Resonances with heavy quarks from lacesasa/talks/prelovsek_sfb16.pdf · Resonances with heavy...
Transcript of Resonances with heavy quarks from lacesasa/talks/prelovsek_sfb16.pdf · Resonances with heavy...
Resonanceswithheavyquarksfromla6ce(BoundstateswillbediscussedbyDanielMohler)
SasaPrelovsekUniversityofLjubljana&JozefStefanInsGtute,Slovenia
SFBmeeGng
UniversityofRegensburg,6and7October2016
1S.Prelovsek,SFBmeeGng2016
incollaboraGonwith:C.B.Lang,D.Mohler,L.Leskovec,U.Skerbis
OutlineLa$ceQCDstudiesconsideringsca+eringoftwohadronsintherestframeq charmoniumresonancesaboveopen-charmthreshold[Lang,Leskovec,Mohler,S.P.,1503.05363,JHEP2015]
q la6cesearchforresonanceX(5568)inBsπ+scat.
q aimedresonancesthatappearinscat.ofhadronswithspinconstrucGonofla6ceoperators[S.P.,Lang,Skerbis,1607.06738]vector-pseudoscalar(e.gJ/ψπforZcresonance)vector-nucleon(e.g.J/ψpforPcresonance)pseudoscalar-nucleon(e.g.πpforRoperresonance)la6cesimulaGonofπNintheRoperchannelwithJP=1/2+[Lang,Leskovec,Padmanath,S.P.,arxiv:1610.01422]
S.Prelovsek,SFBmeeGng2016 2
D0collaboraGon,1602.07588
Bsπ+invariantmass
[Lang,Mohler,S.P.,1607.03185,PRD2016]
H1(p)H2(-p)
AllphysicalstateswithgivenJPCappearasEninprinciple(example:charmoniumwith1++)
• “single-meson”statesJ/ΨmJ/ψ=E1
• “two-meson”states
S.Prelovsek,SFBmeeGng2016 3
J PC O = qΓq, (qΓ1q) !p1(qΓ2q) !p2
, [qΓ3q ][qΓ4q],...
ψ(3770), 1−− : cc , (cu)(uc) = DD , [cu][cu]
Cij (t) = 0Oi (t)Oj+(0) 0 =
n∑ Zi
n Z jn* e−En t, Zi
n = 0Oi n
Meson(like)systemwithgivenJPCiscreatedbyanumberofinterpolaGngfields
La6cegivesdiscreteenergiesofeigenstates:En
DD,...
forP=0(alerextrapolaGons)
Enrigorouslyrendertwo-hadronscameringmatrix(forexampleDDscameringmatrix)
4
xxx
xx E(L)
Rigoroustreatmentofhadronsnearorabovethresholdscameringoftwospin-lessmesonsinrestframe
δ(E)E(L) energiesfromla6cewithspaGalextentL
scameringphaseshilsatinfinitevolume
S.Prelovsek,SFBmeeGng2016
L
twomesonsinala6cebox
analyGcproposal:Luscher1991 DD̄ ! (3770) ! DD̄example
DD̄
Scameringoftwomesons
5
one-channel(elasGc)scameringwithtotalmomentumP=0:E=Ecm
En(L)δ(E)Luscher’seq.
ScameringmatrixforparGalwavel
Boundstate(B):
cot[δ(EB)]=i,EB<m1+m2
Resonance(R)(ofBreit-Wignertype):
M1(p)
M2(-p)
Re[E]
Im[E]
m1+m2threshold
B
R
LocaGonsofpolesofT(E)forres.andboundst.
exp
S(E) = e2i�(E), S(E) = 1 + 2iT (E), T (E) =
1
cot �(E)� i
T (E) =�E �
E2 �m2R + i E �
, �(E) = g2p2l+1
E2
Twotypesofplotswillbeshown:
• E(L)energiesoflat.eigenstates
• mphy=mR,mBextractedfromE(L)
S.Prelovsek,SFBmeeGng2016 7
CharmoniawellbelowDDpreciselyknown
Perez-Rubio,Collins,Bali,1503.08440,PRD2015seealso:FNAL/MILC,1412.1057
TheomissionofcharmannihilaGonisthemainremaininguncertainty
m=E(P=0):ag0Lg∞mqgmq
phy
[PDG]
Excitedcharmoniawithinsingle-hadronapproach
S.Prelovsek,SFBmeeGng2016 8
justccinterpolatorsused,strongdecayofresonancesaboveDDnottakenintoaccount
Had.Spec.Coll,1610.01073
Resonanceψ(3770)andboundst.ψ(2S)fromDDscameringinp-wave
Lang,Leskovec,Mohler,S.P.,1503.05363,JHEP2015S.Prelovsek,SFBmeeGng2016 9
cquarku,dquarks
DD̄ ! (3770) ! DD̄First(exploratory)la6cesimulaGonofacharmoniumresonanceaboveopen-charmthresholdtakingintoaccountitsstrongdecay
WickcontracGons
evaluatedusing
-disGllaGon[Peardonet.al.,2009]
-stochasGcdisGllaGon
[Morningstaretal.,2011]
Eigen-energiesEninfinitevolume
Lang,Leskovec,Mohler,S.P.,1503.05363,JHEP2015S.Prelovsek,SFBmeeGng2016 10
En ! �(En)
mπ=266MeVL=2fm
PACS-CSmπ=156MeV
L=2.9fm
Resonanceψ(3770)andboundst.ψ(2S)fromDDscameringinp-wave
Lang,Leskovec,Mohler,S.P.,1503.05363,JHEP2015
S.Prelovsek,SFBmeeGng2016 11
En ! �(En) ! p3 cot �(p)/ps
ThisquanGtypresentedasitisapprox.linearnearsimpleBWresonance:• BWfit(i):
• fit(ii):capturesalsoboundst.:R:mR:zero,ΓR:slopenearzero
B:cotδ=i
DDthreshold
mπ=266MeVmπ=156MeV
p = i|p| ! p
3cot� = (i|p|)3i = |p|3 > 0
p3 cot �ps
(2S)
DDscat.inp-waveissimulatedT-matrixisdeterminedfromEnFitofT-matrixgives:BWresonanceψ(3770):mR(magentadiamonds):δ=π/2Γ(givenbelow):fromslopenearδ=π/2Boundstateψ(2S)frompoleinT:mB(magetnatriangles):cotδ=i
ψ(3770),fit(ii) Mass[MeV] g(nounit)
Lat(mπ=266MeV) 3774±6±10 19.7±1.4
Lat(mπ=156MeV) 3789±68±10 28±21
Exp. 3773.15±0.33 18.7±1.4
Resonanceψ(3770)andboundst.ψ(2S)fromDDscameringinp-wave
Lang,Leskovec,Mohler,S.P.,1503.05363,JHEP2015]
O : c c, DD, J PC =1−−
extractedmassesofhadrons
S.Prelovsek,SFBmeeGng2016 12
� =g2
6⇡
p3
s
D0coll.foundresonanceX(5568)inBsπ+scamering
S.Prelovsek,SFBmeeGng2016 14
D0collaboraGonfebruary20161602.07588• Γ=22MeV• JPnotmeasured• Theonlyhadronwith4differentflavors?!
Bsπ+invariantmass
SearchforX(5568)inBsπ+scamering
S.Prelovsek,SFBmeeGng2016 15
• soonalerD0result,severalphenomenologicalstudiesappeared• thosewhocouldfindsupport,suggestedithasJP=0+• ifX(5568)isJP=0+:-theonlystrongdecaychannelisBsπ+
-thenextthresholdisBKanditis210MeVaboveX(5568)!-exoGcresonanceinelasGcchannel!?Thisissomethingla6ceQCDcando!
• note:allotherexoGccandidates(Zc,Zb,....)areresonancesbutlie-nexttoahigherthreshold-aboveseveralthresholds
thisismuchmorechallengingthatiswhyitisdifficulttoestablishthoseexoGcstatesonla6ce
[Lang,Mohler,S.P.,1607.03185,PRD2016]
S.Prelovsek,SFBmeeGng2016 16
AnalyGcexpectaGonforEnifX(5568)exists
basedonmXandΓXasmeasuredbyD0exp
Employedoperators:Bsπ+andBK
BKthreshold210MeVhigher;theinterpolatorsareemployedjustforcompleteness
[Lang,Mohler,S.P.,1607.03185,PRD2016]
ResultsofEnfromactualla6cesimulaGon
S.Prelovsek,SFBmeeGng2016 17
AnalyGcexpectaGonforEnifX(5568)exists
basedonmXandΓXasmeasuredbyD0expLa6ceAnalyGc(ifXexists)
L=2.9fm
La6ceresult(obtainedbeforemarch22nd2016–seenextslide):• noindicaGonofX(5568)• interacGonsinBsπ+andBKsystemaresmall[Lang,Mohler,S.P.,1607.03185,PRD2016]
S.Prelovsek,SFBmeeGng2016 18
LHCbdatapublishedin1608.00435:PRL2016
Bsπ+invariantmass Bsπ+invariantmass
La6ceoperatorsforscameringofparGcleswithspin
S.Prelovsek,SFBmeeGng2016 19
Previoustwoexamplesconcernedscameringoftwospinlesshadrons:pseudoscalar-pseudoscalar(DDandBsπ+)
[S.P.,Lang,Skerbis,1607.06738]
MoGvaGon
La6ceoperatorsforscameringofparGcleswithspin 20
• MainlyPPscameringwassimulatedonla6ceuptonowscameringphaseshilextracted(Phasnospin)
• H(1)H(2):whereoneorbothHcarryspinwasexploredmostlyonlyforL=0
manyinteresGngchannelssGllunexplored,parGcularlyforL>0
IwillconsiderconstrucGonofH(1)H(2)interpolators
whereHisoneofP,V,Nhadrons,whichis(almost)stablewithrespecttostrongdecay:
P=psuedoscalar(JP=0^-)=π,K,D,B,ηc,...
V=vector(JP=1^-)=D*,B*,J/ψ,ϒb,Bc*,...(butnotdirectlyapplicabletoρasisunstable...)
N=nucleon(JP=1/2^+)=p,n,Λ,Λc,Σ,...(butnotdirectlyapplicabletoN-(1535)asisunstable...)
Iwillconsiderinterpolatorsforchannels:
PV:mesonresonancesandQQ-likeexoGcs(e.g.πJ/ψ,DD*..)
PN:baryonresonances(e.g.πN,KN...)andpentaquarks
NV:baryonresonancesandpentaquarksNN:nucleon-nucleonanddeuterium,baryon-baryon
SasaPrelovsek
MoGvaGon
La6ceoperatorsforscameringofparGcleswithspin 2
• MainlyPPscameringwassimulatedonla6ceuptonowscameringphaseshilextracted(Phasnospin)
• H(1)H(2):whereoneorbothHcarryspinwasexploredmostlyonlyforL=0
manyinteresGngchannelssGllunexplored,parGcularlyforL>0
IwillconsiderconstrucGonofH(1)H(2)interpolators
whereHisoneofP,V,Nhadrons,whichis(almost)stablewithrespecttostrongdecay:
P=psuedoscalar(JP=0^-)=π,K,D,B,ηc,...
V=vector(JP=1^-)=D*,B*,J/ψ,ϒb,Bc*,...(butnotdirectlyapplicabletoρasisunstable...)
N=nucleon(JP=1/2^+)=p,n,Λ,Λc,Σ,...(butnotdirectlyapplicabletoN-(1535)asisunstable...)
Iwillconsiderinterpolatorsforchannels:
PV:mesonresonancesandQQ-likeexoGcs(e.g.πJ/ψ,DD*..)
PN:baryonresonances(e.g.πN,KN...)andpentaquarks
NV:baryonresonancesandpentaquarksNN:nucleon-nucleonanddeuterium,baryon-baryon
SasaPrelovsek
• O=HHneededtocreate/annihilateHHsystem
• EnrelatedtophaseshilsforHHscamering-twospinlessparGclesLuscher(1991):
-twoparGcleswitharbitraryspin
Briceno,PRD89,074507(2014)
(otherauthors:somespecificcases)
Somepreviousrelatedworkonla6ceHHoperatorsforhadronswithspinandL≠0
SasaPrelovsek La6ceoperatorsforscameringofparGcleswithspin 3
ParGal-wavemethodforHH:Berkowitz,Kurth,Nicolson,Joo,Rinaldi,Strother,Walker-Loud,1508.00886Wallace,Phys.Rev.D92,034520(2015),[arXiv:1506.05492]ProjecGonmethodforHH:M.Göckeleretal.,Phys.Rev.D86,094513(2012),[arXiv:1206.4141].Helicityoperatorsforsingle-H:Thomas,EdwardsandDudek,Phys.Rev.D85,014507(2012),[arXiv:1107.1930]SomeaspectsofhelicityoperatorsforHH:Wallace,Phys.Rev.D92,034520(2015),[arXiv:1506.05492].Dudek,EdwardsandThomas,Phys.Rev.D86,034031(2012),[arXiv:1203.6041].WhichCGofH1andH2toH1H2irrepsarenonzero;valuesofCGnotpublished:MooreandFleming,Phys.Rev.D74,054504(2006),[arXiv:hep-lat/0607004].etc...However:forala6cepracGGonerwhowasinterestedinacertainchannel,forexample(PVscameringinL=2orVNscameringwithλV=1andλN=1/2)thereweresGlllotsofpuzzlestobeatbeforeconstrucGngareliableinterpolator..
rotaGonsRinversionI
Werestricttototalmomentumzero
La6ceoperatorsforscameringofparGcleswithspin 5
H(1)(p)H(2)(-p),Ptot=0AdvantageofPtot=0:• parityPisagoodnumber• channelswithevenandoddLdonotmixinthesameirrep
nottrueforPtot≠0
SasaPrelovsek
BuildingblocksH:requiredtransformaGonproperGesofH
annihilaGonfield
msisagoodquantumnumberatp=0:msisnotgoodquantumnumberingeneralforp≠0:inthiscaseitdenotesmsofcorrespondingHms(p=0)
toprovecorrecttransformaGonproperGesofHH
WignerDmatrix
Non-pracGcalchoiceofH:canonicalfieldsH(c)
SasaPrelovsek La6ceoperatorsforscameringofparGcleswithspin 6
L(p)isboostfrom0top;drawback:H(c)(p)dependonm,E,..
withcorrecttransformaGonproperGesunderRandI
Non-pracGcalchoiceofH:canonicalfieldsH(c)
SasaPrelovsek La6ceoperatorsforscameringofparGcleswithspin 6
L(p)isboostfrom0top;drawback:H(c)(p)dependonm,E,..
withcorrecttransformaGonproperGesunderRandI
PracGcalchoiceofHwithcorrecttransformaGonproperGesunderRandI
TheseHareemployedasbuildingblockinourHHoperatorssimpleexamples
relevantrotaGons::Owith24el.forJ=integer;O2with48elementsforJ=half-integerThegroupincludinginversionI:Ohwith48el.forJ=integer;O2
hwith96elementsforJ=half-integer
TherepresentaGonOJreducibleunderO(2).IrreduciblerepresentaGons(irreps)aredenotedbyΓandrowsr
RequiredtransformaGonproperGesofO=HH
SasaPrelovsek La6ceoperatorsforscameringofparGcleswithspin 7
T(R)givenforallirrepsinBernard,Lage,Meißner,Rusetsky,JHEP2008,0806.4495WeusesameconvenGonsforrows.
goodparitysincePtot=0!
conGnuumR
discreteR
“seed”:EachHacanhaveanypolarizaGonmsanddirecGonpwithgiven|p|.DifferentchoicesleadtodifferentlinearlyindependentOn
MethodI:ProjecGonoperators
8
Someexamplesfor|p|=1:PVinT1+,nmax=2:
PNinH+,nmax=1:
VNinH-,nmax=3:
Disadvantage:
notinformaGvewhichconGnuumnumbers(parGalwaveLorhelicity)eachOncorresponds
Thisisremediedinnexttwomethod.s
T(R)givenforallirrepsinBernard,Lage,Meißner,Rusetsky,JHEP2008,0806.4495
SasaPrelovsek La6ceoperatorsforscameringofparGcleswithspin
Proof(inourpaperandbackupslides):thecorrecttransformaGonproperGes
followfromtransformaGonsofH(slide4)andproperGesofC,YlmandD.
ExampleofPVoperatorsSubducGontoirrepsdiscussedlateron.
MethodII:ParGal-waveoperators
SasaPrelovsek La6ceoperatorsforscameringofparGcleswithspin 9
ProposedforNNin[Berkowitz,Kurth,Nicolson,Joo,Rinaldi,Strother,Walker-Loud,CALLAT,1508.00886]ThereYlm*appearswherewehaveYlm
Clebsch-GordansSphericalHarmonics
buildingblocksH
menGonedonslide6belowStarGngannihilaGonoperator(beforesubducGontoirreps)
MethodIII:helicityoperators
SasaPrelovsek 10
• buildingblocksinparGal-waveoperatorsareHms(p)andmsisnotgoodforp≠0:• HelicityλisprojecGonofStop.ItisgoodalsoforparGclesinflight
• DefiniGonofsingle-hadronhelicityoperator• HelicityisnotmodifiedunderR(pandStransformthesameway)
• Two-hadronO:• Proof:
[HHinconGnuum:Jacob,Wick(1959)][forsingleHonla6ce:HSC,Thomasetal.(2012)][notwidelyusedforHHonla6ceyet]
pisarbitrarymomentumingivenshell|p|;Rdoesnotmodifyλ1,2,soH1,2havechosenλ1,2inallterms
rotaGonfrompztop
goodms
R’=RaR
denotedbysuperscripth
MethodIII:helicityoperators(conGnued)
SasaPrelovsek La6ceoperatorsforscameringofparGcleswithspin 11
UsingdefiniGonsofandparityprojecGon
• Harebuildingblocksfromslide6below:acGonsofRandIonHms(p)aregiveninslide4• ThereareseveralchoicesofR0pwhichrotatefrompztop:
-theseleadtodifferentphasesindefiniGonofHλh:inconvenience
-buttheyleadtothesameOabove(moduloirrelevantoverallfactor):sonoproblemforsuchconstrucGon
• Simplechoiceformomentumshell|p|=1:p=pzandR0p=IdenGty
• paperprovidesdetailshowtousefuncGonsfromMathemaGcaforconstrucGon,alsosinceMathemaGcausesnon-convenGonaldefniGonofD
,choiceofsigninourpaper
SubducGonofOJtoirreduciblerepresentaGons
SasaPrelovsek La6ceoperatorsforscameringofparGcleswithspin 12
ParGal-waveoperatorsOJ,mJ,L,S
HelicityoperatorsOJ,mJ,λ1,λ2
TherepresentaGonOJisirreducibleunderconGnuumR.ButitisreducibleunderRindiscretegroupla6ceO(2).
OperatorsthattransformaccordingtoirrepΓandrowrobtainedviasubducGon.
SubducGonmatricesS[Dudeketal.,PRD82,034508(2010)
Edwardsetal,PRD84,074508(2011)]
conGnumR discreteRindiscretegroupO(2)subducGon
Single-hadronoperatorsH:experiencebyHadronSpectrumcollaboraGonPhys.Rev.D82,034508(2010)• subducedoperatorsO[J]
ΓcarrymemoryofconGnuumspinanddominantlycoupletostateswiththisJ
ExpectaGonforparGal-waveandhelicityoperatorsHHobtainedbysubducGon:
• woulddominantlycoupletoeigen-stateswithconGnuum(J,L,S)
• woulddominantlycoupletoeigen-stateswithconGnuum(J,λ1,λ2)
valuableforsimulaGons
givephysicsintuiGononquant.num.
onelaststepbeforereachingtheresults...
P(1)V(-1)operators,T1+,row=r=1
SasaPrelovsek La6ceoperatorsforscameringofparGcleswithspin 14
JP=1+,S=1,L=0
JP=1+,S=1,L=2JP=1+,λV=0JP=1+,λV=1
projecGonop.parGal-waveop.helicityop.
ParGal-waveandhelicityoperatorsexpressedintermsofprojecGonoperatorsthroughout.
N(1)P(-1)operators,G1+,row=r=1,p-wave
SasaPrelovsek La6ceoperatorsforscameringofparGcleswithspin 14
JP=1/2+,S=1/2,L=1
JP=1/2+,λN=1/2
projecGonop.parGal-waveop.helicityop.
employedinla6cesimulaGonofπNsca+eringinp-wavetostudytheRoperchannelwithJP=1/2+[Lang,Leskovec,Padmanath,S.P.,arxiv:1610.01422]
PV,PN,VN,NNallirreps,|p|=0,1consistentresultsfoundinthreemethods
SasaPrelovsek La6ceoperatorsforscameringofparGcleswithspin 13
givenin[S.Prelovsek,U.Skerbis,C.B.Lang,arXiv:1607:06738]
ExplicitexpressionsforallH(1)(p)H(2)(-p)
PV:mesonresonancesandQQ-likeexoGcs(e.g.πJ/ψ,DD*forZc)PN:baryonresonances(e.g.πNforN*,KN...)andpentaquarksNV:baryonresonancesandpentaquarks(e.g.pJ/ψforPc)NN:nucleon-nucleonanddeuterium,baryon-baryon
Operatorsvaluabletostudyresonanceswithheavyquarks
Conclusions
S.Prelovsek,SFBmeeGng2016 35
Ihavediscussed• firststudyofcharmoniumresonancethattakesintoaccountitsstrongdecay• searchforanexoGcstateX(5568)thatcontainsfourdifferentflavorsinelasGcscamering:wedidnotfindevidenceforitfromla6ce,inagreementwithrecentLHCbresult
• construcGonofla6ceoperatorsforsimulaGngscameringoftwo-hadronswithspin:neccessarytoextractinformaGononresonancesthatappearinPV,PNandVN,NNscamering
La6cesetup
S.Prelovsek,SFBmeeGng2016 37
• Wilon-cloverquarks
• Fermilabmethodforcandb:[ElKhadra,Kronfeldetal,1997]ResthadronenergieshavesizablediscreGzaGonerrorsbuttheselargelycancelinspli6ngs.
Onlyspli6ngswithrespecttoachosenreferencemassarecomparedtoexperiment.
• evaluaGngWickcontracGonstosimulatescameringonthela6ceischallengingandcomputaGonallyintensive–thatispartofthereasonwhyasmallnumberofstudieshavebeenmade.Weapplytwomethods
-disGllaGon(Ensemble1)[Peardonet.al.,HSC,2009]-stochasGcdisGllaGon(Ensemble2)[Morningstaretal.,2011]
PACS-CS