Studies of Hyperons and Antihyperons in Nuclei

0.55 MB·English

by  Josef Pochodzalla

Studies of Hyperons and Antihyperons in Nuclei
Josef POCHODZALLA∗
JohannesGutenberg-UniversitätMainz,InstitutfürKernphysik,D-55099Germany
E-mail: [email protected]
Alexander BOTVINA
1 InstituteforNuclearResearch,RussianAcademyofSciences,117312Moscow,Russia
1
E-mail: [email protected]
0
2
Alicia SANCHEZ LORENTE

n
JohannesGutenberg-UniversitätMainz,InstitutfürKernphysik,D-55099Germany
a
J E-mail: [email protected]

7
1 Stored antiproton beams at the international FAIR facility will provide unique opportunities to

study hyperons as well as antihyperons in nuclear systems. Precise γ-spectroscopy of multi-
]
x strange hypernuclei will serve as a laboratory for the hyperon-hyperon interaction. Exclusive
e
hadron-antihadron pair production close to threshold can measure the potential of a antihadron
-
l
c relativetothatofthecoincidenthadrons.
u Inthepresentworkweexploretheproductionofexcitedstatesindoublehypernucleifollowing
n
the micro-canonical break-up of an initially excited double hypernucleus which is created by
[
the absorption and conversion of a stopped Ξ− hyperon. Generally the formation of excited

1
hypernuclearstatesrelativetogroundstatesdominatesinthismodel. Fordifferentinitialtarget
v
1 nucleiwhichabsorbtheΞ−,differentdoublehypernucleinucleidominate. Wealsocomparethe
8 modelpredictionswiththecorrelatedpionspectrameasuredbytheE906collaboration.
1
Inantiprotonnucleusreactionstheevent-by-eventtransversemomentumcorrelationsofhadron-
3
. antihadron pairs produced close to threshold contain information on the difference between the
1
0 nuclear potential of the hadron and the associated antihadron. For produced D-meson pairs at
1
6.7GeV/cthesensitivityofthetransversemomentacorrelationwillprobablybetosmalltode-
1
: ducedifferencesbetweenthepotentialsforD+andD−mesons. However,forΞΞpairsproduced
v
i at2.9GeV/ctheasymmetryissufficientlysensitivetopredicteddifferencesbetweentheΞand
X
Ξ potentials even if the momentum and density dependence of the the potential are taken into
r
a
account.
XLVIIIInternationalWinterMeetingonNuclearPhysicsinMemoriamofIleanaIori
25-29January2010
Bormio,Italy
∗Speaker.
(cid:13)c Copyrightownedbytheauthor(s)underthetermsoftheCreativeCommonsAttribution-NonCommercial-ShareAlikeLicence. http://pos.sissa.it/
StudiesofHyperonsandAntihyperonsinNuclei JosefPOCHODZALLA
1. Introduction
Quantum Chromo Dynamics (QCD) is the theory of the force responsible for the binding of
nucleonsandnucleiandthusofasignificantfractionoftheordinarymatterinouruniverse. While
the internal structure of hadrons and the spectra of their excited states are important aspects of
QCD,itisatleastequallyimportanttounderstandhownuclearphysicsemergesinamorerigorous
way out of QCD and how nuclear structures - nuclei on the small scale and dense stellar objects
on the large scale - are formed. In particular the role of strangeness in neutron stars has not been
settledyet.
The study of hypernuclei can illuminate features that are obscured in conventional nuclear
systems. The hyperon offers a selective probe of the hadronic many-body problem as it is not
restricted by the Pauli principle. Since direct scattering experiments between two hyperons are
impractical, the precise spectroscopy of multi-strange hypernuclei provides a unique chance to
explore the hyperon-hyperon interaction. Significant progress in nuclear structure calculations in
chiral effective field theory nurtures the hope that detailed information on excitation spectra of
double hypernuclei will provide unique information on the hyperon-hyperon interactions. At the
same time, the Λ-N and Λ-Λ weak interaction can be studied by hypernuclei decays, opening a
inimitablewindowforthefour-baryon,strangenessnon-conservingweakinteraction.
Furthermore,thephysicsofstrangenessinhadronicsystemsisaconstantlydevelopingfield. It
bringsupnew,oftenunexpectedresults,newchallengesandopenquestionslikeanti-hypernuclei,
kaonicnuclei,exotichadronicstateslikethecontroversiallydiscussedpentaquarkbaryonsandthe
H-dibaryon. Based on G-parity transformation [1] Dürr and Teller predicted within an early form
of a relativistic field theory a strongly attractive potential for antiprotons in nuclei [2]. First in-
vestigationsofantiproton-nucleusscatteringcrosssections[3,4,5]showedhoweverdisagreement
with a strong attractive potential. Later, X-ray transitions in antiprotonic atoms [6, 7, 8, 9, 10]
gavealsohintsforanattractivepotentialalbeitwithlargeuncertainties[11,12]. Morecomprehen-
sivestudies[13]ofantiprotonicX-raysaswellasrecentanalysesoftheproductionofantiprotons
in reactions with heavy ions resulted in attractive real potentials in the range of about -100 to -
150MeV[14,15,16]. ItisobviousthatG-paritycanonlyprovidealinkbetweentheNN andNN
interactions for distances where meson exchange is a valid concept [17, 18]. For distances lower
than about 1 fm, quark degrees of freedom may play a decisive role. Nevertheless this considera-
tionstillindicatesthatadirectcomparisonoftheinteractionsofbaryonsandantibaryonsinnuclei
mayhelptoshedsomelightonthenatureofshort-rangebaryon-baryonforces.
2. ProductionofDoubleHypernuclei
ThesimultaneousproductionandimplementationoftwoΛparticlesintoanucleusisintricate.
Thereisapossibilitytoproducemulti-strangehypernucleiinheavyioncollisionsviacoalescence
[19,20]. ThefirstobservationofantihypernucleibytheSTARcollaborationimpressivelyillustrates
the potential of this method [21]. However, high resolution spectroscopy of excited states is not
feasible. To produce double hypernuclei in a more ‘controlled’ way the conversion of a captured
Ξ− andaprotonintotwoΛparticlescanbeused. Thisprocessreleases–ignoringbindingenergy
effects – only 28MeV. For light nuclei there exists therefore a significant probability of the order
2
StudiesofHyperonsandAntihyperonsinNuclei JosefPOCHODZALLA
Z
N
S
Figure 1: Present knowledge on S=-1 nuclei (blue) and S=-2 nuclei (yellow). Only very few individual
events of double hypernuclei have been detected and identified so far. First antihypertritons were recently
observedbytheSTARcollaboration[21].
ofafewpercentthatbothΛhyperonsaretrappedinthesameexcitednuclearfragment[22,23,24,
25,26,27].
Unfortunately Ξ− hyperons produced in reactions with stable hadron beams have usually
rather high momenta. Therefore, direct capture of the Ξ− in the nucleus is rather unlikely. Even
in case of the (K−,K+) double strangeness exchange reaction, Ξ− hyperons are produced with
typical momenta of 500 MeV/c at beam momenta around 1.8 GeV/c [24, 28]. The advantage of
this production process is that the outgoing K+ can be used as a tag for the reaction. A drawback
is the low kaon beam intensity and hence the need for thick primary targets. Furthermore, as a
consequence of the large momentum transfer, the probability to form bound Ξ− states directly is
rathersmallonthelevelof1%[29,30]andtheproductionofquasi-freeΞ−dominates. StilltheΞ−
hyperonsinthequasi-freeregionmaybeabsorbedintothetargetnucleusviaarescatteringprocess
onanucleonwhichitselfisknockedoutoftheprimarynucleus. Thistwo-stepprocessispredicted
toexceedthedirectcapturebymorethanafactorof6[23].
On the other hand most (∼ 80%) Ξ− hyperons escape from the primary target nucleus in
(K−,K+)reactions. However,inasecondstep,theseΞ− hyperonscanbesloweddowninadense,
solid material (e.g. a nuclear emulsion) and form Ξ− atoms [31]. After an atomic cascade, the
Ξ-hyperoniseventuallycapturedbyasecondarytargetnucleusandconvertedviatheΞ−p→ΛΛ
reaction into two Λ hyperons. In a similar two-step process relatively low momentum Ξ− can
alsobeproducedusingantiprotonbeamsinpp→Ξ−Ξ+ orpn→Ξ−Ξ◦ reactionsifthisreactions
happens in a complex nucleus where the produced Ξ− can re-scatter [32, 33]. The advantage as
comparedtothekaoninducedreactionisthatantiprotonsarestableandcanberetainedinastorage
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StudiesofHyperonsandAntihyperonsinNuclei JosefPOCHODZALLA
ring. Thisallowsaratherhighluminosityevenwithverythinprimarytargets.
Because of the two-step mechanism, spectroscopic studies, based on two-body kinematics
likeinsinglehypernucleusproduction,cannotbeperformed. Spectroscopicinformationondouble
hypernucleicanthereforeonlybeobtainedviatheirdecayproducts. Thekineticenergiesofweak
decay products are sensitive to the binding energies of the two Λ hyperons. While the double
pionic decay of light double hypernuclei can be used as an effective experimental filter to reduce
the background [34] the unique identification of hypernuclei groundstates only via their pionic
decay is usually hampered by the limited resolution. Instead, γ-rays emitted via the sequential
decayofexciteddoublehypernucleimayprovidepreciseinformationonthelevelstructure.
2.1 StatisticalDecayofexcitedDoublyStrangeNuclei
The PANDA experiment[33]whichisplannedattheinternationalFacilityforAntiprotonand
Ion Research FAIR in Darmstadt aims at the high resolution γ-ray spectroscopy of double hyper-
nuclei[32]. Animportantquestionistowhatextentdoublehypernucleiinexcited, particlestable
states are populated following the break-up of an highly excited doubly strange nucleus which is
formed after the absorption and conversion of a stopped Ξ−. For light nuclei even a relatively
small excitation energy may be comparable with their binding energy. We therefore consider the
explosive decay of the excited nucleus into several smaller clusters as the principal mechanism of
de-excitation.
To describe this break-up process we have developed a model [35] which is similar to the
famous Fermi model for particle production in nuclear reactions [36]. We assume that the nu-
cleuswithmassnumbersA , chargeZ , andthenumberofΛhyperonsH (hereH =2)breaks-up
0 0 0 0
simultaneouslyintocoldandslightlyexcitedfragments,whichhavealifetimelongerthanthede-
cay time, estimated as an order of 100-300 fm/c. In the model we consider all possible break-up
channels, which satisfy the mass number, hyperon number (i.e. strangeness), charge, energy and
momentumconservations,andtakeintoaccountthecompetitionbetweenthesechannels.
Theexcitationenergyoftheinitial,highlyexciteddoubleΛnucleusisdeterminedbythebind-
ingenergyofthecapturedΞ−hyperon. Unfortunately,stillverylittleisestablishedexperimentally
ontheinteractionofΞ− hyperonswithnuclei. Variousdatasuggestanuclearpotentialwelldepth
around 20MeV (see e.g. [37, 10]). Calculations of light Ξ atoms [31] predict that the conversion
ofthecapturedΞ− fromexcitedstateswithcorrespondinglysmallbindingenergiesdominates. In
a nuclear emulsion experiment a Ξ− capture at rest with two single hyperfragments has been ob-
served[38]whichwasinterpretedasΞ− +12C→4H+9Bereaction. Thededucedbindingenergy
Λ Λ
of the Ξ− varied between 0.62MeV and 3.70MeV, depending whether only one out of the two
hyperfragments or both fragments were produced in an excited particle stable state. In order to
takeintoaccounttheuncertaintiesoftheexcitationenergyoftheconvertedΞ−-states,thecalcula-
tionswereperformedforarangeofenergies0≤B ≤E ,constructinginthiswaytheexcitation
Ξ max
functionsfortheproductionofhypernuclei.
Fig.2showsasanexampletheproductionofground(g.s.) andexcited(ex.s.) statesofsingle
+onefreeΛ(SHP),twin(THP)anddouble(DHP)hypernucleiincaseofa12Ctargetasafunction
oftheassumedΞ− bindingenergy. WithincreasingΞ− bindingenergytheexcitationenergyofthe
excited primary 13 B∗ nucleus decreases from left to right from about 40MeV to 15MeV. For all
ΛΛ
excitation energies above 20MeV the production of excited double hypernuclei dominates (green
4
StudiesofHyperonsandAntihyperonsinNuclei JosefPOCHODZALLA
Excitation energy [MeV]
40 35 30 25 20 15
100
10-1
t
n
e
v
e 10-2 12C target

r
e DHP g.s.
p ex. s.
eld 10-3 Λ + SH--P e gx..ss..
Yi THP g.s and g.s.
-- g.s and ex. s.
10-4 -- ex.s. and ex.s
Λ + Λ
10-5
0 5 10 15 20 25
Ξ- Binding energy [MeV]
Figure2: Predictedproductionprobabilityofground(g.s.) andexcitedstates(ex.s.) inonesingle(SHP),
twin(THP)anddoublehypernuclei(DHP)afterthecaptureofaΞ−ina12Cnucleusanditsconversioninto
twoΛhyperons. ThelowerandupperscaleshowsthebindingenergyofthecapturedΞ−andtheexcitation
energyoftheinitial13 Bnucleus,respectively(fromRef.[35]).
ΛΛ
triangles). Thiscanbetracedbacktotheopeningofseveralthresholdsforvariousexciteddouble
hypernuclei already at moderate excitation energies. Only for small binding energies and hence
largeexcitationenergiestheproductionofsingleandtwinhypernucleiissignificant(∼10%). The
non-monotonic behaviour for single hypernucleus + one free Λ production reflects the fact that
the various lowest thresholds are relative high and widely separated, e.g. 12B+Λ at B =23.9MeV
Λ Ξ
followed by 11B+n+Λ at 11.3MeV. Twin-hypernuclei are only produced for Ξ− binding energies
Λ
belowthethresholdfor8Li+5HewithB =13.6MeV.Asdiscussedabovethefrequentobservation
Λ Λ Ξ
oftwin-hypernuclei[39,40,41,42,38,43]signalsaconversionfromaΞstatewithonlymoderate
bindingenergy. InthisrangeofB theproductionprobabilityofdoublehypernucleiiscomparable
Ξ
topreviousestimateswithinacanonicalstatisticalmodel[23,24]. Itisimportanttostressthatthese
numbers do not include a possible pre-equilibrium emission of hyperons during the capture and
conversion stage. With respect to the number of stopped Ξ− hyperons, pre-equilibrium processes
will decrease the yield of double hypernuclei relative to the yield for single hypernuclei (see e.g.
[27]). IndeedinthesimulationsfortheplannedPANDAexperiment[34]ajointcapture×conversion
probabilityof5%wasassumedtomimicthispre-equilibriumstage.
UsingdifferentΞ-absorbingstablesecondarytargetnuclei9Be,10B,11B,12Cand13Conefinds
that different double hypernuclei dominate for each target [35]. Thus combining the information
shown in Fig. 2 with the measurement of two pion momenta from the subsequent weak decays a
unique assignment of various newly observed γ-transitions to specific double hypernuclei seems
possibleasintendedbythe PANDAcollaboration[32,34].
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StudiesofHyperonsandAntihyperonsinNuclei JosefPOCHODZALLA
2.2 TheE906Puzzle
In2001theBNLexperimentE906reportedtheobservationofthe4 Hhypernucleusbymea-
ΛΛ
suringthesequentialpionicdecaysaftera(K−,K+)reactiondepositedtwounitsofstrangenessina
9Betarget[44](seeFig.3). Twostructuresinthecorrelatedπ− momentaat(133,114)MeV/cand
at(114,104)MeV/cwereobserved. Thefirststructurewasinterpretedastheproductionof3H+4H
Λ Λ
twinswhilethebumpat(114,104)MeV/cwasattributedtopionicdecaysofthedoublehypernu-
cleus4 H.However,asitwaspointedoutbyKumagai-FuseandOkabealsotwinΛ-hypernuclear
ΛΛ
decaysof3Hand6Heareapossiblecandidatetoformthispeakifexcitedresonancestatesof6Li
Λ Λ
are considered [45]. More recently Randeniya and Hungerford showed that the published E906
datacanbereproducedwithouttheinclusionof4 Hdecayandthatitismorelikelythatthedecay
ΛΛ
of7 HewasobservedintheE906experiment[46]. Intheiranalysisthisdoublehypernucleuswas
ΛΛ
accompanied by a background of coincident decays of single hypernuclei pairs 3H+4H, 3H+3H,
Λ Λ Λ Λ
and4H+4H,respectively.
Λ Λ
Fig. 4 shows the predicted relative probabilities for the production of particle stable twin
and double hypernuclei in the E906 experiment after the capture and conversion of a stopped Ξ−
in a secondary 9Be target Ξ−+9Be→10 Li∗. As before a Ξ− binding energy of 0.5MeV seems
ΛΛ
reasonable corresponding to an 10 Li excitation of about 29MeV. The produced yields for this
ΛΛ
excitationenergyareshowninFig.3. Here,groundstateandexcitedstate(s)-iftheyexist-have
been added and the pion momenta for groundstate decays are assumed. Note, that the production
of4H+4Htwinsisevenatanexcitationenergyof35MeVenergeticallynotpossibleand-unlike
Λ Λ
toacanonicalcalculations[24]-doesthereforenotoccurinourmicro-canonicalmodel.
Let usfirst discussthe structure at(114,104)MeV/cwhich hasbeen attributedto double hy-
pernucleidecays. Generallytheproductionofdoublehypernucleiisenergeticallyfavoredoverthe
productionoftwins: allpossiblechannelswithtwin-productionlieenergeticallysignificantlyabove
the thresholds for 9 Li, 7 He and 6 He production in case of the 10 Li compound picture. Cor-
ΛΛ ΛΛ ΛΛ ΛΛ
respondingly the production of 3H and 6He twins which has been suggested as a possible source
Λ Λ
of the peak structure around (114,104)MeV/c [45], is in our model by a factor of 30 lower than
the7 Heproductionprobability. UnlikeinthecanonicalmodelofRef.[24]the7 Heprobability
ΛΛ ΛΛ
exceeds also the one of a 4 H by more than two orders of magnitude and the production of 5 H
ΛΛ ΛΛ
by a factor of about 17 in our model. Of course, a direct comparison with the E906 data requires
a detailed consideration of the branching ratios for pionic two-body decays many of which are
not known so far. Keeping that caveat in mind our microcanonical model supports independently
on the assumed production scheme the interpretation of the E906 observation by Randeniya and
Hungerford[46]intermsof7 Hedecays. Decaysfromthegroundorevenexitedstatesof8 Lior
ΛΛ ΛΛ
9 Licanpossiblycontributesomebackgroundtothestructureat(114,104)MeV/c.
ΛΛ
In order to describe the (133,114)MeV/c structure of the E906 experiment, the production
of 3H+4H twins seems mandatory [44]. However, the 3H+4H+t mass lies above the initial mass
Λ Λ Λ Λ
m =m(Ξ−)+m(9Be) and can therefore not be produced in the Ξ−+9Be compound production
0
scheme (see right part of Fig. 4). With an energy of 12.6MeV below m , the channel 4H+6He is
0 Λ Λ
the most likely twin in the present scenario, followed by the 4H+5He+n decay. Given however
Λ Λ
theexperimentalprecisionofabout1 MeV/cforthemomentumcalibrationinE906[44],neither
thedecaysof4H+6Hewith(133,108)MeV/cnordecaysof4H+5Hepairswith(133,99)MeV/c
Λ Λ Λ Λ
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StudiesofHyperonsandAntihyperonsinNuclei JosefPOCHODZALLA
Figure3: MomentaoftwocorrelatedpionsmeasuredbytheE906collaboration(greysquares). Overlaid
areproductionyieldsofvarioustwinpairs(blue),doublehypernucleiincludingtheirexcitedstates(green)
anddoublehypernucleiwithastablegroundstateonly(red). Theareasofthecirclesareproportionaltothe
productionyieldspredictedbythestatisticalmodel. Pionicdecayprobabilitiesarenotincludedinthisplot.
seemtoexplainthestructurearound(133,114)MeV/c. Ofcourseinparticularthefirstonecould
contribute to this enhancement in the tail region. Even more intriguing is however the fact that
the statistical models predict a production of 4H+4H twins exceeding the 3H+4H production.
Λ Λ Λ Λ
Considering furthermore the branching ratios for two-body π− decays of Γ /Γ ≈0.26
π−+3He total
[47] and Γ /Γ ≈0.5 [48] the absence of a bump which could be attributed to 4H+4H
π−+4He total Λ Λ
is particularly puzzling. A similar conclusion is obtained [35] within the quasi-free/rescattering
pictureofYamamotoetal. [24]resultingintheproductionofexcited8 Heor8 Hnuclei.
ΛΛ ΛΛ
At first sight it seems that an alternative production process than the ones discussed so far
is required to explain the singular structure at (133,114)MeV/c in terms of 3H+4H twins. Note
Λ Λ
however that in the initial analysis of the E906 data the bump at (133,114)MeV/c served as a
calibration point for the pion momenta, taking the decay of 3H+4H twins as granted [44, 49]. If
Λ Λ
that structure were indeed caused by 4H+6He twins with (133,108)MeV/c, it would of course
Λ Λ
influencethemomentumscaleintheregionofthe(114,104)MeV/cbump. Thisbumpwouldthen
be shifted to approximately (108,97)MeV/c. Considering the uncertainty of ∆B also such a
ΛΛ
momentumscalewouldbecompatiblewiththedecayof7 Heand8 Lioramixtureofboth. The
ΛΛ ΛΛ
absence of 9 Li nuclei may be related to the decreasing pionic decay probability with increasing
ΛΛ
nuclearmass. Clearly,thepresentstatisticaldecaymodelneedstobecomplementedbyquantitative
weakdecaycalculations(seee.g. Ref.[50])tofurthercorroborateourconjecture.
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StudiesofHyperonsandAntihyperonsinNuclei JosefPOCHODZALLA
100
Λ Λ-hypernuclei
10-1 4Λ ΛH g.s.
5Λ ΛH g.s
10-2 5Λ ΛHe g.s.
6Λ ΛHe g.s.
7Λ ΛHe g.s.
10-3 8Λ ΛHe g.s.
8Λ ΛHe ex.s.
10-4 9Λ ΛHe g.s.
9Λ ΛHe ex.s.
10-5 89ΛΛ ΛΛLLii gg..ss..
ent 10-6 98ΛΛ Λ ΛLLi i eexx..ss.
v
e
r 100
eld pe 10-1 33ΛΛHH ++ 34ΛΛHH gg..ss.. Twin Λ-hypernuclei
Yi 4ΛH + 6ΛHe g.s.

-- g.s + ex.s
10-2 3ΛH + 7ΛHe g.s.
-- g.s + ex.s
10-3 4ΛH + 5ΛHe g.s.
-- ex.s. + g.s.
10-4 4Λ--H e +x .4sΛ H+ gg..ss..
-- ex.s. + ex.s
10-5 BΞ = 0 MeV
10-6
0 5 10 15 20 25 30 35 40 45 50
Excitation energy [MeV]
Figure4: Relativeproductionprobabilityofdouble(toppart)andtwinhypernuclei(lowerpart)forapri-
mary10 Linucleusasafunctionofitsexcitationenergy.
ΛΛ
3. AntihyperonsinNuclei
Concerningantibaryons,realiableinformationontheirnuclearpotentialareavailableonlyfor
antiprotons. Antihyperons annihilate quickly in normal nuclei and spectroscopic information is
thereforenotdirectlyaccessible. Mishustinrecentlysuggestedtostudydeeplyboundantibaryonic
nuclei via various characteristic signals in their decay process [51, 52]. It is however not obvious
whether these proposed observables will provide unique and quantitative signals of deeply bound
antihyperonicsystems.
Quantitative information on the antihyperon potentials relative to that of the corresponding
hyperon may be obtained via exclusive antihyperon-hyperon pair production close to threshold in
antiproton-nucleusinteractions[53]. Oncethesehyperonsleavethenucleusandaredetected,their
asymptotic momentum distributions will reflect the depth of the respective potentials. However,
sinceintheppcenter-of-massthedistributionoftheproducedbaryon-antibaryonpairwillusually
notbeisotropic,theanalysiscanrelyonlyonthetransversemomentaoftheoutgoingbaryons. In
Ref. [53] it was demonstrated that the individual transverse momentum distributions alone do not
8
StudiesofHyperonsandAntihyperonsinNuclei JosefPOCHODZALLA
allowtoextractunambiguousinformationonthepotentialofantihyperons. Instead,thetransverse
momentum asymmetry α defined in terms of the transverse momenta of the coincident particles
T
canbeusedtoexploreevent-by-eventcorrelations:
p (Λ)−p (Λ)
T T
α = . (3.1)
T
p (Λ)+p (Λ)
T T
Inapurelyclassical,non-relativisticpicturethisasymmetryisoftheorderof∆U/4·E ,where∆U
0
isthepotentialdifferenceandE thetypicalkineticenergyofthehadrons.
0
3.1 Antihyperon-HyperonPairProductionandPropagationinNuclei
In Ref. [53] we have examined the influence of the potentials on the transverse momentum
asymmetry of coincident hyperons and antihyperons by means of a schematic Monte Carlo simu-
lation. Albeit crude, this classical approach allows to explore the role of different features of the
reactioninatransparentway.
Theabsorptionoftheantiprotonsenteringthetargetnucleusdeterminesthepointsofannihi-
lation inside the nucleus and the paths which the eventually produced hyperons and antihyperons
havetopassinsidethenucleuspriortoemission. Becauseofthestrongabsorptionoftheantihyper-
ons,theemittedhyperon-antihyperonpairsare-unlikeininclusivereactions[54,55]-createdclose
tothecoronaofthetargetnucleusatatypicaldensityof20to25%ofthecentralnucleardensity.
InreactionsclosetothresholdtheFermimotionoftheprotonsinsidethenucleartargetcontributes
significantly to the final momenta. Lacking any detailed experimental information it is assumed
thattheannihilationcrosssectionsforantihyperonsshowasimilarmomentumdependenceasthe
ppsystem[5,56].
The energy and the momentum of the baryons propagating within the nucleus are related
accordingto[57]:
(E−V)2=(M +S)2+P 2 (3.2)
0 in
Here V and S denote the real part of the vector and scalar potential, respectively. The relation
betweenthemomentainsideandoutsideofthenuclearpotentialareapproximatedby
(cid:113)
P 2+M2=( (M +S)2+P 2+V)2. (3.3)
out 0 0 in
Refractiveeffectsatthepotentialboundarywereignored. Thedefaultparametersforthescalarand
vectorpotentialsofthevariousbaryonsatnormalnucleardensityρ wereadoptedfromRef.[58].
0
Sincetheantiprotonannihilationandthesubsequentantihadron-hadronpairproductiontakeplace
inthenuclearperipheryatlowdensitiesρ weassumedalineardensitydependence∝ρ/ρ forall
0
vectorandscalarpotentials.
3.2 TransverseMomentumCorrelationsatPANDA
For a compact representation of event-by-event correlations we examine the transverse mo-
mentum asymmetry α as a function of the longitudinal asymmetry α , where α is defined by
T L L
analogytoEq.3.1intermsofthelongitudinalmomentumcomponents:
p (Λ)−p (Λ)
L L
α = . (3.4)
L
p (Λ)+p (Λ)
L L
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StudiesofHyperonsandAntihyperonsinNuclei JosefPOCHODZALLA
Figure 5: Left part: Average transverse momentum asymmetry of ΛΛ(solid line), ΞΞ (dashed line) and
D+D− pairs(dottedline)producedexclusivelyin1.66, 2.9and6.7GeV/cp12Cinteractions, respectively.
Rightpart: thesameasinpart(a)buttakingthemomentumdependenceofthepotentialintoaccount.
In future more sophisticated analysis methods which e.g. use mixed events as a reference, further
detailsofthesecorrelationsmayberevealed.
Transverse momentum correlations can in principle be analyzed for each hadron-antihadron
pairproducedexclusivelyin pAinteractions. Asexamples,thesolid,dashedanddottedhistograms
in figure 5a show the average transverse momentum asymmetries of ΛΛ, ΞΞ and D+D− pairs
produced in 1.66, 2.9 and 6.7GeV/c p + 12C interactions, respectively. For simplicity, isotropic
center-of-massdistributionswereassumedincaseoftheΞΞandD+D− production. FortheΞand
Ξ baryons the same absorption cross sections as for the Λ and Λ were adopted, whereas for D−
andD+ mesonsenergyindependentabsorptioncrosssectionsof10and90mb,respectively,were
taken. IntheleftpartofFig.5nomomentumdependenceofthepotentialswasconsidered.
In line with the classical picture mentioned above (α ∝∆U/4·E ) the smaller asymmetries
T 0
for the heavier particles are a consequence of the the large Ξ hyperon and D meson laboratory
momenta. InthesimulationsofFig.5bthemomentumdependenceofthepotentialswasaddedby
means of the scaling factor [59]. As expected the transverse asymmetry is shifted towards more
negative values. Nevertheless the asymmetry remains sizable even for the ΞΞ case. At PANDA
when reaching the design luminosity a measurement of α for ΞΞ pairs with a precision of about
T
10%willrequireameasurementtimeoftypicallylessthanaday. Furthermoreitputsonlymoderate
constraintsonthedetectorperformance,e.g. thetrackingcapabilitiesofthecentralvertexdetector.
The fact that energy and momentum conservation are the main ingredients of the proposed
methodraiseshopethatsimilarresultsmightbeobtainedbymoresophisticatedcalculations. Since
mostoftheemittedhyperon-antihyperonpairsarecreatedinthenuclearperipheryatsubsaturation
density, a neutron skin of neutron rich target nuclei may help to explore different effective poten-
tials. Possibledeflectionsatthepotentialboundarywhichareignoredinthepresentworkmaybe
10