eta-meson photoproduction off protons and deuterons

We present a unitary and gauge-invariant model with coupled channels, which provides a consistent description of pion photoproduction off nucleons in the E$_{0+}$ channel and eta-meson photoproduction off protons and deuterons. An effective field theory wi

η-mesonphotoproductiono protonsand

deuterons

C.Deutsch-Sauermann1,B.FrimanandW.N¨orenberg

arXiv:nucl-th/9701022v1 14 Jan 1997GSI,Planckstr.1,D-64291Darmstadt,GermanyandInstitutf¨urKernphysik,TechnischeHochschuleDarmstadt,D-64289Darmstadt,Germany1Introductionandsummary

Inrecentyearsthephysicsoftheη-mesonhasbeenstudiedintensively.Newmeasurementsofη-productioninhadronicandheavy-ioncollisionshavebeenperformedatSATURNE[1],LosAlamos[2],Brookhaven[3]andGSI[4].Theavailabilityofhigh-duty-factorelectronaccelerators,MAMIinMainzandELSAinBonn,hasopenedthepossibilitytoperformpreciseexperimentswithelectromagneticprobes,e.g.photon-andelectron-inducedη-mesonproduc-tiono nucleons[5–7]andnuclei[8,9].Theaccuratemeasurementsofelectro-magneticprocessesprovidestrongconstraintsonmodelsfortheelementaryη-meson–hadronandphoton–hadroninteractions,whicharethebasisforatheoreticaldescriptionofη-mesonpropagationinhadronicmatterandpro-ductioninheavy-ioncollisions.Thetheoreticalinterpretationofthedatahas

We present a unitary and gauge-invariant model with coupled channels, which provides a consistent description of pion photoproduction off nucleons in the E$_{0+}$ channel and eta-meson photoproduction off protons and deuterons. An effective field theory wi

leadtothedevelopmentofnewmodelsforphoton-inducedη-mesonproduc-tion[10–12].

Inthisletter,wepresentamodelforη-mesonphotoproductiono nucleonsanddeuteronsthroughthedominantE0+channel.Ane ective eldtheorywithhadronsandphotonsisconstructed,usingacoupled-channelsmodel

[13]forπNscatteringandpion-inducedη-productionintheS11channelasastartingpointandcouplingtheelectromagnetic eldtothehadronsinagauge-invariantway.Ascomparedtoexistingmodelsthefollowingsubstantiallynewfeaturesare:

Resonanceandbackgroundcontributionsaretakenintoaccountinastrictlyunitaryway.Theconsistentinclusionof nal-stateinteractionsbetweenthehadronsisimportant.

InadditiontothedominantS11(1535)resonance,whichcouplesstronglytotheηNchannel,wealsotakethesecondresonanceS11(1650)intheπNS11channelintoaccount.We ndthattheupperresonanceisessential,al-thoughitssmalldirectcouplingtotheηNchannelcanbeneglected.ThisisduetothecouplingoftheS11(1650)totheηNchannelthroughinter-mediateπNstates.Becauseofthemodi cationsduetothesecondreso-nance,agreementwithexperimentaldatacanbeobtainedonlywhentheρ-andω-mesonexchangetermsareincluded.Thesetermsarenotneededin[10]becausetheretheS11(1650)resonanceisneglected.ThehadronicandelectromagneticcouplingconstantsoftheS11(1535)are,duetolargeinterferencee ects,di erentfromthoseobtainedinone-resonancemodels. Thehadronicpartofthemodel,whichdescribesthe nal-stateinteractionsbetweenthehadrons,isdeterminedexclusivelyby ttingelasticπNscatter-ingdata.TheconsistencyischeckedbycomparingthecrosssectionfortheinelasticchannelπN→ηNwithexperiment.Sincethehadronicparametersare xed,theelectromagneticcouplingconstantsareuniquelydeterminedbythephotoproductiondata.Thusweobtainvaluesforthehelicityampli-tudesoftheresonances.Theseareofgreatinterestasatestforthequarkmodel.Withinourmodelweachieveaconsistentdescriptionofthepionphotoproductiono nucleonsintheE0+channelandoftheη-mesonpho-toproductiono nucleonsanddeuterons.

2Themodel

Letusbrie ysummarizethehadronicpartofourmodel(fordetailssee[13]).AsalreadymentionedtherearetwoN resonancesin√pion-nucleonscatteringintheS11channelatcenter-of-massenergiesbelow

We present a unitary and gauge-invariant model with coupled channels, which provides a consistent description of pion photoproduction off nucleons in the E$_{0+}$ channel and eta-meson photoproduction off protons and deuterons. An effective field theory wi

at1650MeV(S11(1650))couplesstronglytotheπNandππNchannelswithbranchingratiosof60–80%and5–20%,respectively,butonlyweaklytotheηNchannelwithadecayprobabilityofapproximately1%.

Inordertodescribetheseexperimentalfacts,weincludethefollowinginter-actiontermsinthelagrangian,

LI= igπNNΨNΨNσ gσππ π2σ

gπNN 1ΨN 2 τΨN π+h.c.

gηNN 1

ΨN 1γ5ΨNζ+h.c. igζNN 2(1)

We present a unitary and gauge-invariant model with coupled channels, which provides a consistent description of pion photoproduction off nucleons in the E$_{0+}$ channel and eta-meson photoproduction off protons and deuterons. An effective field theory wi

secondresonance[13].Atestoftheconsistencyofthemodelisprovidedbythecrosssectionfortheprocessπ +p→η+n.Thedataforthisprocessarewelldescribedbythemodelwithoutfurtheradjustmentoftheparameters.ItisimportanttonotetheessentialroleplayedbytheS11(1650)resonancenotonlyintheelasticbutalsointheinelasticchannel.Inpreviouscalculations

[10,16]thisresonancehasnotbeenincluded.

Inthispaperweextendthemodelbyintroducingelectromagneticinteractions.Westressthatthehadronicpartofthemodelisnotmodi edinanyway.TolowestorderintheelectromagneticinteractiontheT-matrixfortheprocessγp→ηpisrelatedtotheK-matrixby

Tηγ=Kηγ iπ iTηiδ(E Hi)Kiγ,(2)

wherethesumisoverallopenchannels,i=π,η,ζ.The nal-stateinteractions,describedbyTηi,isentirelyduetostronginteractions.Inaccordancewithexperiment[5]weassumethatthetotalcrosssectionforphotoproductionofη-mesonsisdominatedbytheS11channelanduseourmodelforπNscatteringandpion-inducedη-mesonproductioninthischanneltodescribethe nal-stateinteractions.

TheresonancecontributionstotheK-matrixelementsKiγareidenti edwiththe rstdiagramshowninFig.2.TheγNN couplingisgivenbythelagrangian

LγNN= ieΨN SkN +VkN τ3 γ5σµνΨNFµν+h.c.,(3)wheremN andmNaretheresonanceandnucleonmasses.Thisinteractionisobviouslygaugeinvariant,becauseitinvolv …… 此处隐藏：17385字，全部文档内容请下载后查看。喜欢就下载吧 ……