observation of antimatter nuclei at rhic-star

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Observation of antimatter nuclei at RHIC-STARTo cite this article Yu-Gang Ma 2013 J Phys Conf Ser 420 012036

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Observation of antimatter nuclei at RHIC-STAR

Yu-Gang Ma

Shanghai Institute of Applied Physics Chinese Academy of Sciences Shanghai 201800 China

E-mail ygmasinapaccn

Abstract In this article we present a brief review on the recent measurements of antimatterparticles at RHIC We highlight the observations of the antihypertriton (3

ΛH) and antihelium-4 nucleus (4He or α) and discuss the current experimental searches for antinuclei in cosmicrays Finally we present a recent calculation result using thermal and coalescence mechanismfor anti-light nuclei production

1 IntroductionRelativistic heavy-ion collision create suitable conditions for a phase transition from hadronto deconfined quark matter which was predicted by the Lattice QCD calculation Duringthe collision a hot and dense partonic matter can be formed ie so-called Quark-GluonPlasma (QGP) Many evidences have demonstrated that the QGP matter has been producedin central Au + Au collisions at RHIC energies [1 2 3 4] In the process large amounts ofenergy are deposited into a more extended volume than that achieved in elementary particlecollisions These nuclear interactions briefly produce hot and dense matter containing roughlyequal numbers of quarks and antiquarks Then the QGP expands rapidly and cools downand undergoes a transition into a hadron gas producing nucleons and their antiparticlesTherefore the relativistic heavy-ion collision can not only provide an environment to study stronginteracting phase transition and QCD matter but also an ideal venue to produce antimatterparticles

The ideal of antimatter can be traced back to the end of 1890s when Schuster discussed ahypothesis of the existence of antiatoms as well as antimatter solar system by hypothesis in hisletter to Nature magazine [5] However the modern concept of antimatter is originated from thenegative energy state solution of a quantum-mechanical equation which was proposed by Diracin 1928 [6] Two years later C Y Chao found that the absorption coefficient of hard γ-rays inheavy elements was much larger than that was expected from the Klein-Nishima formula or anyother [7 8] This ldquoabnormalrdquo absorption is in fact due to the creation of the pair of electron andits anti-partner so-called positron This experiment gives the first indirect observation of thefirst anti-matter particle namely positron Two years later Anderson observed positron with acloud chamber [9] Since the observation of the anti-proton (p) [19] in 1955 antimatter nucleisuch as d 3H 3He have been widely studied in both cosmic rays [10 11 12] and acceleratorexperiments [13 14 15 16 17 18] for the purposes of dark matter exploration and the studyof manmade matter such as quark gluon plasma respectively

The recent progress regard the observation of antihypertriton (3Λ

H) [20] and antihelium-

4 (4He or α) [21] nucleus in relativistic heavy ion collisions reported by the RHIC-STAR

11th International Conference on Nucleus-Nucleus Collisions (NN2012) IOP PublishingJournal of Physics Conference Series 420 (2013) 012036 doi1010881742-65964201012036

Published under licence by IOP Publishing Ltd 1

experiment as well as the longtime confinement of antihydrogen atoms [22] based on anantiproton decelerator facility by ALPHA collaboration have already created a lot of excitationin both nuclear and particle physics community All of the measurements performed above haveimplications beyond the fields of their own Such as the study of hypernucleus in heavy ioncollisions is essential for the understanding of the interaction between nucleon and hyperon (YNinteraction) which plays an important role in the explanation of the structure of neutron starFurthermore as we learned from heavy ion collisions the production rate for 4He producedby colliding the high energy cosmic rays with interstellar materials is too low to be observedEven one 4He or heavier antinucleus that observed in the cosmic rays should be a great hint ofthe existence of massive antimatter in the Universe Finally the successful trap of antihydrogenatoms can lead to a precise test of the CPT symmetry law as well as a measurement of thegravitational effects between antimatter and matter in the future

In this article we focus on the above mentioned discoveries on antihypertriton [20] andantihelium-4 [21] at the RHIC as well as the current effort of the hunting antimatter nuclei incosmic rays A brief review on the formation and observation of 3

ΛH through their secondary

vertex reconstructions via decay channel 3Λ

H rarr3He + π+ with a branch ratio of 25 in highenergy heavy ion collisions is presented in Sec 2 Section 3 discusses the particle identificationof 4He nucleus by measuring their mass value directly with the newly commissioned detectorTime Of Flight (TOF) at RHIC-STAR Section 4 discusses the status of the hunting antimatternuclei in cosmic rays In Section 5 we discuss the antimatter nuclei production mechanismFinally we give a summary

2 Observation of the first antimatter hypernucleus 3Λ

HDifferent from the normal (anti-)nuclei which only consist of (anti-) u and d quarks (anti-)hypernucleus also includes the (anti-)strange quark degree of freedom of which the typical oneis Λ-hypernucleus The simplest hypernucleus observed so far is hypertriton which is composedof one neutron one proton and one Λ-hyperon Due to the presence of hyperon hypernucleusprovides an ideal environment to learn the hyperon-nucleon interaction responsible in part forthe binding of hypernuclei and lifetime which is of fundamental interest in nuclear physics andnuclear astrophysics So far many hypernuclei have been identified even for the observation ofdouble-Λ hypernucleus [23] No anti-hypernucleus was observed until the STAR collaborationannounced the first anti-matter hypernucleus ie 3

ΛH [20] in 2010 In the technique viewpoint

the identification of 3Λ

H can be achieved by reconstructing their secondary vertex via the decay

channel of 3Λ

H rarr3He + π+ which occurs with a branching ratio of 25 (assuming that this

branching fraction is the same as that for 3ΛH [24]) [20 25] The data used for 3

ΛH analysis

was collected by the STAR experiment at Relativistic Heavy Ion Collider (RHIC) using thecylindrical Time Projection Chamber (TPC) which is 4 meters in diameter and 42 meters longin the beamline direction [26] The identification of tracks can be achieved by correlating theirionization energy loss 〈dEdx〉 in TPC with their magnetic rigidity Figure 1C shows 〈dEdx〉for negative tracks versus the magnetic rigidity The different bands stand for different kinds ofparticles Figure 1D is the distribution of a new variable z = Ln(〈dEdx〉〈dEdx〉B)which isused to identify 3He and 3He here 〈dEdx〉B is the expected value of 〈dEdx〉

Topological cuts including the distance between two daughter tracks 3He and π+ (lt1cm)distance of closest approach (DCA) between 3

ΛH and primary vertex (lt1cm) decay length

of 3Λ

H(gt24cm) and the DCA of π track (gt08cm) are employed to enhance the signal to

background ratio The invariant mass of 3ΛH and 3

ΛH were calculated based on the conservation

of momentum and energy in the decay process The results are shown in Figure 1A for 3ΛH and

Figure 1B for 3Λ

H The successfully reproduced combinatorial background with a rotationstrategy can be described by double exponential function f(x) prop exp[minus(xp1)]minus exp[minus(xp2)]


2

Co

un

ts (

Ke

Vc

m)

rangd

Ed

xlang

A

C

295 3 305 310

50

100

150

200

250

300

350

signal candidates

rotated background

signal+background fit

295 3 305 310

20

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120

140

signal candidates

rotated background


) 2 Invariant mass (GeVc+π + He3

) 2 Invariant mass (GeVcshyπHe + 3

0 1 2 3 40

10

20

30

He3

π

rangdEdxlangExpected

shy04 shy02 0 02 040

100

200

300

400 rigiditygt1 GeVc

He3

He3

He)3

Rigidity (GeVc) z(

Co

un

tsC

ou

nts

B

D

Figure 1 (A and B) Reconstructed invariant mass distribution of 3He and π open circlesstand for the signal distribution while solid lines are the rotated combination background Bluedashed lines are the Gaussian (signal) plus double exponential (background) function fit to thedistribution (C) 〈dEdx〉 as a function of rigidity (p|Z|) for negative particles theoretical〈dEdx〉 value for 3He and π are also plotted (D) shows that a clean 3He and 3He samplecan be obtained with cut |z(3He)| lt 02 Adapted from the Ref [20]

where x = mminusm(3He)minusm(π) and p1 p2 are the parameters Finally the signals are countedby subtracting the double exponential background of 3

ΛH and 3Λ

H

As an example to show how 3Λ

H looks like Figure 2 depicts a typical Au + Au collisionreconstructed in the STAR TPC Different tracks are curved by a uniform magnetic field of 05T parallel to the beamline The event of interest here includes a 3

ΛH candidate created at theprimary collision vertex near the center of the TPC where the dashed black line is the trajectoryof the 3

ΛH candidate which cannot be directly measured The heavy red and blue lines are the

trajectories of the 3He and π+ decay daughters respectively which are directly measuredThe3ΛH travels a few centimeters before it decays

The measurement of 3ΛH (3

ΛH) lifetime provides us an effective tool to understand the Y(Λ)-

N(pn) interactions [27 24] And the secondary vertex reconstruction of 3ΛH (3

ΛH) makes us

to be able to perform a calculation of its lifetime via equation N(t) = N(0)exp(minustτ) wheret = l(βγc) βγc = pm l is the decay length of 3

ΛH p is their momentum m is their massvalue while c is the speed of light 3

ΛH and 3Λ

H samples are combined together to get a better

statistics with the assumption of the same lifetime of 3ΛH and 3

ΛH base on the CPT symmetry


3

50 cm

HΛ

3

He3

A

+π+πHe

3

B

Figure 2 A typical event in the STAR detector that includes the production and decay of3Λ

H candidate (A) with the beam axis normal to the page (B) with the beam axis horizontalSee details in text Adapted from the Ref [20]

Co

un

t

A

5 10 15 20 25

210

310

Λ

HΛ3

(cm)τc

2χ

3 4 5 6 7 8 9 10 11

0

05

1

15

2

25

= 0082

χ

= 1082χ

cm14

27 plusmn = 55 τc

H life

tim

e (

ps)

Λ3

B

shy1 0 1 2 3 4 5 6 70

50

100

150

200

250

300

350

400

450

(PDG)Λfree

ΛSTAR free

Dalitz 1962

Glockle 1998PR136 6B(1964)

819(1968)

PRL20

PR1801307(1969)

46(1970)

NPB16

66(1970)

PRD1

269(1973)

NPB67

STAR

) (cm) World dataγβdecayshylength(

Figure 3 A) The yields of 3Λ

H (solid squares) and Λ (open circles) vs cτ distribution The

solid lines stand for the cτ fits and the insert plot describes χ2 distribution of the best fits (B)Comparison between the present measurement and theoretical calculation [27 24] as well as theprevious measurements [28 29 30 31 32 33] Adapted from the Ref [20]

theory The measured yield is corrected for the tracking efficiency and acceptance of TPCas well as the reconstruction efficiency of 3

ΛH and 3Λ

H Then the l(βγ) distribution can be


4

fitted with an exponential function to extract the lifetime parameter cτ The best fitting with χ2

minimization method yielded cτ = 55+27minus14plusmn008 which corresponds a lifetime of 182+89

minus45plusmn27 ps asshown in Figure 3A Figure 3B shows a comparison of the present measurement with theoreticalcalculation [27 24] as well as the previous measurements [28 29 30 31 32 33] It seems thatthe present measurement of 3

ΛH lifetime is consistent with calculation with phenomenological3ΛH wave function [27] and a more recent three-body calculation [24]

In hot and dense environment high production rate of 3ΛH (3

ΛH) due to equilibration among

strange quarks and light quarks (ud) is proposed to be a signature of the formation of QGP[20 34] By comparing the yields of 3

ΛH and 3He the baryon strangeness correlation factorcan be extracted Our recent calculation [35] indicates that the strangeness population factorS3 =3

Λ H(3He times Λp) is an effective tool to distinguish QGP phase and pure hadronic phaseThe definition of S3 incorporates the Λp ratio in order to remove the sensitivity on yielddifferences on Λ and p as a function of beam energy It is interesting to note that S3 increaseswith beam energy in a system with partonic interactions (Melting AMPT) while it is almostunchanged in a purely hadronic system (Default AMPT) from Fig 4 The measurement fromAGS [36] in spite of large statistical uncertainty gives the value 13 The AGS measurement ofS4 =4

Λ H(4HetimesΛp) offers further indirect support for the lower value of S3 at the AGS [36] A

preliminary 3ΛH3He result for Au+Au collisions at 200 GeV from the STAR Collaboration [37]

in combination with the measured Λp ratio from the same experiment [38 39 40] allows us toinfer that the measured S3 at RHIC is consistent with unity within errors These experimentalresults are consistent with the melting AMPT calculations and are in contrast to the defaultAMPT calculations The data imply that the local correlation strength between baryon numberand strangeness is sensitive to the effective number of degrees of freedom of the system createdat RHIC and this number is significantly larger in a system dominated by partonic interactionscompared with a pure hadronic gas

3 Observation of the heaviest antimatter nucleus 4HeThe STAR collaboration also reported its observation of 4He nucleus [21 41] in April 2011

with 10 billion gold-gold collisions taken in the year 2007 and 2010 In additional to the particleidentification method by combining energy loss (〈dEdx〉) and rigidity provided by TPC theobservation of 4He nucleus relies on the measured traveling time of tracks given by the barrelTOF [42] of the STAR experiment (Solenoidal Tracker At RHIC) which is composed of 120trays surrounding the Time Projection Chamber (TPC) [26] TPC is the central detector usedin our measurements of antimatter which is situated in a solenoidal magnetic field and is usedfor three-dimensional imaging of the ionization trail left along the path of charged particles asshown in Fig 5 In this figure tracks from an event which contains a 4He are shown withthe 4He track highlighted in bold red With the barrel TOF the mass value of particles canbe calculated via m2 = p2(t2L2 minus 1) for particle identification where t and L are the time offlight and path length of the track respectively On the other hand the online high level trigger(HLT) was employed to select collisions which contain tracks with charge Ze = plusmn2e for fastanalysis The trigger efficiency for 4He is about 70 with respect to offline reconstruction witha selection rate less than 04 Fig 6 presents the 〈dEdx〉 versus rigidity (p|Z|) distributionThe colored bands stand for the helium sample collected by HLT A cut of the DCA less than3 cm for negative tracks (05 cm for positive tracks) is used to reject the background In theleft panel a couple of 4He candidates are identified and well separated from 3He at the lowmomentum region A clear 4He signal has been observed and centered around the expected〈dEdx〉 value of 4He in the right panel

The 〈dEdx〉 of 3He (3He) and 4He (4He ) merge together at higher momentum regionand nσdEdx

defined as nσdEdx= 1

R ln(〈dEdx〉〈dEdx〉B) (R is the resolution of 〈dEdx〉) isused for further particle identification Fig 7 shows the combined particle identification with


5

Figure 4 The S3 ratio as a function of beam energy in minimumbias Au + Au collisionsfrom the default AMPT where the hadroinc freedom of degree is dominated (open circles) andthe melting AMPT where the partonic interaction is dominated (open squares) plus coalescencemodel calculations The available data from AGS [36] are plotted for reference The Λp ratiosfrom the model are also plotted Adapted from the Ref [35]

nσdEdxand mass2Z2 value distribution Two clusters of 4He and 4He located at nσdEdx

= 0

mass2Z2 = 348 (GeVc2)2 can be clearly separated from 3He and 3He as well as 3H and 3H arepresented in the top panel and bottom panel By counting 4He signal with the cuts windowminus2 lt nσdEdx

lt 3 and 282 (GeVc2)2 lt mass2Z2 lt 408 (GeVc2)2 as indicated in the top

panel 16 4He candidates are identified Together with 2 4He candidates detected by TPC alonein the year 2007 which is presented in the figure 18 4He candidates are observed by the STARexperiment So far 4He is the heaviest antimatter nucleus observed in the world Right afterthe public report of 4He from the STAR collaboration the LHC-ALICE collaboration alsoclaimed the observation of 4 4He particles [43]


6

Figure 5 A three-dimensional rendering of the STAR TPC surrounded by the TOF barrelshown as the outermost cylinder Tracks from an event which contains a 4He are shown withthe 4He track highlighted in bold red Adapted from the Ref [21]

4 Experimental searches for antinuclei in Cosmic rays

As we discussed in previous sections most efforts on searching for antinuclei center on inhigh-energy nuclear physics laboratories Nevertheless it is still a big challenge to captureany antinucleus in cosmos The search of 4He and heavier antinucleus in universe is one ofthe major motivations of space based apparatus such as the Alpha Magnetic Spectrometer[10] Both the RHIC-STAR experimental result and model calculation provide a backgroundestimation of 4He for the future observation in Cosmos production [21] Recently the effortto search for the Cosmic-Ray Antideuterons and Antihelium by the Balloon-borne Experimentwith Superconducting Spectrometer (BESS) collaboration has been made [44 45] Howeverno Antideuterons candidate was found using data collected during four BESS balloon flightsfrom 1997 to 2000 [44] No Antihelium candidate was found in BESS-Polar I data among84 times 106 |Z| = 2 nuclei from 10 to 20 GV (absolute rigidity) or in BESS-Polar II dataamong 40 times 107 |Z|= 2 nuclei from 10 to 14 GV [45] They derived an upper limit of 19 times10minus4 (m2 s srGeVnucleon)minus1 for the differential flux of cosmic-ray antideuterons at the 95confidence level between 017 and 115 GeVnucleon at the top of the atmosphere [44] For


7

shy05 0 050

20

40

60

80

shyπ

shy

K

p

d

H3

He

3

He

4

Negative Particles

1230

20

40

60

80

p|Z| (GeVc)

(keV

cm

)rang

dE

dx

lang

shy05 0 050

20

40

60

80

+π

+K

pd

H3

He

3 He

4

Positive Particles

1 2 3

Figure 6 〈dEdx〉 as a function of p|Z|) for negatively charged particles (left panel) andpositively charged particles (right panel) The black curves represent the expected values foreach particle species The lower edges of the colored bands correspond to the HLTrsquos onlinecalculation of 3σ below the 〈dEdx〉 band center for 3He The grey bands indicate the 〈dEdx〉 ofdeuteron proton kaon pion from Minimum bias events at 200GeV Adapted from the Ref [21]

antihelium assuming that antihelium has the same spectral shape as helium a 95 confidenceupper limit for the possible abundance of antihelium relative to helium of 69 times 10minus8 wasdetermined combining all BESS data including the two BESS-Polar flights With no assumedantihelium spectrum and a weighted average of the lowest antihelium efficiencies for each flightan upper limit of 10 times 10minus7 from 16 to 14 GV was determined for the combined BESS-Polardata Under both antihelium spectral assumptions these are the lowest limits obtained to date[44] Fig 12 shows the new upper limits of antiheliumhelium from the BESS experiment [44]The search for antihelium in cosmos remains an experimental challenge

5 Production mechanisms of antimatter light-nucleusAntimatter particles including e p d 3He 3

ΛH 4He and antihydrogen atoms have been observed

in the past eighty years Most of these antimatter particles were produced by nucleon-nucleonreactions where their production rate can be described by both thermodynamic model andcoalescence model [46 47 48 49] In thermodynamic model the system created is characterizedby the chemical freeze-out temperature (Tch) kinetic freeze-out temperature (Tkin) as well as thebaryon and strangeness chemical potential microB and microS respectively (Anti)nucleus is regardedas an object with energy EA = Amp (A is the atomic mass number mp is the mass of proton)emitted by the fireball [46] The production rate are proportional to the Boltzmann factoreminusmpAT as shown in Equ (1)

EAd3NA

d3PA=

gV

(2π)3EAe

minusmpAT (1)

where PA and g are the momentum and degeneracy of (anti)nucleus V is the volume of thefireball In coalescence picture (anti)nucleus is formed by coalescence at the last stage of thesystem evolution since there exists strong correlation between the constituent nucleons in their


8

2 4 6 8 10 12

shy14

shy12

shy10

shy8

shy6

shy4

shy2

0

2

4

He4

He3

H3shy14shy12shy10

shy8shy6shy4shy2024

2 4 6 8 10 12shy16

shy14

shy12

shy10

shy8

shy6

shy4

shy2

0

2

4

He4

He3

H3

2 4 6 8 10 12shy16shy14shy12shy10

shy8shy6shy4shy2024

2)2 (GeVc2Z2mass

dE

dx

σn

Figure 7 Top (bottom) panel shows the nσdEdxversus mass2Z2 distribution for negative

(positive) particles The horizontal dashed lines mark the nσdEdx= 0 while the vertical

ones stand for the theoretical mass values of 3He(3He) and 4He(4He) The signals of 4He and4He are counted in the cuts window of minus2 lt nσdEdx

lt 3 and 282(GeVc2)2 lt mass2Z2 lt

408(GeVc2)2 Adapted from the Ref [41]

phase space [18 50 51] The production probability is described by Equ (2)

EAd3NA

d3PA= BA(Ep

d3Np

d3Pp)Z(En

d3Nn

d3Pn)AminusZ (2)


9

Figure 8 The new upper limits of antiheliumhelium at the top of the atmosphere calculatedassuming the same energy spectrum for He as for He with previous experimental results Thelimit calculated with no spectral assumption is about 25 higher Adapted from Ref [45]

where E d3Nd3p

stands for the invariant yield of nucleons or (anti)nucleus Z is the atomic number

And pA pp pn are the momentum of (anti)nucleus protons and neutrons with pA = Atimes pp isassumed BA is the coalescence parameter

Figure 9 shows the calculated differential yields of p(p) Λ(Λ) and light (anti)nuclei as well


10

(GeVc)T

p

0 05 1 15 2 25 3 35 4 45 0

shy1010

shy910

shy810

shy710

shy610

shy510

shy410

shy310

shy210

shy110

1

10

210

p

01timesΛ

d

310timesHΛ

He3

ΛΛ

He4

STAR

(GeVc)T

p

0 05 1 15 2 25 3 35 4 45 5

shy10

shy9

shy8

shy7

shy6

shy5

shy4

shy3

shy2

shy1

1

10

2

p

01timesΛ

d

310timesHΛ

He3

He4

BlastWave + Coal

)2

GeV

2dy (

cT

dp

Tp

πN

22

d

Figure 9 Differential invariant yields versus pT distributions for p(p) Λ(Λ) and light(anti)nuclei as well as (anti)hypertriton and di-Λ The open symbols are experimental datapoints from the STAR measurement [52 53 18] and the black lines represent our calculationsfrom the hydrodynamical blast-wave model plus a coalescence model Adapted from Ref [49]

as (anti)hypertriton versus transverse momentum (pT ) distribution Our calculations [49] basedon the hydrodynamic motivated BlastWave model can reproduce the data points extracted bythe STAR experiment [52 53 18] Within the same framework we make predictions for theproduction rates of 3

ΛH (3Λ

H) and 4He (4He) etc by coupling with a naive coalescence model[49] With those producation rates we can explore relative particle production abundanceof (anti)nucleus and compare with data taken at RHIC Figure 10 shows the particle ratiosof (anti)nucleus both thermal model [46] and coalescence model [49] can fit the antinucleusto nucleus ratios at RHIC energy While the coalescence model has a better description for3ΛH3He and 3

ΛH3He than thermal model [49] In a microscopic picture both coalescence and

thermal production of (anti)nucleus predict an exponential trend for the production rate asa function of baryon number The exponential behavior of (anti)nucleus production rate innuclear nuclear reaction has been manifested in Figure 11 which depicts the invariant yields(d2N(2πpTdpTdy)) evaluated at the average transverse momentum (pT |B| = 0875GeVc)region versus baryon number distribution The solid symbols represent our coalescence modelcalculation which can fit the measured data points very well By fitting the model calculationwith an exponential function eminusr|B| a reduction rate of 1692 (1285) can be obtained for eachadditional antinucleon (nucleon) added to antinucleus (nucleus) compared to 16+10

minus06 times 103

(11+03minus02 times 103) for nucleus and (antinucleus) obtained by the STAR experiment The yield

of next stable antinucleus (antilithium-6) is predicted to be reduce by a factor of 26 times 106


11

Ra

tio

shy310

shy210

shy110

1

PHENIX data

STAR data

Coalescence model

Thermal model

pp dd3

Λ HΛ H3

He3

He3

He4

He4

He3He

4

He3

He4 3

ΛHe3H

3

ΛHe3

H

Figure 10 The comparison of particle ratios between data and model calculations The datapoints are taken from the STAR and the PHENIX experiments [20 21 17 3] The coalescentresults are based on naive coalescence algorithm with a momentum difference lower than 100MeVand a coordinator space difference less than 2R (R is the nuclear force radius) while the thermalpredication is taken from [46] Adapted from Ref [49]

compare to 4He and is impossible to be produced within current accelerator technology Theexcitation of (anti)nucleus from a highly correlated vacuum was discussed in reference [54]This new production mechanism can be tested with the measurement of the production rateof (anti)nucleus any deviation of the production rate of (anti)nucleus from usual reductionrate may indicate the exist of the direct excitation mechanism The low production rate of4He antinucleus in nuclear interaction implies that any observation of of 4He or even heavierantinucleus should be indicative of the existence of a large amount of antimatter somewhere inthe Universe

6 SummaryWe present a brief review on the 4He which is the heaviest antimatter nucleus observed so far[21] as well as 3

ΛH which is the first antimatter hypernucleus [20] Observation of both anti-nuclei

demonstrates that the RHIC is an excellent facility for antimatter production In the viewpointof antimatter production thermal model and coalescence model can essentially describe theproduction yield of antimatter and antimatter-matter ratio In our recent calculation basedon the hydrodynamic motivated BlastWave model coupled with a coalescence model at RHICenergy we demonstrate that the current approach can reproduce the differential invariant yieldsand relative production abundances of light antinuclei and antihypernuclei [49] The exponential


12

Baryon Number

shy6 shy4 shy2 0 2 4 6

)2

Ge

V2

dy (

cT

dp

Tp

πN

22

d

shy1110

shy1010

shy910

shy810

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shy310

shy210

shy110

1

10

210

p

d

3He

4He

p

d

3He

4He

STAR data

Coalescence

Figure 11 Invariant yields d2N(2πpTdpTdy) of (anti)nucleus at the average transversemomentum region (pT |B| = 0875GeVc) as a function of baryon number (B) The open symbolsrepresents the data points extracted by the STAR experiment at RHIC energy while solid onesare reproduced by coalescence model The lines represent the exponential fit for our coalescenceresults of positive particles (right) and negative particles (left) with formula eminusr|B| Adaptedfrom Ref [49]

behavior of the differential invariant yields versus baryon number distribution is studied Byextrapolating the distribution to B = -6 region the production rate of 6Li in high energyheavy ion collisions is about 10minus16 its observation with the current accelerator technology seemsimpractical As addressed in Sec 4 the observation of 4He and even heavier antinuclei in Cosmicrays is a great hint of the existence of massive antimatter in Universe Model calculations andexperimental measurements in high energy heavy ion collisions can simulate the interactionsbetween high energy protons and interstellar materials Thus current STAR results and modelcalculations provide a good background estimation for the future observation of 4He and evenheavier antinuclei in Universe

This work is partially supported by the NSFC under contracts No 11035009 1122010100511275250 and 10905085 the Knowledge Innovation Project of Chinese Academy of Sciencesunder Grant No KJCX2-EW-N01

References[1] BRAHMS Collaboration I Arsene et al Nucl Phys A 2005 757 1[2] PHOBOS Collaboratio B B Back et al Nucl Phys A 2005 757 28[3] STAR Collaboration J Adams et al Nucl Phys A 2005 757 102[4] PHENIX Collaboration S S Adcox et al Nucl Phys A 2005 757 184


13

[5] A Schuster Nature 1898 58 (1503) 367[6] P A M Dirac Proc R Soc Lond A 1928 117 610[7] C Y Chao Proc Nat Acad Sci 1930 16 431[8] C Y Chao Phys Rev 1930 36 1519[9] C D Anderson Phys Rev 1933 43 491[10] S Ahlen et al Nucl Instr and Meth in Phys Res A 1994 350 351[11] S Orito et al Phys Rev Lett 2000 84 1078[12] M Casolino et al Adv Space Res 2008 42 455[13] DE Dorfan J Eades LM Lederman W Lee CC Ting Phys Rev Lett 1965 14 1003[14] Y M Antipov et al Yad Fiz 1970 12 311 Nucl Phys 1971 B31 235[15] B Cork G R Lambertson O Piccioni W A Wenzel Phys Rev 1956 104 1193[16] N K Vishnevsky et al Yad Fiz 1974 20 694[17] PHENIX Collaboration J Adams et al Phys Rev Lett 2005 94 122302[18] STAR Collaboration B I Abelev et al e-Print arXiv09090566 [nucl-ex][19] O Chamberlain E Segre C Wiegand and T Ypsilantis Phys Rev 1955 100 947[20] STAR Collaboration B I Abelev et al Science 2010 328 58[21] STAR Collaboration B I Abelev et al Nature 2011 473 353[22] ALPHA Collaboration G B Andresen et al Nature Physics 2011 7 558[23] J K Ahn et al Phys Rev Lett 2001 87 132504[24] H Kamada J Golak K Miyagawa H Witala W Glockle Phys Rev C 1998 57 1595[25] J H Chen Nucl Phys A 2010 835 117[26] M Anderson et al Nucl Instrum Methods Phys Res A 2003 499 659[27] R H Dalitz G Rajasekharan Phys Lett 1962 1 58[28] R J Prem P H Steinberg Phys Rev 1964 136 B1803[29] G Bohm et al Nucl Phys B 1970 16 46[30] G Keyes et al Phys Rev Lett 1968 20 819[31] R E Phillips J Schneps Phys Rev 1969 180 1307[32] G Keyes et al Phys Rev D 1970 1 66[33] G Keyes J Sacton J H Wickens M M Block Nucl Phys B 1973 67 269[34] V Koch A Majumder J Randrup Phys Rev Lett 2005 95 182301[35] S Zhang et al Phys Lett B 2010 684 224[36] T A Armstrong et al Phys Rev C 2004 70 024902[37] JH Chen Nucl Phys A 2009 830 761c[38] STAR Collaboration BI Abelev et al Phys Rev Lett 2006 97 152301[39] STAR Collaboration J Adams et al Phys Rev Lett 2007 98 062301[40] STAR CollaborationBI Abelev et al Phys Rev C 200979 034909[41] L Xue J Phys G 2011 38 124072[42] B Bonner et al Nucl Instrum Methods Phys Res A 2003 508 181

M Shao et al Nucl Instrum Methods Phys Res A 2008 492 344[43] N Sharma J Phys G 2011 38 124189[44] H Fuke et al Phys Rev Lett 2005 95 081101[45] K Abe et al Phys Rev Lett 2012 108 131301[46] A Andronic P Braun-Munzinger J Stachele H Stocker Phys Lett B 2011 697 203[47] J Cleymans S Kabana I Kraus H Oeschler K Redlich and N Sharma Phys Rev C 2011 84 054916[48] J Steinheimer K Gudima A Botvina I Mishustin M Bleicher H Stocker Phys Lett B 2012 714 85[49] L Xue Y G Ma J H Chen S Zhang Phys Rev C 2012 85 064912[50] H Sato and K Yazaki et al Phys Lett B 1981 98 153[51] R Scheibl U Heinz Phys Rev C 1999 59 1585[52] STAR Collaboration BI Abelev et al Phys Lett B 2007 655 104[53] STAR Collaboration G Agakishiev et al Phys Rev Lett 2012 108 072301[54] W Greiner Int J Mod Phys E 1996 5 1


14

Observation of antimatter nuclei at RHIC-STAR

Yu-Gang Ma

Shanghai Institute of Applied Physics Chinese Academy of Sciences Shanghai 201800 China

E-mail ygmasinapaccn

Abstract In this article we present a brief review on the recent measurements of antimatterparticles at RHIC We highlight the observations of the antihypertriton (3

ΛH) and antihelium-4 nucleus (4He or α) and discuss the current experimental searches for antinuclei in cosmicrays Finally we present a recent calculation result using thermal and coalescence mechanismfor anti-light nuclei production

1 IntroductionRelativistic heavy-ion collision create suitable conditions for a phase transition from hadronto deconfined quark matter which was predicted by the Lattice QCD calculation Duringthe collision a hot and dense partonic matter can be formed ie so-called Quark-GluonPlasma (QGP) Many evidences have demonstrated that the QGP matter has been producedin central Au + Au collisions at RHIC energies [1 2 3 4] In the process large amounts ofenergy are deposited into a more extended volume than that achieved in elementary particlecollisions These nuclear interactions briefly produce hot and dense matter containing roughlyequal numbers of quarks and antiquarks Then the QGP expands rapidly and cools downand undergoes a transition into a hadron gas producing nucleons and their antiparticlesTherefore the relativistic heavy-ion collision can not only provide an environment to study stronginteracting phase transition and QCD matter but also an ideal venue to produce antimatterparticles

The ideal of antimatter can be traced back to the end of 1890s when Schuster discussed ahypothesis of the existence of antiatoms as well as antimatter solar system by hypothesis in hisletter to Nature magazine [5] However the modern concept of antimatter is originated from thenegative energy state solution of a quantum-mechanical equation which was proposed by Diracin 1928 [6] Two years later C Y Chao found that the absorption coefficient of hard γ-rays inheavy elements was much larger than that was expected from the Klein-Nishima formula or anyother [7 8] This ldquoabnormalrdquo absorption is in fact due to the creation of the pair of electron andits anti-partner so-called positron This experiment gives the first indirect observation of thefirst anti-matter particle namely positron Two years later Anderson observed positron with acloud chamber [9] Since the observation of the anti-proton (p) [19] in 1955 antimatter nucleisuch as d 3H 3He have been widely studied in both cosmic rays [10 11 12] and acceleratorexperiments [13 14 15 16 17 18] for the purposes of dark matter exploration and the studyof manmade matter such as quark gluon plasma respectively

The recent progress regard the observation of antihypertriton (3Λ

H) [20] and antihelium-

4 (4He or α) [21] nucleus in relativistic heavy ion collisions reported by the RHIC-STAR


Published under licence by IOP Publishing Ltd 1











channel of 3Λ



ΛH analysis




of 3Λ





Figure 1B for 3Λ



2

Co

un

ts (

Ke

Vc

m)

rangd

Ed

xlang

A

C

295 3 305 310

50

100

150

200

250

300

350

signal candidates

rotated background


295 3 305 310

20

40

60

80

100

120

140

signal candidates

rotated background




0 1 2 3 40

10

20

30

He3

π


shy04 shy02 0 02 040

100

200

300


He3

He3

He)3

Rigidity (GeVc) z(

Co

un

tsC

ou

nts

B

D



ΛH and 3Λ

H









ΛH) makes us



ΛH and 3Λ





3

50 cm

HΛ

3

He3

A

+π+πHe

3

B



Co

un

t

A

5 10 15 20 25

210

310

Λ

HΛ3

(cm)τc

2χ

3 4 5 6 7 8 9 10 11

0

05

1

15

2

25

= 0082

χ

= 1082χ

cm14

27 plusmn = 55 τc

H life

tim

e (

ps)

Λ3

B

shy1 0 1 2 3 4 5 6 70

50

100

150

200

250

300

350

400

450

(PDG)Λfree

ΛSTAR free

Dalitz 1962

Glockle 1998PR136 6B(1964)

819(1968)

PRL20

PR1801307(1969)

46(1970)

NPB16

66(1970)

PRD1

269(1973)

NPB67

STAR






ΛH and 3Λ



4



















5



= 0





6





7

shy05 0 050

20

40

60

80

shyπ

shy

K

p

d

H3

He

3

He

4

Negative Particles

1230

20

40

60

80

p|Z| (GeVc)

(keV

cm

)rang

dE

dx

lang

shy05 0 050

20

40

60

80

+π

+K

pd

H3

He

3 He

4

Positive Particles

1 2 3






EAd3NA

d3PA=

gV

(2π)3EAe

minusmpAT (1)



8

2 4 6 8 10 12

shy14

shy12

shy10

shy8

shy6

shy4

shy2

0

2

4

He4

He3

H3shy14shy12shy10

shy8shy6shy4shy2024

2 4 6 8 10 12shy16

shy14

shy12

shy10

shy8

shy6

shy4

shy2

0

2

4

He4

He3

H3

2 4 6 8 10 12shy16shy14shy12shy10

shy8shy6shy4shy2024

2)2 (GeVc2Z2mass

dE

dx

σn







EAd3NA

d3PA= BA(Ep

d3Np

d3Pp)Z(En

d3Nn

d3Pn)AminusZ (2)


9


where E d3Nd3p





10

(GeVc)T

p

0 05 1 15 2 25 3 35 4 45 0

shy1010

shy910

shy810

shy710

shy610

shy510

shy410

shy310

shy210

shy110

1

10

210

p

01timesΛ

d

310timesHΛ

He3

ΛΛ

He4

STAR

(GeVc)T

p

0 05 1 15 2 25 3 35 4 45 5

shy10

shy9

shy8

shy7

shy6

shy5

shy4

shy3

shy2

shy1

1

10

2

p

01timesΛ

d

310timesHΛ

He3

He4

BlastWave + Coal

)2

GeV

2dy (

cT

dp

Tp

πN

22

d



ΛH (3Λ




minus06 times 103




11

Ra

tio

shy310

shy210

shy110

1

PHENIX data

STAR data

Coalescence model

Thermal model

pp dd3

Λ HΛ H3

He3

He3

He4

He4

He3He

4

He3

He4 3

ΛHe3H

3

ΛHe3

H







12

Baryon Number


)2

Ge

V2

dy (

cT

dp

Tp

πN

22

d

shy1110

shy1010

shy910

shy810

shy710

shy610

shy510

shy410

shy310

shy210

shy110

1

10

210

p

d

3He

4He

p

d

3He

4He

STAR data

Coalescence






13




14











channel of 3Λ



ΛH analysis




of 3Λ





Figure 1B for 3Λ



2

Co

un

ts (

Ke

Vc

m)

rangd

Ed

xlang

A

C

295 3 305 310

50

100

150

200

250

300

350

signal candidates

rotated background


295 3 305 310

20

40

60

80

100

120

140

signal candidates

rotated background




0 1 2 3 40

10

20

30

He3

π


shy04 shy02 0 02 040

100

200

300


He3

He3

He)3

Rigidity (GeVc) z(

Co

un

tsC

ou

nts

B

D



ΛH and 3Λ

H









ΛH) makes us



ΛH and 3Λ





3

50 cm

HΛ

3

He3

A

+π+πHe

3

B



Co

un

t

A

5 10 15 20 25

210

310

Λ

HΛ3

(cm)τc

2χ

3 4 5 6 7 8 9 10 11

0

05

1

15

2

25

= 0082

χ

= 1082χ

cm14

27 plusmn = 55 τc

H life

tim

e (

ps)

Λ3

B

shy1 0 1 2 3 4 5 6 70

50

100

150

200

250

300

350

400

450

(PDG)Λfree

ΛSTAR free

Dalitz 1962

Glockle 1998PR136 6B(1964)

819(1968)

PRL20

PR1801307(1969)

46(1970)

NPB16

66(1970)

PRD1

269(1973)

NPB67

STAR






ΛH and 3Λ



4



















5



= 0





6





7

shy05 0 050

20

40

60

80

shyπ

shy

K

p

d

H3

He

3

He

4

Negative Particles

1230

20

40

60

80

p|Z| (GeVc)

(keV

cm

)rang

dE

dx

lang

shy05 0 050

20

40

60

80

+π

+K

pd

H3

He

3 He

4

Positive Particles

1 2 3






EAd3NA

d3PA=

gV

(2π)3EAe

minusmpAT (1)



8

2 4 6 8 10 12

shy14

shy12

shy10

shy8

shy6

shy4

shy2

0

2

4

He4

He3

H3shy14shy12shy10

shy8shy6shy4shy2024

2 4 6 8 10 12shy16

shy14

shy12

shy10

shy8

shy6

shy4

shy2

0

2

4

He4

He3

H3

2 4 6 8 10 12shy16shy14shy12shy10

shy8shy6shy4shy2024

2)2 (GeVc2Z2mass

dE

dx

σn







EAd3NA

d3PA= BA(Ep

d3Np

d3Pp)Z(En

d3Nn

d3Pn)AminusZ (2)


9


where E d3Nd3p





10

(GeVc)T

p

0 05 1 15 2 25 3 35 4 45 0

shy1010

shy910

shy810

shy710

shy610

shy510

shy410

shy310

shy210

shy110

1

10

210

p

01timesΛ

d

310timesHΛ

He3

ΛΛ

He4

STAR

(GeVc)T

p

0 05 1 15 2 25 3 35 4 45 5

shy10

shy9

shy8

shy7

shy6

shy5

shy4

shy3

shy2

shy1

1

10

2

p

01timesΛ

d

310timesHΛ

He3

He4

BlastWave + Coal

)2

GeV

2dy (

cT

dp

Tp

πN

22

d



ΛH (3Λ




minus06 times 103




11

Ra

tio

shy310

shy210

shy110

1

PHENIX data

STAR data

Coalescence model

Thermal model

pp dd3

Λ HΛ H3

He3

He3

He4

He4

He3He

4

He3

He4 3

ΛHe3H

3

ΛHe3

H







12

Baryon Number


)2

Ge

V2

dy (

cT

dp

Tp

πN

22

d

shy1110

shy1010

shy910

shy810

shy710

shy610

shy510

shy410

shy310

shy210

shy110

1

10

210

p

d

3He

4He

p

d

3He

4He

STAR data

Coalescence






13




14

Co

un

ts (

Ke

Vc

m)

rangd

Ed

xlang

A

C

295 3 305 310

50

100

150

200

250

300

350

signal candidates

rotated background


295 3 305 310

20

40

60

80

100

120

140

signal candidates

rotated background




0 1 2 3 40

10

20

30

He3

π


shy04 shy02 0 02 040

100

200

300


He3

He3

He)3

Rigidity (GeVc) z(

Co

un

tsC

ou

nts

B

D



ΛH and 3Λ

H









ΛH) makes us



ΛH and 3Λ





3

50 cm

HΛ

3

He3

A

+π+πHe

3

B



Co

un

t

A

5 10 15 20 25

210

310

Λ

HΛ3

(cm)τc

2χ

3 4 5 6 7 8 9 10 11

0

05

1

15

2

25

= 0082

χ

= 1082χ

cm14

27 plusmn = 55 τc

H life

tim

e (

ps)

Λ3

B

shy1 0 1 2 3 4 5 6 70

50

100

150

200

250

300

350

400

450

(PDG)Λfree

ΛSTAR free

Dalitz 1962

Glockle 1998PR136 6B(1964)

819(1968)

PRL20

PR1801307(1969)

46(1970)

NPB16

66(1970)

PRD1

269(1973)

NPB67

STAR






ΛH and 3Λ



4



















5



= 0





6





7

shy05 0 050

20

40

60

80

shyπ

shy

K

p

d

H3

He

3

He

4

Negative Particles

1230

20

40

60

80

p|Z| (GeVc)

(keV

cm

)rang

dE

dx

lang

shy05 0 050

20

40

60

80

+π

+K

pd

H3

He

3 He

4

Positive Particles

1 2 3






EAd3NA

d3PA=

gV

(2π)3EAe

minusmpAT (1)



8

2 4 6 8 10 12

shy14

shy12

shy10

shy8

shy6

shy4

shy2

0

2

4

He4

He3

H3shy14shy12shy10

shy8shy6shy4shy2024

2 4 6 8 10 12shy16

shy14

shy12

shy10

shy8

shy6

shy4

shy2

0

2

4

He4

He3

H3

2 4 6 8 10 12shy16shy14shy12shy10

shy8shy6shy4shy2024

2)2 (GeVc2Z2mass

dE

dx

σn







EAd3NA

d3PA= BA(Ep

d3Np

d3Pp)Z(En

d3Nn

d3Pn)AminusZ (2)


9


where E d3Nd3p





10

(GeVc)T

p

0 05 1 15 2 25 3 35 4 45 0

shy1010

shy910

shy810

shy710

shy610

shy510

shy410

shy310

shy210

shy110

1

10

210

p

01timesΛ

d

310timesHΛ

He3

ΛΛ

He4

STAR

(GeVc)T

p

0 05 1 15 2 25 3 35 4 45 5

shy10

shy9

shy8

shy7

shy6

shy5

shy4

shy3

shy2

shy1

1

10

2

p

01timesΛ

d

310timesHΛ

He3

He4

BlastWave + Coal

)2

GeV

2dy (

cT

dp

Tp

πN

22

d



ΛH (3Λ




minus06 times 103




11

Ra

tio

shy310

shy210

shy110

1

PHENIX data

STAR data

Coalescence model

Thermal model

pp dd3

Λ HΛ H3

He3

He3

He4

He4

He3He

4

He3

He4 3

ΛHe3H

3

ΛHe3

H







12

Baryon Number


)2

Ge

V2

dy (

cT

dp

Tp

πN

22

d

shy1110

shy1010

shy910

shy810

shy710

shy610

shy510

shy410

shy310

shy210

shy110

1

10

210

p

d

3He

4He

p

d

3He

4He

STAR data

Coalescence






13




14

50 cm

HΛ

3

He3

A

+π+πHe

3

B



Co

un

t

A

5 10 15 20 25

210

310

Λ

HΛ3

(cm)τc

2χ

3 4 5 6 7 8 9 10 11

0

05

1

15

2

25

= 0082

χ

= 1082χ

cm14

27 plusmn = 55 τc

H life

tim

e (

ps)

Λ3

B

shy1 0 1 2 3 4 5 6 70

50

100

150

200

250

300

350

400

450

(PDG)Λfree

ΛSTAR free

Dalitz 1962

Glockle 1998PR136 6B(1964)

819(1968)

PRL20

PR1801307(1969)

46(1970)

NPB16

66(1970)

PRD1

269(1973)

NPB67

STAR






ΛH and 3Λ



4



















5



= 0





6





7

shy05 0 050

20

40

60

80

shyπ

shy

K

p

d

H3

He

3

He

4

Negative Particles

1230

20

40

60

80

p|Z| (GeVc)

(keV

cm

)rang

dE

dx

lang

shy05 0 050

20

40

60

80

+π

+K

pd

H3

He

3 He

4

Positive Particles

1 2 3






EAd3NA

d3PA=

gV

(2π)3EAe

minusmpAT (1)



8

2 4 6 8 10 12

shy14

shy12

shy10

shy8

shy6

shy4

shy2

0

2

4

He4

He3

H3shy14shy12shy10

shy8shy6shy4shy2024

2 4 6 8 10 12shy16

shy14

shy12

shy10

shy8

shy6

shy4

shy2

0

2

4

He4

He3

H3

2 4 6 8 10 12shy16shy14shy12shy10

shy8shy6shy4shy2024

2)2 (GeVc2Z2mass

dE

dx

σn







EAd3NA

d3PA= BA(Ep

d3Np

d3Pp)Z(En

d3Nn

d3Pn)AminusZ (2)


9


where E d3Nd3p





10

(GeVc)T

p

0 05 1 15 2 25 3 35 4 45 0

shy1010

shy910

shy810

shy710

shy610

shy510

shy410

shy310

shy210

shy110

1

10

210

p

01timesΛ

d

310timesHΛ

He3

ΛΛ

He4

STAR

(GeVc)T

p

0 05 1 15 2 25 3 35 4 45 5

shy10

shy9

shy8

shy7

shy6

shy5

shy4

shy3

shy2

shy1

1

10

2

p

01timesΛ

d

310timesHΛ

He3

He4

BlastWave + Coal

)2

GeV

2dy (

cT

dp

Tp

πN

22

d



ΛH (3Λ




minus06 times 103




11

Ra

tio

shy310

shy210

shy110

1

PHENIX data

STAR data

Coalescence model

Thermal model

pp dd3

Λ HΛ H3

He3

He3

He4

He4

He3He

4

He3

He4 3

ΛHe3H

3

ΛHe3

H







12

Baryon Number


)2

Ge

V2

dy (

cT

dp

Tp

πN

22

d

shy1110

shy1010

shy910

shy810

shy710

shy610

shy510

shy410

shy310

shy210

shy110

1

10

210

p

d

3He

4He

p

d

3He

4He

STAR data

Coalescence






13




14



















5



= 0





6





7

shy05 0 050

20

40

60

80

shyπ

shy

K

p

d

H3

He

3

He

4

Negative Particles

1230

20

40

60

80

p|Z| (GeVc)

(keV

cm

)rang

dE

dx

lang

shy05 0 050

20

40

60

80

+π

+K

pd

H3

He

3 He

4

Positive Particles

1 2 3






EAd3NA

d3PA=

gV

(2π)3EAe

minusmpAT (1)



8

2 4 6 8 10 12

shy14

shy12

shy10

shy8

shy6

shy4

shy2

0

2

4

He4

He3

H3shy14shy12shy10

shy8shy6shy4shy2024

2 4 6 8 10 12shy16

shy14

shy12

shy10

shy8

shy6

shy4

shy2

0

2

4

He4

He3

H3

2 4 6 8 10 12shy16shy14shy12shy10

shy8shy6shy4shy2024

2)2 (GeVc2Z2mass

dE

dx

σn







EAd3NA

d3PA= BA(Ep

d3Np

d3Pp)Z(En

d3Nn

d3Pn)AminusZ (2)


9


where E d3Nd3p





10

(GeVc)T

p

0 05 1 15 2 25 3 35 4 45 0

shy1010

shy910

shy810

shy710

shy610

shy510

shy410

shy310

shy210

shy110

1

10

210

p

01timesΛ

d

310timesHΛ

He3

ΛΛ

He4

STAR

(GeVc)T

p

0 05 1 15 2 25 3 35 4 45 5

shy10

shy9

shy8

shy7

shy6

shy5

shy4

shy3

shy2

shy1

1

10

2

p

01timesΛ

d

310timesHΛ

He3

He4

BlastWave + Coal

)2

GeV

2dy (

cT

dp

Tp

πN

22

d



ΛH (3Λ




minus06 times 103




11

Ra

tio

shy310

shy210

shy110

1

PHENIX data

STAR data

Coalescence model

Thermal model

pp dd3

Λ HΛ H3

He3

He3

He4

He4

He3He

4

He3

He4 3

ΛHe3H

3

ΛHe3

H







12

Baryon Number


)2

Ge

V2

dy (

cT

dp

Tp

πN

22

d

shy1110

shy1010

shy910

shy810

shy710

shy610

shy510

shy410

shy310

shy210

shy110

1

10

210

p

d

3He

4He

p

d

3He

4He

STAR data

Coalescence






13




14



= 0





6





7

shy05 0 050

20

40

60

80

shyπ

shy

K

p

d

H3

He

3

He

4

Negative Particles

1230

20

40

60

80

p|Z| (GeVc)

(keV

cm

)rang

dE

dx

lang

shy05 0 050

20

40

60

80

+π

+K

pd

H3

He

3 He

4

Positive Particles

1 2 3






EAd3NA

d3PA=

gV

(2π)3EAe

minusmpAT (1)



8

2 4 6 8 10 12

shy14

shy12

shy10

shy8

shy6

shy4

shy2

0

2

4

He4

He3

H3shy14shy12shy10

shy8shy6shy4shy2024

2 4 6 8 10 12shy16

shy14

shy12

shy10

shy8

shy6

shy4

shy2

0

2

4

He4

He3

H3

2 4 6 8 10 12shy16shy14shy12shy10

shy8shy6shy4shy2024

2)2 (GeVc2Z2mass

dE

dx

σn







EAd3NA

d3PA= BA(Ep

d3Np

d3Pp)Z(En

d3Nn

d3Pn)AminusZ (2)


9


where E d3Nd3p





10

(GeVc)T

p

0 05 1 15 2 25 3 35 4 45 0

shy1010

shy910

shy810

shy710

shy610

shy510

shy410

shy310

shy210

shy110

1

10

210

p

01timesΛ

d

310timesHΛ

He3

ΛΛ

He4

STAR

(GeVc)T

p

0 05 1 15 2 25 3 35 4 45 5

shy10

shy9

shy8

shy7

shy6

shy5

shy4

shy3

shy2

shy1

1

10

2

p

01timesΛ

d

310timesHΛ

He3

He4

BlastWave + Coal

)2

GeV

2dy (

cT

dp

Tp

πN

22

d



ΛH (3Λ




minus06 times 103




11

Ra

tio

shy310

shy210

shy110

1

PHENIX data

STAR data

Coalescence model

Thermal model

pp dd3

Λ HΛ H3

He3

He3

He4

He4

He3He

4

He3

He4 3

ΛHe3H

3

ΛHe3

H







12

Baryon Number


)2

Ge

V2

dy (

cT

dp

Tp

πN

22

d

shy1110

shy1010

shy910

shy810

shy710

shy610

shy510

shy410

shy310

shy210

shy110

1

10

210

p

d

3He

4He

p

d

3He

4He

STAR data

Coalescence






13




14





7

shy05 0 050

20

40

60

80

shyπ

shy

K

p

d

H3

He

3

He

4

Negative Particles

1230

20

40

60

80

p|Z| (GeVc)

(keV

cm

)rang

dE

dx

lang

shy05 0 050

20

40

60

80

+π

+K

pd

H3

He

3 He

4

Positive Particles

1 2 3






EAd3NA

d3PA=

gV

(2π)3EAe

minusmpAT (1)



8

2 4 6 8 10 12

shy14

shy12

shy10

shy8

shy6

shy4

shy2

0

2

4

He4

He3

H3shy14shy12shy10

shy8shy6shy4shy2024

2 4 6 8 10 12shy16

shy14

shy12

shy10

shy8

shy6

shy4

shy2

0

2

4

He4

He3

H3

2 4 6 8 10 12shy16shy14shy12shy10

shy8shy6shy4shy2024

2)2 (GeVc2Z2mass

dE

dx

σn







EAd3NA

d3PA= BA(Ep

d3Np

d3Pp)Z(En

d3Nn

d3Pn)AminusZ (2)


9


where E d3Nd3p





10

(GeVc)T

p

0 05 1 15 2 25 3 35 4 45 0

shy1010

shy910

shy810

shy710

shy610

shy510

shy410

shy310

shy210

shy110

1

10

210

p

01timesΛ

d

310timesHΛ

He3

ΛΛ

He4

STAR

(GeVc)T

p

0 05 1 15 2 25 3 35 4 45 5

shy10

shy9

shy8

shy7

shy6

shy5

shy4

shy3

shy2

shy1

1

10

2

p

01timesΛ

d

310timesHΛ

He3

He4

BlastWave + Coal

)2

GeV

2dy (

cT

dp

Tp

πN

22

d



ΛH (3Λ




minus06 times 103




11

Ra

tio

shy310

shy210

shy110

1

PHENIX data

STAR data

Coalescence model

Thermal model

pp dd3

Λ HΛ H3

He3

He3

He4

He4

He3He

4

He3

He4 3

ΛHe3H

3

ΛHe3

H







12

Baryon Number


)2

Ge

V2

dy (

cT

dp

Tp

πN

22

d

shy1110

shy1010

shy910

shy810

shy710

shy610

shy510

shy410

shy310

shy210

shy110

1

10

210

p

d

3He

4He

p

d

3He

4He

STAR data

Coalescence






13




14

shy05 0 050

20

40

60

80

shyπ

shy

K

p

d

H3

He

3

He

4

Negative Particles

1230

20

40

60

80

p|Z| (GeVc)

(keV

cm

)rang

dE

dx

lang

shy05 0 050

20

40

60

80

+π

+K

pd

H3

He

3 He

4

Positive Particles

1 2 3






EAd3NA

d3PA=

gV

(2π)3EAe

minusmpAT (1)



8

2 4 6 8 10 12

shy14

shy12

shy10

shy8

shy6

shy4

shy2

0

2

4

He4

He3

H3shy14shy12shy10

shy8shy6shy4shy2024

2 4 6 8 10 12shy16

shy14

shy12

shy10

shy8

shy6

shy4

shy2

0

2

4

He4

He3

H3

2 4 6 8 10 12shy16shy14shy12shy10

shy8shy6shy4shy2024

2)2 (GeVc2Z2mass

dE

dx

σn







EAd3NA

d3PA= BA(Ep

d3Np

d3Pp)Z(En

d3Nn

d3Pn)AminusZ (2)


9


where E d3Nd3p





10

(GeVc)T

p

0 05 1 15 2 25 3 35 4 45 0

shy1010

shy910

shy810

shy710

shy610

shy510

shy410

shy310

shy210

shy110

1

10

210

p

01timesΛ

d

310timesHΛ

He3

ΛΛ

He4

STAR

(GeVc)T

p

0 05 1 15 2 25 3 35 4 45 5

shy10

shy9

shy8

shy7

shy6

shy5

shy4

shy3

shy2

shy1

1

10

2

p

01timesΛ

d

310timesHΛ

He3

He4

BlastWave + Coal

)2

GeV

2dy (

cT

dp

Tp

πN

22

d



ΛH (3Λ




minus06 times 103




11

Ra

tio

shy310

shy210

shy110

1

PHENIX data

STAR data

Coalescence model

Thermal model

pp dd3

Λ HΛ H3

He3

He3

He4

He4

He3He

4

He3

He4 3

ΛHe3H

3

ΛHe3

H







12

Baryon Number


)2

Ge

V2

dy (

cT

dp

Tp

πN

22

d

shy1110

shy1010

shy910

shy810

shy710

shy610

shy510

shy410

shy310

shy210

shy110

1

10

210

p

d

3He

4He

p

d

3He

4He

STAR data

Coalescence






13




14

2 4 6 8 10 12

shy14

shy12

shy10

shy8

shy6

shy4

shy2

0

2

4

He4

He3

H3shy14shy12shy10

shy8shy6shy4shy2024

2 4 6 8 10 12shy16

shy14

shy12

shy10

shy8

shy6

shy4

shy2

0

2

4

He4

He3

H3

2 4 6 8 10 12shy16shy14shy12shy10

shy8shy6shy4shy2024

2)2 (GeVc2Z2mass

dE

dx

σn







EAd3NA

d3PA= BA(Ep

d3Np

d3Pp)Z(En

d3Nn

d3Pn)AminusZ (2)


9


where E d3Nd3p





10

(GeVc)T

p

0 05 1 15 2 25 3 35 4 45 0

shy1010

shy910

shy810

shy710

shy610

shy510

shy410

shy310

shy210

shy110

1

10

210

p

01timesΛ

d

310timesHΛ

He3

ΛΛ

He4

STAR

(GeVc)T

p

0 05 1 15 2 25 3 35 4 45 5

shy10

shy9

shy8

shy7

shy6

shy5

shy4

shy3

shy2

shy1

1

10

2

p

01timesΛ

d

310timesHΛ

He3

He4

BlastWave + Coal

)2

GeV

2dy (

cT

dp

Tp

πN

22

d



ΛH (3Λ




minus06 times 103




11

Ra

tio

shy310

shy210

shy110

1

PHENIX data

STAR data

Coalescence model

Thermal model

pp dd3

Λ HΛ H3

He3

He3

He4

He4

He3He

4

He3

He4 3

ΛHe3H

3

ΛHe3

H







12

Baryon Number


)2

Ge

V2

dy (

cT

dp

Tp

πN

22

d

shy1110

shy1010

shy910

shy810

shy710

shy610

shy510

shy410

shy310

shy210

shy110

1

10

210

p

d

3He

4He

p

d

3He

4He

STAR data

Coalescence






13




14


where E d3Nd3p





10

(GeVc)T

p

0 05 1 15 2 25 3 35 4 45 0

shy1010

shy910

shy810

shy710

shy610

shy510

shy410

shy310

shy210

shy110

1

10

210

p

01timesΛ

d

310timesHΛ

He3

ΛΛ

He4

STAR

(GeVc)T

p

0 05 1 15 2 25 3 35 4 45 5

shy10

shy9

shy8

shy7

shy6

shy5

shy4

shy3

shy2

shy1

1

10

2

p

01timesΛ

d

310timesHΛ

He3

He4

BlastWave + Coal

)2

GeV

2dy (

cT

dp

Tp

πN

22

d



ΛH (3Λ




minus06 times 103




11

Ra

tio

shy310

shy210

shy110

1

PHENIX data

STAR data

Coalescence model

Thermal model

pp dd3

Λ HΛ H3

He3

He3

He4

He4

He3He

4

He3

He4 3

ΛHe3H

3

ΛHe3

H







12

Baryon Number


)2

Ge

V2

dy (

cT

dp

Tp

πN

22

d

shy1110

shy1010

shy910

shy810

shy710

shy610

shy510

shy410

shy310

shy210

shy110

1

10

210

p

d

3He

4He

p

d

3He

4He

STAR data

Coalescence






13




14

(GeVc)T

p

0 05 1 15 2 25 3 35 4 45 0

shy1010

shy910

shy810

shy710

shy610

shy510

shy410

shy310

shy210

shy110

1

10

210

p

01timesΛ

d

310timesHΛ

He3

ΛΛ

He4

STAR

(GeVc)T

p

0 05 1 15 2 25 3 35 4 45 5

shy10

shy9

shy8

shy7

shy6

shy5

shy4

shy3

shy2

shy1

1

10

2

p

01timesΛ

d

310timesHΛ

He3

He4

BlastWave + Coal

)2

GeV

2dy (

cT

dp

Tp

πN

22

d



ΛH (3Λ




minus06 times 103




11

Ra

tio

shy310

shy210

shy110

1

PHENIX data

STAR data

Coalescence model

Thermal model

pp dd3

Λ HΛ H3

He3

He3

He4

He4

He3He

4

He3

He4 3

ΛHe3H

3

ΛHe3

H







12

Baryon Number


)2

Ge

V2

dy (

cT

dp

Tp

πN

22

d

shy1110

shy1010

shy910

shy810

shy710

shy610

shy510

shy410

shy310

shy210

shy110

1

10

210

p

d

3He

4He

p

d

3He

4He

STAR data

Coalescence






13




14

Ra

tio

shy310

shy210

shy110

1

PHENIX data

STAR data

Coalescence model

Thermal model

pp dd3

Λ HΛ H3

He3

He3

He4

He4

He3He

4

He3

He4 3

ΛHe3H

3

ΛHe3

H







12

Baryon Number


)2

Ge

V2

dy (

cT

dp

Tp

πN

22

d

shy1110

shy1010

shy910

shy810

shy710

shy610

shy510

shy410

shy310

shy210

shy110

1

10

210

p

d

3He

4He

p

d

3He

4He

STAR data

Coalescence






13




14

Baryon Number


)2

Ge

V2

dy (

cT

dp

Tp

πN

22

d

shy1110

shy1010

shy910

shy810

shy710

shy610

shy510

shy410

shy310

shy210

shy110

1

10

210

p

d

3He

4He

p

d

3He

4He

STAR data

Coalescence






13




14




14

observation of antimatter nuclei at rhic-star

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