Hadron spectroscopy and interac/ons from la3ce QCDsasa/talks/prelovsek_qcdatwork16.pdf · •...

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

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

Evaluation of Feynman path integrals in discretized space-time

Non-perturba:vemethod:QCDonlaNce


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

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

Stateswellbelowthreshold:“easy”�precisionspectrum


•  m=EnforP=0ag0,Lg∞,mqgmqphy

•  AvailablefromanumberoflaNceQCDcollabora:onsforanumberofyears


HighPrecisionQCDm=En

7

GlanceatPDG:almostallhadronsarehadronicresonances(decaystrongly)

q stableonstrongdecay

€

u u

€

s u

€

c u

€

uud

Inpar:cular:allexo:ccandidates

(tetraquarks,pentaquarks)

stronglydecay

Hadronsnearorabovestrongdecaythreshold

Rigorousapproach

ScaZeringinonechannel

”challenging” �


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


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

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)

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

ρ:reviewoflaNceresultstheonlyresonancestudiedbyseveralcollabora:ons


Γ =gρππ2

6πp3

E 2fromT.Yamazaki[1503.0867]

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

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


� =g2

6⇡

p3

s

T ∝ 1cotδ − i

En ! �(En)

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


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++


WhichFockcomponentsareessen:alforX(3872)withI=0?


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


essen:al donoseemnotessen:al

energiesofeigenstatesonlaNceE(L)(thesearenotmphy)

O:all O:allwithoutccinterpola:ngfields

mπ≈266MeV

localaizeddiquarkan:diquark


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]

BoundstateofaηcandpfromlaNce


[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.

Hadronsthatdecaytoseveralfinalstates

ScaZeringintwoormorechannels

”very challenging” �


•  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


loca:onofpolesinTmatrixincomplexplane

[BESIII, 2013, 1303.5949, PRL]

Zc+(3900) g J/Ψ π+

ccdu

ChargedcharmoniumZc+:manifestlyexo:c

IG=1+,JPC=1+-(Cisforneutralpartner)

23

Zc+(3900)channel:IG=1+,JPC=1+-HALQCDmethodV(r)

24

[HALQCD,Ikedaetal,1602.03465]

HALQCDisanothermethodtoextractscaZeringmatrixfromlaNce(consideredtobelessrigorousthantheLuscher’smethodforcoupledchannels)

Zc+channel,three-bodyY(4260)decay:laNce&exp



DD*th

DD*th

Zc+

Zc+

Zc+ → J /ψ π + = (cc)(du)


Zc+channel:HALQCDmethod,polesofSincomplexplane


Z = Ec.m.

SecondRiemannsheetforallthreechannelsshown.

Remarks:•  HALQCDmethodnotconsideredasrigorousastheLuscher’smethodforcoupledchannels•  3x3matrixSinZcchannelhasnotbeendeterminedbyLuschermethodyet•  HALQCDmethodhasnotverifiedanyoftheconven:onalresonancesyet(tomyknowledge)•  Luscher’smethodhasbeenverifiedonconven:onalres.likeρ,K*,ψ(3770),D0(2400)...

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)


LaNcesetup


•  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

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


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)

Y(4140),JPC=??+,ccss


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)

Illustra:onhoweigenstateD0*(2400)dominatedby“qq”

dissapearswhenqqinterpolatorsomiZed


Effec:veenergiesatt=8ploZed.

D(1)π(-1)D0

*(2400)D(0)π(0)

[Mohler,S.P.,Woloshyn,PRD87(2013)034501]

uc J PC = 0++

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


Hybrids:someofthemhaveexo:cJPClargeoverlapwithO=qFijq

33

JPC

LaNceExperiment

O : c̄c

single-mesonapprox:-usedun:lfewyearsago:

-ignoresstrongdecaysofresonances

-ignoreseffectsofthresholds

Protonandneutroncons:tutemorethan99%

ofthebrightsideofuniverse


BMWcollabora:onScience347,2015

BMWcollabora:onScience322,2008

QCD+QEDmu≠md

mn-mpQCDmu=md

mn,mp

Hadron spectroscopy and interac/ons from la3ce QCDsasa/talks/prelovsek_qcdatwork16.pdf · •...

Documents

Transcript of Hadron spectroscopy and interac/ons from la3ce QCDsasa/talks/prelovsek_qcdatwork16.pdf · •...