hadron spectroscopy and interac/ons from la3ce qcdsasa/talks/prelovsek_qcdatwork16.pdf · •...
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Hadronspectroscopyandinterac/onsfromla3ceQCD
SasaPrelovsekUniversityofLjubljana&JozefStefanIns:tute,Slovenia
QCD@Work2016
Mar:naFranca,Italy,26.6.-30.6.2016
1SasaPrelovsek,Hadroninterac:onsfromlaNce
incollabora:onwithC.Lang,D.Mohler,L.Leskovec,R.Woloshyn
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Outlinewithchallenges
SasaPrelovsek,Hadroninterac:onsfromlaNce 2
E
strongdecaythreshold:m1+m2
hadronicresonancesR
shallowboundstates
stateswellbelowthreshold
WhenoneaimstostudyahadronwithgivenJPC:theloca:onofthethresholdinthatchannelpaysamajorrole.Ifthehadronmassisabovethreshold,itcanstronglydecaytoH1H2aslongasquantumnumbersallowdecay.• Hadronswellbellowthreshold:”easy” allreproducedbylaNceUnfortunatelynoneofexo:cexperimentalcandidatesisfoundwellbelowthreshold.• Hadronresonancesabovethresholdandstatesslightlybelowthreshold:challengingsimulatescaZeringoftwohadronsH1H2onlaNceanddeterminethescaZeringmatrixanumberofpioneeringresultsinpastfewyears• hadronsaboveseveralthresholds:very challenging veryfewresultsavailableü Iwillreportonsomeexamplesforeachcaseconven:onal(ρ,...)andexo:chadrons(X(3872),Zc+,...)begivenalongtheway
H1H2
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Evaluation of Feynman path integrals in discretized space-time
Non-perturba:vemethod:QCDonlaNce
SasaPrelovsek,Hadroninterac:onsfromlaNce 3
LQCD = − 14Gµν
a Gaµν + qiγµ (
q=u,d,s,c,b,t∑ ∂ µ + igs Ga
µ T a )q−mqqq
input: gs , mq
output: hadron properties hadron interactions
Dx ei S/!∫ DG Dq Dq e−SQCD /!
∫
€
S = dt L[x(t)]∫
€
SQCD = d4x LQCD[G(x), q(x)∫ , q (x)]
quantummechanicsquantumfieldtheoryinEuclidianspace-:me
x,t(Minkovsky)gx,it(Euclidean)
L
a
precisioncal.a~0.05-0.15fmL~2-8fm
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AlleigenstateswithgivenJPCappearinprinciple(example:protonchannel½+)
• singlehadronstatesχc1(1P)m=E1forP=0(aierextrapola:on)
• two-hadronstatesDD*SasaPrelovsek,Hadroninterac:onsfrom
laNce 4
J PC O = qΓq, (qΓ1q) !p1(qΓ2q) !p2
, [qΓ3q ][qΓ4q],...
ρ(770), 1−− : du, (dd)(du) = π π
X(3872), 1++ : cc , (cu)(uc) = DD* , [cu][cu]
p 1/2+ : uud, (uud)(uc) = pπ
Cij (t) = 0Oi (t)Oj+(0) 0 =
n∑ 0Oi n e−En t nOj
+ 0 =n∑ Zi
n Z jn* e−En t
Discreteenergiesofeigenstates:En
Enrigorouslyrendertwo=hadronscaZeringmatrix(forexampleDD*scaZeringmatrix)
meson
sbaryon
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Stateswellbelowthreshold:“easy”�precisionspectrum
SasaPrelovsek,Hadroninterac:onsfromlaNce 5
• m=EnforP=0ag0,Lg∞,mqgmqphy
• AvailablefromanumberoflaNceQCDcollabora:onsforanumberofyears
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SasaPrelovsek,Hadroninterac:onsfromlaNce 6
HighPrecisionQCDm=En
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7
GlanceatPDG:almostallhadronsarehadronicresonances(decaystrongly)
q stableonstrongdecay
€
u u
€
s u
€
c u
€
uud
Inpar:cular:allexo:ccandidates
(tetraquarks,pentaquarks)
stronglydecay
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Hadronsnearorabovestrongdecaythreshold
Rigorousapproach
ScaZeringinonechannel
”challenging” �
SasaPrelovsek,Hadroninterac:onsfromlaNce 8
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9
xxx
xx
E(L)
Extrac:ngscaZeringphaseshii
δ(E)E(L) energiesfromlaNcewithspa:alextentL
scaZeringphaseshiisatinfinitevolume
SasaPrelovsek,Hadroninterac:onsfromlaNce
L
twomesonsinalaNcebox
analy:cproposal:Luscher1991 example
ππσ ∝ sin2 δ
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SasaPrelovsek,Hadroninterac:onsfromlaNce 10
Rela:onbetweenEandδ(E)
E(L) = m12 +!p12 + m2
2 +!p22 +ΔE
!p1,2 =2πL!n
-duetostronginterac:on-givesrigorousinfoonδ
analy:cproposal:Luscher1991
Energiesoftwohadronsinabox: boundarycondi:on
p=2π/L
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ScaZeringoftwomesons
11
one-channel(elas:c)scaZeringwithtotalmomentumP=0:E=Ecm
En(L)δ(E)Luscher’seq.
ScaZeringmatrixforpar:alwavel
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
Loca:onsofpolesofT(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)
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Verifyingapproachonconven:onalρ
12
ρmeson Mass[MeV] gρππ(nounit)
Lat(mπ=266MeV) 772±6±8 5.61±0.12
Exp. 775 5.97
Ecmδ(Ecm)
generalized
Luscher’srela:on
Γ =gρππ2
6πp3
E 2
Cjk (t) = 0 Oj (t)Ok+(0) 0 , O = qq, (qq)(qq) 1−−
Lang,Mohler,S.P.,VidmarPRD84(2011)054503
=(Ea)2
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ρ:reviewoflaNceresultstheonlyresonancestudiedbyseveralcollabora:ons
SasaPrelovsek,Hadroninterac:onsfromlaNce 13
Γ =gρππ2
6πp3
E 2fromT.Yamazaki[1503.0867]
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S.Prelovsek,HadronSpectrum 14
Kπ , I=1/2: p-wave phase shift
[S.P.,Lang,Leskovec,Mohler,1307.0736,PRD2013]mπ≈266MeV
K*(892)resonanceKπ
€
BW : δ = acotmR2 − Ecms
2
mR Γ
reviewedbyTakeshiYamazaki,plenarytalk
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DDscat.inp-waveissimulatedT-matrixisdeterminedfromEnandinterpolatednearthreshold:
Boundstateψ(2S)frompoleinT:
cotδ(pB)=imB(triangles)
Resonanceψ(3770):δ(mR)=90omR(diamonds),Γ(givenbelow)
ψ(3770) 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)fromDDscaZeringinp-wave
2mD
Lang,Leskovec,Mohler,S.P.,1503.05363,JHEP2015]
O : c c, DD, J PC =1−−
physicalmassesmphy
SasaPrelovsek,Hadroninterac:onsfromlaNce 15
� =g2
6⇡
p3
s
T ∝ 1cotδ − i
En ! �(En)
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X(3872)asboundstatefromDD*scaZering,JPC=1++,I=0
16
LaNce• groundstate:χc1(1P)
• DD*scaZeringmatrixnearth.determined
• Apoleoffoundjustbelowth.(violetstar)
• ThepoleaZributedtoX(3872),whichisa
shallowboundstate
T ∝ 1cotδ − i
=∞
pcotδ(p) = 1a0+12r0p
2
[M.Padmanath,C.B.Lang,S.P.,1503.03257,PRD2015]
mπ≈266MeV,a=0.124fm,L=2fm
O : c c, DD*, [cu]3c[cu]3c, [cu]6c[cu]6c
physicalmassesmphy
FirstevidenceforX(3872)fromlaNceS.P.andLeskovec:1307.5172,PRL2013
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SasaPrelovsek,Hadroninterac:onsfromlaNce 17
WhichFockcomponentsareessen:alforX(3872)withI=0?
O : c c, DD*, J /ψω, χc1σ , ηcσ , [cu]3c[cu]3c, [cu]6c[cu]6c
(c̄q)1c(cq̄)1c , (c̄c)1c(q̄q)1c
JPC=1++
[M.Padmanath,C.B.Lang,S.P.,1503.03257,PRD2015]
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WhichFockcomponentsareessen:alforX(3872)withI=0?
SasaPrelovsek,Hadroninterac:onsfromlaNce
18
O : c c, DD*, J /ψω, χc1σ , ηcσ , [cu]3c[cu]3c, [cu]6c[cu]6c
upperredsquareiscandidateforX(3872):itisfoundonlyifccinthebasis
X(3872)notfoundifccnotinthebasis,although[cu][cu]inthebasis
[M.Padmanath,C.B.Lang,S.P.,1503.03257,PRD2015]
essen:al donoseemnotessen:al
energiesofeigenstatesonlaNceE(L)(thesearenotmphy)
O:all O:allwithoutccinterpola:ngfields
mπ≈266MeV
localaizeddiquarkan:diquark
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SasaPrelovsek,Hadroninterac:onsfromlaNce 19
Masspredic:onformissingBs0andBs1
[C.Lang,D.Mohler,S.P.,R.Woloshyn:1501.0164,PLB2015]
Ds0(2317)andDs1(2460)belowDKandD*Kthresholds
[D.Mohler,C.Lang,L.Leskovec,S.P.,R.Woloshyn:1308.3175,PRL2013
1403.8103,PRD2014][Mar:nezTorres,E.Oset,S.P.,A.Ramos:1412.1706,JHEP2015]
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BoundstateofaηcandpfromlaNce
SasaPrelovsek,Hadroninterac:onsfromlaNce 20
[NPLQCD,1410.7069,PRD,mπ~800MeV]
TwopentaquarkresonancesinJ/ψandpfromexp
⌘c p
c̄c uud
J/ p
c̄c uud~20MeVbelowth.mηc+mp
~400MeVaboveth.mJ/Ψ+mp
m-(mηc+mp)
LHCb:1507.03414
nolaNceresultsforthesePcyet:challengingasitcaninprincipledecaytoseveraldecaych.
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Hadronsthatdecaytoseveralfinalstates
ScaZeringintwoormorechannels
”very challenging” �
SasaPrelovsek,Hadroninterac:onsfromlaNce 21
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• qq,Kπ,Kηinterpolators• anumberofdifferent0<P≤2• foreachEn:onedeterminantequa:onformanyunknowns• T-matrixparametrizedtogetaroundthisproblem• theloca:onofpolesofT-matrixincomplexplainisgivenbelow• K*(892)andκarebelowthresholdforthismπ
• K0*(1400),K2*areresonances• mπ=391MeV,NL=16,20,24[Dudek,Edwards,Thomas,Wilson,HSC,1406.4158,PRL;1411.2004]
ResonancesinKπ,Kηcoupledchannels
SasaPrelovsek,Hadroninterac:onsfromlaNce 22
loca:onofpolesinTmatrixincomplexplane
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[BESIII, 2013, 1303.5949, PRL]
Zc+(3900) g J/Ψ π+
ccdu
ChargedcharmoniumZc+:manifestlyexo:c
IG=1+,JPC=1+-(Cisforneutralpartner)
23
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Zc+(3900)channel:IG=1+,JPC=1+-HALQCDmethodV(r)
24
[HALQCD,Ikedaetal,1602.03465]
HALQCDisanothermethodtoextractscaZeringmatrixfromlaNce(consideredtobelessrigorousthantheLuscher’smethodforcoupledchannels)
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Zc+channel,three-bodyY(4260)decay:laNce&exp
SasaPrelovsek,Hadroninterac:onsfromlaNce 25
[HALQCD,Ikedaetal,1602.03465]
DD*th
DD*th
Zc+
Zc+
Zc+ → J /ψ π + = (cc)(du)
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SasaPrelovsek,Hadroninterac:onsfromlaNce 26
Zc+channel:HALQCDmethod,polesofSincomplexplane
[HALQCD,Ikedaetal,1602.03465]
Z = Ec.m.
SecondRiemannsheetforallthreechannelsshown.
Remarks:• HALQCDmethodnotconsideredasrigorousastheLuscher’smethodforcoupledchannels• 3x3matrixSinZcchannelhasnotbeendeterminedbyLuschermethodyet• HALQCDmethodhasnotverifiedanyoftheconven:onalresonancesyet(tomyknowledge)• Luscher’smethodhasbeenverifiedonconven:onalres.likeρ,K*,ψ(3770),D0(2400)...
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Conclusionsforthe:mebeing
HadronspectroscopyfromlaNce(inbrief):u hadronswellbelowthresholdpreciselyobtained:D,K...andalltheothers:✔✔✔
u La3ceQCDcanextractscaReringmatrixandcross-sec/onforscaReringoftwohadrons✔✔(mosteasilyifthereisonlyonechannel)
u Hadronresonancesareextractedfrompeaksinthecross-sec/onsviaBW-typefitsresonancesverified:ρ,K*,K0*(1430),K2,D0
*,D1,a1,b1,Ψ(3770),..✔✔
u ShallowboundstatesappearaspolesinscaReringmatrixshallowboundstatesverified:Ds0,Ds1,Bs0,Bs1,X(3872)withI=0,..✔✔u FirststepstoextractscaZeringmatrixforscaZeringwithtwoormorecoupledchannels✔indica:onthatZc+isnotausualresonance(withpoleonthesecondRiemannsheet)
SasaPrelovsek,Hadroninterac:onsfromlaNce 27
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LaNcesetup
SasaPrelovsek,Hadroninterac:onsfromlaNce 28
• Wilon-cloverquarks
• Fermilabmethodforcandb:[ElKhadra,Kronfeldetal,1997]Resthadronenergieshavesizablediscre:za:onerrorsbuttheselargelycancelinspliNngs.
OnlyspliNngswithrespecttoachosenreferencemassarecomparedtoexperiment.
• evalua:ngWickcontrac:onstosimulatescaZeringonthelaNceischallengingandcomputa:onallyintensive–thatispartofthereasonwhyasmallnumberofstudieshavebeenmade.Weapplytwomethods
-dis:lla:on(Ensemble1)[Peardonet.al.,HSC,2009]-stochas:cdis:lla:on(Ensemble2)[Morningstaretal.,2011]
PACS-CS
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ComparinglaNceresultsforX(3872),JPC=1++,I=0
29
LaNce
LaNceevidenceforX(3872):• [1][Lee,DeTar,Na,Mohler,updateofproc1411.1389]mπ≈310MeV,a=0.15fm,L=2.4fm,HISQ
• [2][S.P.andLeskovec:1307.5172,PRL2013]
• [3][M.Padmanath,C.B.Lang,S.P.,1503.03257,PRD2015]
• Posi:onofDD*thresholddependsonmu/d,andmaybeaffectedbydiscre:za:oneffectsrelatedtocharmquark
[1][2][3]
c c, DD* c c, DD* c c, DD*,[cu][cu]
mπ≈266MeV,a=0.124fm,L=2fm
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SasaPrelovsek,Hadroninterac:onsfromlaNce 30
SearchforchargedpartnerofX(3872);channelIG=1-,JPC=1++,ccdu
• Horizontallines:energiesofexpectedtwo-mesonstatesinlimitofnointerac:on:E=E[M1(p1)]+E[M2(p2)]• Circles:energiesofeigenstatesfromlaZ• Onlyexpectedtwo-mesonstatesobserved.• Nola3cecandidateforchargedX(3872).Inagreementwithabsenceofsuchstateinexp.• Nola3cecandidateforotherchargedstate
below4.3GeV.
• TwoBelle2008statesareexp.unconfirmed.[M.Padmanath,C.B.Lang,S.P.,PRD2015,1503.03257]
Z+(4050)
Z+(4250)
Belle2008 D(-p) D*(p) p = n 2⇡L
O : (c̄u)(d̄c), (c̄c)(d̄u), [c̄d̄][cu]
mπ≈266MeV
eigen-energiesE(L)
(notmphy)
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Y(4140),JPC=??+,ccss
SasaPrelovsek,Hadroninterac:onsfromlaNce 31
Experiment:peakinJ/ψΦjustaboveJ/ψΦthresholdfound:CDF2009,CMS2012,D02013,Babar2015
notfound:Belle2010,LHCb2012LaNce:• S.OzakiandS.Sasaki,1211.5512,PRDcaveat:strangequarkannihila:onneglectednoresonantY(4140)structurefound• M.Padmanath,C.B.Lang,S.P.,1503.03257,PRD
channelJP=1+consideredonly:expectedtwo-par:cle
eigenstatesfoundandχc1,X(3872)butnotY(4140)
mπ≈266MeV
Y (4140) ! J/ �
c̄c s̄s
J/ΨΦscaZeringphaseshii[rad]
E(L)JPC=1++
O : c̄c, (c̄s)(s̄c), (c̄c)(s̄s), [c̄s̄][cs]
χc1
X(3872)
Y(4140)
δ
X(3872)
Y(4274)
χc1
eigenenergiesE(L)
(notmphy)
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Illustra:onhoweigenstateD0*(2400)dominatedby“qq”
dissapearswhenqqinterpolatorsomiZed
SasaPrelovsek,Hadroninterac:onsfromlaNce 32
Effec:veenergiesatt=8ploZed.
D(1)π(-1)D0
*(2400)D(0)π(0)
[Mohler,S.P.,Woloshyn,PRD87(2013)034501]
uc J PC = 0++
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Charmonia:single-mesonapproxima:on
[HSC,L.Liuetal:1204.5425,JHEP]• mπ≈400MeV,L≈2.9fm,Nf=2+1• iden:fica:onwithn2S+1LJmul:pletsusing<O|n>• green:lat,black:exp
SasaPrelovsek,Hadroninterac:onsfromlaNce
Hybrids:someofthemhaveexo:cJPClargeoverlapwithO=qFijq
33
JPC
LaNceExperiment
O : c̄c
single-mesonapprox:-usedun:lfewyearsago:
-ignoresstrongdecaysofresonances
-ignoreseffectsofthresholds
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Protonandneutroncons:tutemorethan99%
ofthebrightsideofuniverse
SasaPrelovsek,Hadroninterac:onsfromlaNce 34
BMWcollabora:onScience347,2015
BMWcollabora:onScience322,2008
QCD+QEDmu≠md
mn-mpQCDmu=md
mn,mp