspond to fits using the Led-

nicky-Lyuboshitz (LL) analytical model with and without aresidual correlation term [23]. The dotted line corresponds toquantum statistics with a source size of 3.13 fm. The shadedband corresponds to the systematic error.

The observed pair excess near C(Q = 0) compared to0.5 suggests that the ΛΛ interaction is attractive, how-ever as mentioned earlier, the data are not corrected forresidual correlations and those effects can give rise to thisexcess. In Fig. 3, the dotted line corresponds to quantumstatistics.

The Lednicky and Lyuboshitz analytical model [23] re-lates the correlation function to source size and also takesinto account the effect of the strong final-state interac-tions (FSI). The following correlation function is used tofit the experimental data

C(Q) = N [1 + λ(− 1

2exp(−r2

0Q2) +

1

4

|f(k)|2

r20

(1− 1

2√π

d0

r0) +

Re f(k)√πr0

F1(Qr0)− Im f(k)

2r0F2(Qr0)) +

ares exp(−r2resQ

2)], (4)

where k = Q/2, F1(z) =∫ 1

0ex

2−z2/z dx and F2(z) =

(1−e−z2)/z in Eq. (4). The scattering amplitude is givenby

f(k) = (1

f0+

1

2d0k

2 − ik)−1, (5)

where f0 = a0 is the scattering length and d0 = reff isthe effective range. Note that a universal sign conven-tion is used rather than the traditional sign convention

for the s-wave scattering length, a0 = −f0 for baryon-baryon systems. More details about the model can befound in Ref. [23]. The free parameters of the LL modelare normalization (N), a suppression parameter (λ), anemission radius (r0), scattering length (a0) and effectiveradius (reff). In the absence of FSI, λ equals unity fora fully chaotic Gaussian source. The impurity in thesample used and finite momentum resolution can sup-press the value of λ-parameter. In addition to this thenon-Gaussian form of the correlation function and theFSI between particles can affect (suppress or enhance)its value. The last term in Eq. (4) is introduced to takeinto account the long tail observed in the measured data,where ares is the residual amplitude and rres is the widthof the Gaussian.

When the amplitude ares in Eq. (4) is made to van-ish, a fit performed on data causes a larger χ2/NDF(dashed line in Fig. 3) and also the obtained r0 is muchsmaller than the expected r0 from previous measure-ments [22, 24, 25], which suggests that the measuredcorrelation is wider than what the fit indicates in thisscenario. This effect can be explained by the presenceof a negative residual correlation in the data, whichis expected to be wider than the correlation from theparent particles. Therefore, to include the effect of aresidual correlation, a Gaussian term ares exp(−Q2r2

res)is incorporated in the correlation function (solid linein Fig. 3). A negative residual correlation contribu-tion is required with ares = −0.044 ± 0.004+0.048

−0.009 and

rres = 0.43±0.04+0.43−0.03 fm, where the first error is statisti-

cal and the second is systematic. Such a wide correlationcould possibly arise from residual correlations caused bydecaying parents such as Σ0 and Ξ, and coupling of NΞto the ΛΛ channel. The fit parameters obtained withthe residual correlation term are N = 1.006 ± 0.001,λ = 0.18 ± 0.05+0.12

−0.06, a0 = −1.10 ± 0.37+0.68−0.08 fm, reff =

8.52 ± 2.56+2.09−0.74 fm and r0 = 2.96 ± 0.38+0.96

−0.02 fm withχ2/NDF = 0.56. All the systematic errors on the pa-rameters are uncorrelated errors. The Gaussian term isempirical and its origin is not fully understood. How-ever, the addition of this term improves fit results andthe obtained r0 is compatible with expectations. TheLL analytical model fit to data suggests that a repulsiveinteraction exists between ΛΛ pairs, whereas the fit tothe same data from K. Morita et al. showed that theΛΛ interaction potential is weakly attractive [26]. Theconclusion about an attractive or a repulsive potential islimited by our statistics and is model dependent. How-ever, all model fits to data suggest that a rather weakinteraction is present between ΛΛ pairs.

The scattering length and the effective radius obtainedfrom the model fit are shown in Fig. 4. For comparison,interaction parameters for pp, nn and pn singlet (s) andtriplet (t) states as well as for pΛ singlet (s) and triplet(t) states are also shown in Fig. 4 [27]. It is observed that|aΛΛ| < |apΛ| < |aNN |. The LL analytical model givesa negative a0 parameter and favors a slightly repulsive

6

interaction in our convention which is different from aweak attractive potential extracted from the NAGARAevent and the KEK result [13, 28, 29]. The fit parametersare still limited by statistics and our fitted a0 is 1.6σ froma sign change. A negative sign for the scattering length(in our convention) is a necessary though not sufficientcondition for the existence of a ΛΛ bound state.

FIG. 4. (color online). The ΛΛ interaction parametersfrom this experiment (solid circle), where the shaded bandrepresents the systematic error. The interaction parametersfrom pp, pn singlet (s) and triplet (t) states, and from nn, pΛ(s) and pΛ (t) states are shown as open markers [27]. Also, theΛΛ interaction parameters which reproduce the NAGARAevent are shown as open stars [28, 29].

If a ΛΛ resonance exists near the threshold, that wouldinduce large correlations between two Λs at small relativemomentum [12, 30]. For the ΛΛ system below the NΞand ΣΣ thresholds (k < 161 MeV/c), the FSI effect isincluded in the correlation function through the s-waveamplitude [31],

f(k) =1

k cot δ − ik, (6)

where k and δ are relative momentum and s-wave phaseshift, respectively. The effective-range approximation fork cot δ is

k cot δ =1

a0+ reff

k2

2. (7)

Equation (6) should satisfy the single-channel unitaritycondition, Imf(k) = k|f(k)|2, with real parameters a0

and reff . When the scattering amplitude is saturated bya resonance, it can be re-written [32] in the form

f(k) =1

(k20 − k2)/(2µγ)− ik

(8)

Comparing the above to Eqs. (6) and (7), one sees that1/a0 = k2

0/(2µγ) and reff = −1/µγ, where k0, µ and γare the relative momentum where the resonance occurs,the reduced mass, and a positive constant, respectively.The scattering length (effective range) becomes positive(negative) so that the k cot δ term vanishes at k = k0 [33].The signs of a0 and reff obtained from the fit to our datacontradict Eq. (8), which suggests the non-existence of aΛΛ resonance saturating the s-wave below the NΞ andΣΣ thresholds. More discussion on the existence of H asa resonance pole can be found in [26].

Assuming that H-dibaryons are stable against strongdecay of Λ, and are produced through coalescence of ΛΛpairs, the yield for theH-dibaryon can be related to the Λyield by d2NH/2πpT dpT dy = 16B(d2NΛ/2πpT dpT dy)2,where B is a constant known as the coalescence coeffi-cient. From pure phase space considerations, the coales-cence rate is proportional to Q3 [34]. For a weakly boundor deuteron-like bound state H, the ΛΛ correlation be-low the coalescence length Q would be depleted. Ourdata show no depletion in the correlation strength in ourmeasured region, which indicates that the value of Q atcoalescence for the H dibaryon, if it exists, must be below0.07 GeV/c where we no longer have significant statistics.Therefore, because the deuteron coalescence coefficientB = (4.0±2.0)×10−4 (GeV/c)2 [35, 36] for aQ of approx-imately 0.22 GeV/c, we estimate that the H dibaryonmust have B less than (1.29± 0.64)× 10−5 (GeV/c)2 forQ < 0.07 GeV/c. The corresponding upper limit for pT -integrated dNH/dy is (1.23± 0.47stat ± 0.61sys)× 10−4 ifthe coalescence mechanism applies to both the deuteronand the hypothetical H particle.

In summary, we report the first measurement of the ΛΛcorrelation function in heavy-ion collisions, for Au+Au at√sNN = 200 GeV. The measured correlation strength at

Q = 0, C(Q = 0) is greater than 0.5 (the expectationfrom quantum statistics alone). In addition to the nor-mal ΛΛ correlation function, a Gaussian term is requiredto fit the data, possibly due to residual correlations. Theextracted Gaussian source radius is compatible with theexpectation from previous measurements of pion, kaonand pΛ correlations [22, 24, 25]. The model fits to datasuggest that the strength of the ΛΛ interaction is weak.Numerical analysis of the final-state interaction effectusing an s-wave scattering amplitude suggests the non-existence of a ΛΛ resonance saturating the s-wave belowthe NΞ and ΣΣ thresholds. A limit on the yield of adeuteron-like bound H-dibaryon is also reported.

ACKNOWLEDGMENTS

We thank S. Pratt for helpful discussions. We thankthe RHIC Operations Group and RCF at BNL, theNERSC Center at LBNL, the KISTI Center in Korea,and the Open Science Grid consortium for providing re-sources and support. This work was supported in part by

7

the Offices of NP and HEP within the U.S. DOE Office ofScience, the U.S. NSF, CNRS/IN2P3, FAPESP CNPq ofBrazil, the Ministry of Education and Science of the Rus-sian Federation, NNSFC, CAS, MoST and MoE of China,the Korean Research Foundation, GA and MSMT ofthe Czech Republic, FIAS of Germany, DAE, DST, andCSIR of India, the National Science Centre of Poland,National Research Foundation (NRF-2012004024), theMinistry of Science, Education and Sports of the Repub-lic of Croatia, and RosAtom of Russia.

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