42.MonteCarloparticlenumberingscheme - PDF document

42.MonteCarloparticlenumberingscheme 42.MONTECARLOPARTICLENUMBERINGSCHEMERevisedSeptember2013byJ.-F.ArguinLBNL),L.Garren(Fermilab),F.Krauss(DurhamU.),C.-J.Lin(LBNL),S.Navas(U.Granada),P.Richardson(DurhamU.),andT.SjÄostrand(LundU.).TheMonteCarloparticlenumberingschemepresentedhereisintendedtofacilitateinterfacingbetweeneventgenerators,detectorsimulators,andanalysispackagesusedinparticlephysics.Thenumberingschemewasintroducedin1988[1]andarevisedversion[2,3]wasadoptedin1998inordertoallowsystematicinclusionofquarkmodelstateswhichareasyetundiscoveredandhypotheticalparticlessuchasSUSYparticles.Thenumberingschemeisusedinseveraleventgenerators,e.g.HERWIG,PYTHIA,andSHERPA,andinterfaces,e.g./HEPEVT/andHepMC.Thegeneralformisa7{digitnumber:nnrnLnq1nq2nq3nJ:Thisencodesinformationabouttheparticle'sspin,°avorcontent,andinternalquantumnumbers.Thedetailsareasfollows:1.Particlesaregivenpositivenumbers,antiparticlesnegativenumbers.ThePDGconventionformesonsisused,sothatK+andB+areparticles.2.Quarksandleptonsarenumberedconsecutivelystartingfrom1and11respectively;todothistheyare¯rstorderedbyfamilyandwithinfamiliesbyweakisospin.3.Incompositequarksystems(diquarks,mesons,andbaryons)nq13arequarknumbersusedtospecifythequarkcontent,whiletherightmostdigitnJ=2J+1givesthesystem'sspin(exceptfortheK0SandK0L).TheschemedoesnotcoverparticlesofspinJ�4.4.Diquarkshave4-digitnumberswithnq1nq2andnq3=0.5.Thenumberingofmesonsisguidedbythenonrelativistic(L{Sdecoupled)quarkmodel,aslistedinTables15.2and15.3.a.Thenumbersspecifyingthemeson'squarkcontentconformtotheconventionnq1=0andnq2nq3.ThespecialcaseK0Listhesoleexceptiontothisrule.b.Thequarknumbersof°avorless,light(u;d;s)mesonsare:11forthememberoftheisotriplet(0;½0;:::),22forthelighterisosinglet(´;!;:::),and33fortheheavierisosinglet(0;Á;:::).Sinceisosingletmesonsareoftenlargemixturesofu u+d dands sstates,22and33areassignedbymassanddonotnecessarilyspecifythedominantquarkcomposition.c.Thespecialnumbers310and130aregiventotheK0SandK0Lrespectively.d.The¯fthdigitnLisreservedtodistinguishmesonsofthesametotal(J)butdi®erentspin(S)andorbital(L)angularmomentumquantumnumbers.ForJ�0thenumbersare:(L;S)=(J1;1)nL=0;(J;0)nL=1;(J;1)nL=2and(J+1;1)nL=3.FortheexceptionalcaseJ=0thenumbersare(0;0)nL=0and(1;1)nL=1(i.e.nL=L).SeeTable42.1.Table42.1:Mesonnumberinglogic.Hereqqstandsfornq2nq3. L=J1,S=1 L=J,S=0 L=J,S=1 L=J+1,S=1 J codeJPCL codeJPCL codeJPCL codeJPCL 0 ||| 00qq10+0 ||| 10qq10++11 00qq310 10qq31+1 20qq31++1 30qq3122 00qq52++1 10qq52+2 20qq522 30qq52++33 00qq732 10qq73+3 20qq73++3 30qq7344 00qq94++3 10qq94+4 20qq944 30qq94++5 e.Ifasetofphysicalmesonscorrespondtoa(non-negligible)mixtureofbasisstates,di®eringintheirinternalquantumnumbers,thenthelightestphysicalstategetsthesmallestbasisstatenumber.ForexampletheK1(1270)isnumbered10313(11P1K1B)andtheK1(1400)isnumbered20313(13P1K1A).f.Thesixthdigitnrisusedtolabelmesonsradiallyexcitedabovethegroundstate.g.Numbershavebeenassignedforcompletenr=0S-andP-wavemultiplets,evenwherestatesremaintobeidenti¯ed.h.Insomeinstancesassignmentswithintheqqmesonmodelareonlytentative;herebestguessassignmentsaremade.i.ManystatesappearingintheMesonListingsarenotyetassignedwithintheqqmodel.Herenq23andnJareassignedaccordingtothestate'slikely°avorsandspin;allsuchunassignedlightisoscalarstatesaregiventhe°avorcode22.WithinthesegroupsnL=0;1;2;:::isusedtodistinguishstatesofincreasingmass.Thesestatesare°aggedusingn=9.Itistobeexpectedthatthesenumberswillevolveasthenatureofthestatesareelucidated.Codesareassignedtoallmesonswhicharelistedintheone-pagetableattheendoftheMesonSummaryTableaslongastheyhaveapreferedorestablishedspin.Additionalheavymesonstatesexpectedfromheavyquarkspectroscopyarealsoassignedcodes.6.Thenumberingofbaryonsisagainguidedbythenonrelativisticquarkmodel,seeTable15.6.ThisnumberingschemeisillustratedthroughafewexamplesinTable42.2.a.Thenumbersspecifyingabaryon'squarkcontentaresuchthatingeneralnq1nq2nq3.b.TwostatesexistforJ=1=2baryonscontaining3di®erenttypesofquarks.Inthelighterbaryon(¤;;;:::)thelightquarksareinanantisymmetric(J=0)statewhilefortheheavierbaryon(§0;0;0;:::)theyareinasymmetric(J=1)state.Inthissituationnq2andnq3arereversedforthelighterstate,sothatthesmallernumbercorrespondstothelighterbaryon.c.Forexcitedbaryonsaschemeisadopted,wherethenrlabelisusedtodenotetheexcitationbandsintheharmonicoscillatormodel,seeSec.15.4.Usingthenotationemployedthere,nrisgivenbytheN-indexoftheDNbandidenti¯er.d.FurtherdegeneraciesofexcitedhadronmultipletswiththesameexcitationnumbernrandspinJareliftedbylabellingsuchmultipletswiththenLindexaccordingtotheirmass,asgivenbyitsNor¢-equivalent.e.Insuchexcitedmultipletsextrasingletsmayoccur,the¤(1520)beingaprominentexample.Insuchcasestheorderingisreversedsuchthattheheaviestquarklabelispushedtothelastposition:nq3�nq1�nq2.f.Forpentaquarkstatesn=9,nrnLnq1nq2givesthefourquarknumbersinordernrnLnq1nq2,nq3givestheantiquarknumber,andnJ=2J+1,withtheassumptionthatJ=1=2forthestatescurrentlyreported.7.Thegluon,whenconsideredasagaugeboson,haso±cialnumber21.Incodesforglueballs,however,9isusedtoallowanotationincloseanalogywiththatofhadrons.8.ThepomeronandodderontrajectoriesandagenericreggeontrajectoryofstatesinQCDareassignedcodes990,9990,and110respectively,wherethe¯nal0indicatestheindeterminatenatureofthespin,andtheotherdigitsre°ecttheexpected\valence"°avorcontent.Wedonotattemptacompleteclassi¯cationofallreggeontrajectories,sincethereiscurrentlynoneedtodistinguishaspeci¯csuchtrajectoryfromitslowest-lyingmember.9.Two-digitnumbersintherange21{30areprovidedfortheStandardModelgaugebosonsandHiggs.10.Codes81{100arereservedforgenerator-speci¯cpseudoparticlesandconcepts.11.ThesearchforphysicsbeyondtheStandardModelisanactivearea,sothesecodesarealsostandardizedasfaraspossible.a.Astandardfourthgenerationoffermionsisincludedbyanalogywiththe¯rstthree.b.Thegravitonandthebosoncontentofatwo-Higgs-doubletscenarioandofadditionalSU(2)U(1)groupsarefoundintherange31{40.c.\One-of-a-kind"exoticparticlesareassignednumbersintherange41{80.d.Fundamentalsupersymmetricparticlesareidenti¯edbyaddinganonzerontotheparticlenumber.Thesuperpartnerofabosonoraleft-handedfermionhasn=1whilethesuperpartnerofaright-handedfermionhasn=2.Whenmixingoccurs,suchasbetweenthewinosandcharged 42.MonteCarloparticlenumberingscheme Table42.2:Someexamplesofoctet(top)anddecuplet(bottom)membersforthenumberingschemeforexcitedbaryons.Hereqqqstandsfornq1nq2nq3.Seethetextforthede¯nitionofthenotation.Thenumbersinparenthesiscorrespondtothemassofthebaryons.Thestatesmarkedas(?)arenotexperimentallycon¯rmed. JP(D;LPN)nrnLnq1nq2nq3nJN8§¥¤1 Octet211,221312311,321,322331,332213 1=2+(56;0+0)00qqq2(939)(1116)(1193)(1318)|1=2+(56;0+2)20qqq2(1440)(1600)(1660)(1690)|1=2+(70;0+2)21qqq2(1710)(1810)(1880)(?)(?)1=2(70;11)10qqq2(1535)(1670)(1620)(1750)(1405) JP(D;LPN)nrnLnq1nq2nq3nJ¢§¥­ Decuplet111,211,221,222311,321,322331,332333 3=2+(56;0+0)00qqq4(1232)(1385)(1530)(1672)3=2+(56;0+2)20qqq4(1600)(1690)(?)(?)1=2(70;11)11qqq2(1620)(1750)(?)(?)3=2(70;11)12qqq4(1700)(?)(?)(?) Higgsinostogivecharginos,orbetweenleftandrightsfermions,thelighterphysicalstateisgiventhesmallerbasisstatenumber.e.Technicolorstateshaven=3,withtechnifermionstreatedlikeordinaryfermions.Stateswhichareordinarycolorsingletshavenr=0.Coloroctetshavenr=1.Ifastatehasnon-trivialquantumnumbersunderthetopcolorgroupsSU(3)1SU(3)2,thequantumnumbersarespeci¯edbytech,ij,whereiandjare1or2.nListhen2i+j.Thecoloron,V8,isaheavygluoncoloroctetandthusis3100021.f.Excited(composite)quarksandleptonsareidenti¯edbysettingn=4andnr=0.g.Withinseveralscenariosofnewphysics,itispossibletohavecoloredparticlessu±cientlylong-livedforcolor-singlethadronicstatestoformaroundthem.Inthecontextofsupersymmetricscenarios,thesestatesarecalledR-hadrons,sincetheycarryoddR-parity.R-hadroncodes,de¯nedhere,shouldbeviewedastemplatesforcorrespondingcodesalsoinotherscenarios,foranylong-livedparticlethatiseitheranun°avoredcoloroctetora°avoredcolortriplet.TheR-hadroncodeisobtainedbycombiningtheSUSYparticlecodewithacodeforthelightdegreesoffreedom,withasmanyintermediatezerosremovedfromtheformerasrequiredtomakeplaceforthelatterattheend.(Toexemplify,asparticlen00000n~qcombinedwithquarksq1andq2obtainscoden00n~qnq1nq2nJ.)Speci¯cally,thenew-particlespindecouplesinthelimitoflargemasses,sothatthe¯nalnJdigitisde¯nedbythespinstateofthelight-quarksystemalone.Anappropriatenumberofnqdigitsisusedtode¯netheordinary-quarkcontent.Asusual,9ratherthan21isusedtodenoteagluon/gluinoincompositestates.Thesignofthehadronagreeswiththatoftheconstituentnewparticle(acolortriplet)wherethereisadistinctnewantiparticle,andelseisde¯nedasfornormalhadrons.ParticlenamesareRwiththe°avorcontentaslowerindex.h.Ablackholeinmodelswithextradimensionshascode5000040.Kaluza-Kleinexcitationsinmodelswithextradimensionshaven=5orn=6,todistinquishexcitationsofleft-orright-handedfermionsor,incaseofmixing,thelighterorheavierstate(cf.11d).Thenonzeronrdigitgivestheradialexcitationnumber,inscenarioswherethelevelspacingallowthesetobedistinguished.Shouldthemodelalsocontainsupersymmetry,excitedSUSYstateswouldbedenotedbyannr�0,withn=1or2asusual.Shouldsomecoloredstatesbelong-livedenoughthathadronswouldformaroundthem,thecodingstrategyof11gapplies,withtheinitialtwonnrdigitspreservedinthecombinedcode.i.MagneticmonopolesanddyonsareassumedtohaveoneunitofDiracmonopolechargeandavariableintegernumbernq1nq2nq3unitsofelectriccharge.Codes411nq1nq2nq30arethenusedwhenthemagneticandelectricalchargesignagreeand412nq1nq2nq30whentheydisagree,withtheoverallsignoftheparticlesetbythemagneticcharge.Fornownospininformationisprovided.12.Occasionallyprogramauthorsaddtheirownstates.Toavoidconfusion,theseshouldbe°aggedbysettingnnr=99.13.Concerningthenon-99numbers,itmaybenotedthatonlyquarks,excitedquarks,squarks,anddiquarkshavenq3=0;onlydiquarks,baryons(includingpentaquarks),andtheodderonhavenq1=0;andonlymesons,thereggeon,andthepomeronhavenq1=0andnq2=0.Concerningmesons(notantimesons),ifnq1isoddthenitlabelsaquarkandanantiquarkifeven.14.Nuclearcodesaregivenas10-digitnumbers10LZZZAAAI.Fora(hyper)nucleusconsistingofnpprotons,nnneutronsandn¤'s,A=np+nn+ngivesthetotalbaryonnumber,Z=npthetotalchargeandL=nthetotalnumberofstrangequarks.Igivestheisomerlevel,withI=0correspondingtothegroundstateandI�0toexcitations,see[4],wherestatesdenotedm;n;p;qtranslatetoI=14.Asexamples,thedeuteronis1000010020and235Uis1000922350.Toavoidambiguities,nuclearcodesshouldnotbeappliedtoasinglehadron,likep,nor¤0,wherequark-contents-basedcodesalreadyexist.Thistextandfulllistsofparticlenumbers,includingexcitedbaryonsandparticlesfromphysicsbeyondthestandardmodel,canbefoundonline[5].TheStdHepMonteCarlostandardizationproject[6]maintainsthelistofPDGparticlenumbers,aswellasnumberingschemesfrommosteventgeneratorsandsoftwaretoconvertbetweenthedi®erentschemes.References:1.G.P.Yostetal.,ParticleDataGroup,Phys.Lett.B204,1(1988).2.I.G.Knowlesetal.,in\PhysicsatLEP2",CERN96-01,v.2,p.103.3.C.Casoetal.,ParticleDataGroup,Eur.Phys.J.C3,1(1998).4.G.Audietal.,Nucl.Phys.A729,3(2003)Seealsohttp://www.nndc.bnl.gov/amdc/web/nubase en.html.5.http://pdg.lbl.gov/current/mc-particle-id/.6.L.Garren,StdHep,MonteCarloStandardizationatFNAL,FermilabPM0091andStdHepWWWsite:http://cepa.fnal.gov/psm/stdhep/. 42.MonteCarloparticlenumberingscheme QUARKSd1u2s3c4b5t6b07t08LEPTONSe11e12131415160¡17018GAUGEANDHIGGSBOSONSg(9)2122Z023W+24h0=H0125Z0=Z0232Z00=Z0333W0=W+234H0=H0235A0=H0336H+37SPECIALPARTICLESG(graviton)39R041LQc42reggeon110pomeron990odderon9990forMCinternaluse81{100DIQUARKS(dd)11103(ud)02101(ud)12103(uu)12203(sd)03101(sd)13103(su)03201(su)13203(ss)13303(cd)04101(cd)14103(cu)04201(cu)14203(cs)04301(cs)14303(cc)14403(bd)05101(bd)15103(bu)05201(bu)15203(bs)05301(bs)15303(bc)05401(bc)15403(bb)15503SUSYPARTICLESedL1000001euL1000002esL1000003ecL1000004eb11000005aet11000006aeeL1000011eeL1000012eL1000013e¹L1000014e11000015ae¿L1000016edR2000001euR2000002esR2000003ecR2000004eb22000005aet22000006aeeR2000011eR2000013e22000015aeg1000021e011000022be021000023be+11000024be031000025be041000035be+21000037beG1000039LIGHTI=1MESONS0111+211a0(980)09000111a0(980)+9000211(1300)0100111(1300)+100211a0(1450)010111a0(1450)+10211(1800)09010111(1800)+9010211(770)0113(770)+213b1(1235)010113b1(1235)+10213a1(1260)020113a1(1260)+202131(1400)090001131(1400)+9000213(1450)0100113(1450)+1002131(1600)090101131(1600)+9010213a1(1640)09020113a1(1640)+9020213(1700)030113(1700)+30213(1900)09030113(1900)+9030213(2150)09040113(2150)+9040213a2(1320)0115a2(1320)+2152(1670)0101152(1670)+10215a2(1700)09000115a2(1700)+90002152(2100)090101152(2100)+90102153(1690)01173(1690)+2173(1990)090001173(1990)+90002173(2250)090101173(2250)+9010217a4(2040)0119a4(2040)+219LIGHTI=0MESONS(u u,d d,ands sAdmixtures)2210(958)331f0(600)9000221f0(980)9010221(1295)100221f0(1370)10221(1405)9020221(1475)100331f0(1500)9030221f0(1710)10331(1760)9040221f0(2020)9050221f0(2100)9060221f0(2200)9070221(2225)9080221!(782)223(1020)333h1(1170)10223f1(1285)20223h1(1380)10333f1(1420)20333!(1420)100223f1(1510)9000223h1(1595)9010223!(1650)30223(1680)100333f2(1270)225f2(1430)9000225f02(1525)335f2(1565)9010225f2(1640)90202252(1645)10225f2(1810)90302252(1870)10335f2(1910)9040225f2(1950)9050225f2(2010)9060225f2(2150)9070225f2(2300)9080225f2(2340)9090225!3(1670)2273(1850)337f4(2050)229fJ(2220)9000229f4(2300)9010229 42.MonteCarloparticlenumberingscheme STRANGEMESONSK0L130K0S310K0311K+321K0(800)09000311K0(800)+9000321K0(1430)010311K0(1430)+10321K(1460)0100311K(1460)+100321K(1830)09010311K(1830)+9010321K0(1950)09020311K0(1950)+9020321K(892)0313K(892)+323K1(1270)010313K1(1270)+10323K1(1400)020313K1(1400)+20323K(1410)0100313K(1410)+100323K1(1650)09000313K1(1650)+9000323K(1680)030313K(1680)+30323K2(1430)0315K2(1430)+325K2(1580)09000315K2(1580)+9000325K2(1770)010315K2(1770)+10325K2(1820)020315K2(1820)+20325K2(1980)09010315K2(1980)+9010325K2(2250)09020315K2(2250)+9020325K3(1780)0317K3(1780)+327K3(2320)09010317K3(2320)+9010327K4(2045)0319K4(2045)+329K4(2500)09000319K4(2500)+9000329CHARMEDMESONSD+411D0421D0(2400)+10411D0(2400)010421D(2010)+413D(2007)0423D1(2420)+10413D1(2420)010423D1(H)+20413D1(2430)020423D2(2460)+415D2(2460)0425D+s431Ds0(2317)+10431D+s433Ds1(2536)+10433Ds1(2460)+20433Ds2(2573)+435BOTTOMMESONSB0511B+521B0010511B+010521B0513B+523B1(L)010513B1(L)+10523B1(H)020513B1(H)+20523B02515B+2525B0s531B0s010531B0s533Bs1(L)010533Bs1(H)020533B0s2535B+c541B+c010541B+c543Bc1(L)+10543Bc1(H)+20543B+c2545c cMESONSc(1S)441c0(1P)10441c(2S)100441J=Ã(1S)443hc(1P)10443c1(1P)20443(2S)100443(3770)30443(4040)9000443(4160)9010443(4415)9020443c2(1P)445c2(2P)100445b bMESONSb(1S)551b0(1P)10551b(2S)100551b0(2P)110551b(3S)200551b0(3P)210551¨(1S)553hb(1P)10553b1(1P)205531(1D)30553¨(2S)100553hb(2P)110553b1(2P)1205531(2D)130553¨(3S)200553hb(3P)210553b1(3P)220553¨(4S)300553¨(10860)9000553¨(11020)9010553b2(1P)555b2(1D)105552(1D)20555b2(2P)100555b2(2D)1105552(2D)120555b2(3P)2005553(1D)5573(2D)100557LIGHTBARYONSp2212n2112++2224+2214021141114STRANGEBARYONS¤3122+3222032123112+3224c03214c3114c03322331203324c3314c3334CHARMEDBARYONS+c4122++c4222+c42120c4112++c4224+c42140c4114+c42320c41320+c432200c4312+c43240c43140c43320c4334+cc4412++cc4422+cc4414++cc4424+cc4432+cc4434++ccc4444BOTTOMBARYONS0b5122b51120b5212+b5222b51140b5214+b5224b51320b52320¡b531200b5322b53140b5324b5332b53340bc5142+bc524200bc54120+bc54220bc5414+bc54240bc534200bc54320bc5434+bcc5442+bcc5444bb55120bb5522bb55140bb5524bb5532bb55340bbc55420bbc5544bbb5554FootnotestotheTables:a)Particularyinthethirdgeneration,theleftandrightsfermionstatesmaymix,asshown.Thelightermixedstateisgiventhesmallernumber.b)Thephysicalestatesareadmixturesofthepuree,eZ0,fW+,eH01,eH02,andeH+states.c)§and¥arealternatenamesfor§(1385)and¥(1530). 42.MonteCarloparticlenumberingscheme N(1440)N0(1440)202112N+(1440)202212¤(1600)2031220(1660)203212+(1660)203222(1660)203112(1690)2033120(1690)203322N(1720)N0(1720)212114N+(1720)212214¤(1890)213124N(1680)N0(1680)202116N+(1680)202216¤(1820)2031260(1915)203216+(1915)203226(1915)203116(2030)2033160(2030)203326c(2880)204126N(1710)N0(1710)212112N+(1710)212212¤(1810)2131220(1880)213212+(1880)213222(1880)213112N(1535)N0(1535)102112N+(1535)102212¤(1670)103122¤(1405)1021320(1620)103212+(1620)103222(1620)103112(1750)1033120(1750)103322c(2625)1041220c(2815)104312+c(2815)104322c(5957)1051220c(6100)105312+c(6100)105322N(1520)N0(1520)102114N+(1520)102214¤(1690)103124¤(1520)1021340(1670)103214+(1670)103224(1670)103114(1820)1033140(1820)103324c(2595)1041240c(2790)104314+c(2790)104324N(1675)N0(1675)102116N+(1675)102216¤(1830)1031260(1775)103216+(1775)103226(1775)103116(1950)1033160(1950)103326N(1650)N0(1650)122112N+(1650)122212¤(1800)1231220(1750)123212+(1750)123222(1750)123112N(1700)N0(1700)112114N+(1700)1122140(1940)113214+(1940)113224(1940)113114¢(1600)(1600)2011140(1600)202114+(1600)202214++(1600)202224(1690)2031140(1690)203214+(1690)203224¢(1620)(1620)1111120(1620)112112+(1620)112212++(1620)112222(1750)1131120(1750)113212+(1750)113222¢(1700)(1700)1211140(1700)122114+(1700)122214++(1700)122224¢(1910)(1910)2211120(1910)222112+(1910)222212++(1910)222222¢(1920)(1920)2211140(1920)222114+(1920)222214++(1920)222224(2080)2231140(2080)223214+(2080)223224¢(1905)(1905)2111160(1905)212116+(1905)212216++(1905)212226(2070)2131160(2070)213216+(2070)213226¢(1950)(1950)2011180(1950)202118+(1950)202218++(1950)202228(2030)2031180(2030)203218+(2030)203228(2250)2033180(2250)203328­(2250)203338