Nilmani Mathur Department of Theoretical Physics, TIFR, INDIA Hadron spectrum : Excited States, Multiquarks and Exotics Hadron spectrum : Excited States,

Nilmani MathurNilmani MathurDepartment of Theoretical Physics, Department of Theoretical Physics,

TIFR, INDIATIFR, INDIA

Hadron spectrum : Hadron spectrum : Excited States, Multiquarks and Excited States, Multiquarks and

Exotics Exotics

Asian School 2011Asian School 2011

Non-quark model statesNon-quark model states States with excited gluonStates with excited gluon

• Hybrid mesons ( meson + Hybrid mesons ( meson + excited glueexcited glue))• Hybrid baryons ( baryon + Hybrid baryons ( baryon + excited glueexcited glue))• Glue balls (Glue balls (consitutent glueconsitutent glue))

Multi-quark statesMulti-quark states• Tetraquark, Pentaquark and higher number of quark statesTetraquark, Pentaquark and higher number of quark states

So far there is no So far there is no conclusiveconclusive experimental evidence experimental evidence of such a stateof such a state

These states are not well understoodThese states are not well understood• Quark model fails to explain these statesQuark model fails to explain these states

Lack of understanding makes experimental identification difficult.Lack of understanding makes experimental identification difficult. Lattice QCD calculations can provide crucial information of such a stateLattice QCD calculations can provide crucial information of such a state

qqqqq


Mesons, Hybrid Mesons and GlueballsMesons, Hybrid Mesons and Glueballs


Exotic Exotic HadronsHadrons

Hadrons whose quantum numbers require a

valence quark content beyond qqq or q¯q are termed “exotics”. Hadrons whose spin, parity and charge conjugation are forbidden in the non-relativistic quark model are also often termed “exotics”.

Experimental status : Experimental status : Aufbau principle of QCD differs dramatically from that of atoms and nuclei: to make more atoms add electrons, to make more nuclei, add neutrons and protons.

…..R.L. Jaffe


S = 0, 1S = 0, 1L = 0, 1, 2, 3…L = 0, 1, 2, 3…

SLL CPSLJ )1( ,)1( , 1

Allowed :Allowed : ,....2,2,2,1,1,1,0,0 PCJ

,....4,3,2,1,0,0 PCJForbiddenForbidden (Exotics)(Exotics) : :


Example of an ExoticExample of an Exotic

States with quantum number :States with quantum number : 11-+-+

It is not possible to write an It is not possible to write an interpolating field for this state interpolating field for this state with a form :with a form :

Possible operators : Possible operators :

anyfor ,1 qq

qBq

DDBqBq

qDq

aqqqq

qDq

qEq

qBqi

BqBqi

qEq

kjijk

kjijkikjijk

kjijk

bi

baa

bablk

ajkl

bablk

ajkl

bablk

ajkl

babj

a

;

;

4

45

155

4

45

4

4

,

,


Asian School 2011Asian School 2011 Paul Eugenio …Lattice Paul Eugenio …Lattice 20062006

Asian School 2011Asian School 2011 Paul Eugenio …Lattice Paul Eugenio …Lattice 20062006



Lattice results for 1Lattice results for 1-+-+

Where is

SIGNAL?


Decay statesDecay states


Decay statesDecay states


Octahedral group and lattice Octahedral group and lattice operatorsoperators

ΛΛ JJ

GG11

GG22

HH

1/21/2⊕⊕7/27/2⊕⊕9/29/2⊕⊕11/211/2 … …

5/25/2⊕⊕7/27/2⊕⊕11/211/2⊕⊕13/213/2 ……

3/23/2⊕⊕5/25/2⊕⊕7/27/2⊕⊕9/29/2 … …

ΛΛ JJ

AA11

AA22

EE

TT11

TT22

00⊕⊕44⊕⊕66⊕⊕88 ……

33⊕⊕66⊕⊕77⊕⊕99 ……

22⊕⊕44⊕⊕55⊕⊕66 ……

11⊕⊕33⊕⊕44⊕⊕55 ……

22⊕⊕33⊕⊕44⊕⊕55 ……

BaryonBaryon MesonMeson

……R.C. Johnson, Phys. Lett.B 113, 147(1982)R.C. Johnson, Phys. Lett.B 113, 147(1982)

Construct operator which transform irreducibly under the symmetries of the latticeConstruct operator which transform irreducibly under the symmetries of the lattice



Dudek, Edwards, Mathur, Richards : Phys. Rev. D77, 034501 (2008)


Dudek, Edwards, Mathur, Richards : Phys. Rev. D77, 034501 (2008)

Asian School 2011Asian School 2011S. Olsen arXiv:0801.1153v1 (hep-ex)S. Olsen arXiv:0801.1153v1 (hep-ex)

Renaissance in Charmonium physics


ZZ++(4430(4430))

Belle, Belle,

Since charged, it cannot be either charmonium or hybridSince charged, it cannot be either charmonium or hybrid

So, tetraquark? So, tetraquark?

Molecule?Molecule?

Small Charm state Small Charm state inside a large inside a large light quark hadron?light quark hadron?Study in baryon is needed.Study in baryon is needed.

………….M. Voloshyn, arXiv:0711.4556v2.M. Voloshyn, arXiv:0711.4556v2

S-K. Choi et al, PRL 100, 142001 (2008)

Recent Babar data do not support itHowever, more recent Belle analysis still claims it


Dudek et. al


Hadron spectrum CollaborationDudek et. al.


Dudek et al, Phys.Rev.Lett.103, 262001 (2009))

Mπ = 700 MeV Nf = 3, as = 0.12 fm, at-1 = 5.6 GeV, L =

2 fm

A more recent calculation


Status of exotic and hybridsStatus of exotic and hybrids

• There is suggestive, though not There is suggestive, though not conclusiveconclusive, , evidence of the existence of exotics and hybrid evidence of the existence of exotics and hybrid both in light and charm quark sectors.both in light and charm quark sectors.

• Lattice calculations find evidence of existence of Lattice calculations find evidence of existence of exotics and hybrid at non-realistic quark masses. exotics and hybrid at non-realistic quark masses. More detail calculations with controlled More detail calculations with controlled systematic and proper understanding of decay systematic and proper understanding of decay channels are necessary.channels are necessary.


GlueballGlueball

A glueball is a purely A glueball is a purely gluonic bound gluonic bound statestate..

In the theory of QCD glueball self coupling In the theory of QCD glueball self coupling admitsadmits

the existence of such a state.the existence of such a state.

Problems in glueball calculations :Problems in glueball calculations :

Glueballs are heavy – correlation functions die rapidly atGlueballs are heavy – correlation functions die rapidly at ٭٭

large time separations.large time separations.

Glueball operators have large vacuum fluctuationsGlueball operators have large vacuum fluctuations ٭٭

Signal to noise ratio is very badSignal to noise ratio is very bad ٭٭


GlueballGlueballOn Lattice, On Lattice, continuum rotational symmetrycontinuum rotational symmetry becomes becomes discrete cubic discrete cubic

symmetrysymmetry

with representationwith representation AA11, A, A2 2 , E, T, E, T1 1 ,T,T22 etc.etc. of different quantum of different quantum

numbers.numbers.

Typical gluon operators :Typical gluon operators :

Fuzzed operator :Try to make the overlap of the ground state of the operator to the glueball as large as possible by killing excited state contributions.

Moringstar and Peardon ….hep-lat/9901004


Generalized Wilson Generalized Wilson loopsloops

• Gluonic terms required for glueballs and hybrids Gluonic terms required for glueballs and hybrids can be extracted from generalized Wilson loopscan be extracted from generalized Wilson loops


Y. Chen…N.Mathur.. et al. Phys. Rev. D73, 014516 (2006)

Exotic Glueball Oddballs!

SU(3) Spectrum


E.B. Gregory et al. PoS LATTICE2008:286,2008

0¯ ¯(1)1¯+(1)

0++(0)0+ ¯(1)1+ ¯(1)

π(137)

0+ (1/2)

ρ(770)

σ(600)

f0(980)

f0(1370)

f0(1500)

a0(980)

a0(1450)

a1(1230)

K0*(1430)

JPG(I)

M (

MeV

)

a2(1320)

2+ ¯(1)

f0(1710)

κ(800)


Tetraquark statesTetraquark states

What is a What is a tetraquark tetraquark state?state?

Large 4 quark Large 4 quark component in Fock component in Fock space in the same space in the same way mesons have way mesons have large 2 quark and large 2 quark and baryons have large baryons have large 3 quark 3 quark components.components.

Why a tetraquark Why a tetraquark state is relevant?state is relevant?

1.1.Old reason – Old reason – There is a There is a mess in light quark scalar mess in light quark scalar sector. Difficult to sector. Difficult to explain observe spectrum explain observe spectrum by two quark states.by two quark states.

2.2.New reason – New reason – Some of Some of the newly observed the newly observed charmonia states may charmonia states may require explanation require explanation through tetraquark through tetraquark states.states.


Two quarks VS Four Two quarks VS Four quarksquarks

Alfred and Jaffe : Nucl.Phys.B578:367 (2000)

nonet q q nonet 22 qq

)800()980(

]][[]][[:

:

)()1(

0

21

]][[

a

dsdusdsu

suduqq

ImIm

qqqq

:observed


Tetraquark and Molecular Tetraquark and Molecular StatesStates

Vary r to see if there is any structure in B-S wave function which will have implication to decaying states.


σσ andand κκ

I. Caprini, G. Colangelo and H. Leutwyler, Phys. Rev. Lett. 96 (2006) 132001.

S. Descotes-Genon and B. Moussallam, Eur. Phys. J. C48 (2006) 553.

Note on the scalar mesons, C. Amsler et al., Review of Particle Physics, Phys. Lett. B667 (2008) 1; M. Ablikim et al., BES collaboration, Phys. Lett. B645 (2007) 19, Phys. Lett. B633 (2006) 681; G. Bonvicini et al., CLEO collaboration, Phys. Rev. D76 (2007) 012001; D. V. Bugg, arXiv:0906.3992 [hep-ph]; J.M. Link et al., FOCUS collaboration, arXiv: 0905.4846 [hep-ex]; E.M. Aitala et al., E791 collaboration, Phys. Rev. D73 (2006) 032004; I. Caprini, Phys. Rev. D77 (2008) 114019.

MeV 544

MeV 4411825

168

m

MeV 24557

MeV 13658

m


)(2

1

, 3

1

55

5

5

dduu

uddu

o

oo

ππππ four quark operator (I=0)four quark operator (I=0)

Asian School 2011Asian School 2011 2 I ,

, 0 I ,

)()(

)(2

1)(3)(

2

1)(2)0()(

tCtD

tGtAtCtDt

Two pion state


Alford & Jaffe : Alford & Jaffe : Nucl.Phys.B578:367 (2000)Nucl.Phys.B578:367 (2000)

mπ : 790 and 840 MeV

Presence of a bound state is suggestive, but not conclusive


)]0(0 )(JI ,[ PCG55

Evidence of a tetraquark state?Evidence of a tetraquark state?

Scattering statesScattering states(Negative scattering(Negative scattering length)length)

)0()0( pEpE

)1()1( pEpE

Scattering statesScattering states

Possible BOUND statePossible BOUND state

σσ(600)?(600)?

d

d

uu

Mathur,…. Liu et. al.. Phys.Rev.D76, 114505 (2007)


Volume dependence of spectral Volume dependence of spectral weightsweights

Volume independence suggests the observed state is an Volume independence suggests the observed state is an one particle stateone particle state

WW00

WW11

Mathur,…. Liu et. al.. Phys.Rev.D76, 114505 (2007)


Suganuma et.al : Suganuma et.al : Prog. Theor. Phys. Suppl. 168, 168 Prog. Theor. Phys. Suppl. 168, 168 (2007)(2007)

Quenched, anisotropic clover : at = 0.045 fm, L = 2.15fm, ms < mq <

2ms

Only ground state

No indication of tetraquark in this mass range


M. Loan et. al : M. Loan et. al : Eur.Phys.J.C57, 579 Eur.Phys.J.C57, 579 (2008)(2008)

Quenched, anisotropic clover fermions

I = 0

I = 2

I = 1


Interpolating fields used :Interpolating fields used :

Prelovsek,…NM,…et. al, arXiv : 1005.0948


Tetraquark States?Tetraquark States?

Prelovsek,….NM … et. al arXiv : 1005.0948


Tetraquark States?Tetraquark States?




nOZ ini ||0



0¯ ¯(1)1¯+(1)

0++(0)0+ ¯(1)1+ ¯(1)

π(137)

0+ (1/2)

ρ(770)

σ(600)

f0(980)

f0(1370)

f0(1500)

a0(980)

a0(1450)

a1(1230)

K0*(1430)

JPG(I))

M (

MeV

)

a2(1320)

2+ ¯(1)

f0(1710)

κ(800)

? MesoniaKK Kπ Mesonium?

ππ Mesonium

?qq

d

u u

dd

N. Mathur et. al.. Phys.Rev.D76, 114505 (2007)


TWQCD :TWQCD : Chiu & Hsieh, PLB646 (2006) 95, PRD73 (2006) Chiu & Hsieh, PLB646 (2006) 95, PRD73 (2006)

111503111503

Need to calculate scattering states before conclusion

)24(

)20(2

2

LnO

LnO

Quenched, overlap fermions for both light and charm mπ > 430 MeV, 0.4ms <mq<mc , a = 0.09 fm, L=1.8 fm, 2.2 fm Extracted only ground state


TWQCD :TWQCD : Chiu & Hsieh, PRD73 (2006) 094510 Chiu & Hsieh, PRD73 (2006) 094510

)24(

)20(2

2

LnO

LnO

Quenched, overlap fermions for both light and charm mπ > 430 MeV, 0.4ms <mq<mc , a = 0.09 fm, L=1.8 fm, 2.2 fm Extracted only ground state

Need to calculate scattering states before conclusion


Liuming Liu : PoS(lat09)099

Staggered sea Only ground state

1,1

*))(( 5

PC

i

JI

DDcqqcO

Change of sign of scattering length indicates possible bound state?


How to distinguish various states?How to distinguish various states?

• Local : Local :

• Tetraquark :Tetraquark :

• Molecular :Molecular :

• Hybrid : Hybrid :

• Glueball : Glueball :

• Solve generalized eigenvalue Solve generalized eigenvalue problem including all operators problem including all operators and find contribution from each and find contribution from each statestate

)()( xqxq

)()()()( 21 xqxqxqxq

)()( xDqxq )()()()( 21 yqyqxqxq


G. Bali : arXiv:0911.1238


ΘΘ+ + onon the Latticethe Lattice

NN

KK

u

ud

S d

u

dSu

d

suudd

ΘΘ++ bound state bound statem(m(ΘΘ++) ~ 1540 MeV) ~ 1540 MeV

Two-particle Two-particle NKNK scattering scattering statestate

S-wave :S-wave : m mKK+ m+ mN N ~ 1432 ~ 1432 MeV MeV

P-wave :P-wave :

Quark content Quark content :: Two possible Two possible statesstates

2222 pmpm NK


ΘΘ+ + onon the Latticethe Lattice

NN

KK

u

ud

S d

u

dSu

d

Most of the experiments do not see Most of the experiments do not see any evidence of a pentaquark stateany evidence of a pentaquark state

Almost all detail quenched lattice calculations do not see any evidence of ΘΘ++ pentaquark state


Story of Story of PentaquarksPentaquarks

The 2006 The 2006 Review of Particle PhysicsReview of Particle Physics : : There has not been a high-statistics confirmation of any of the original

experiments that claimed to see the Θ+; there have been two high-statistics repeats from Jefferson Lab that have clearly shown the original positive claims in those two cases to be wrong; there have been a number of other high-statistics experiments, none of which have found any evidence for the Θ+; and all attempts to confirm the two other claimed pentaquark states have led to negative results. The conclusion that pentaquarks in general, and the Θ+, in particular, do not exist, appears compelling.

The 2008 The 2008 Review of Particle PhysicsReview of Particle Physics : : There are two or three recent experiments that find weak evidence for

signals near the nominal masses, but there is simply no point in tabulating them in view of the overwhelming evidence that the claimed pentaquarks do not exist... The whole story—the discoveries themselves, the tidal wave of papers by theorists and phenomenologists that followed, and the eventual "undiscovery"—is a curious episode in the history of science.


Future study on latticeFuture study on lattice

• Future calculations with dynamical fermions and Future calculations with dynamical fermions and realistic quark masses.realistic quark masses.

• Calculations for spin-3/2 pentaquarks as claimed Calculations for spin-3/2 pentaquarks as claimed by a lattice study by a lattice study Phys. ReV D72, 074507 (2005).Phys. ReV D72, 074507 (2005).

• Study of charm pentaquarks as predicted by Study of charm pentaquarks as predicted by models.models.


BH = 16.6±2.1±4.6 MeV

NPLQCD, arXiv:1012.3812v1

H-dibaryon (uuddss)

at mπ ~ 390 MeV

Charmonium-Nucleon bound state

Taichi Kawana’s talkAttractive potential

Also S. Aoki’s talk



PANDAPANDAAntiproton Annihilation at Darmstadt at the High Antiproton Annihilation at Darmstadt at the High Energy Storage Ring at GSIEnergy Storage Ring at GSIAn Experiment at FAIR “Facility of Antiproton and Ion An Experiment at FAIR “Facility of Antiproton and Ion Research"Research"

Special detector, high luminosity (Special detector, high luminosity (L~ 2x1032 cm-2s-1) and and phase space cooled antiproton beam.phase space cooled antiproton beam.

Energy resolution ~50 keV Physics :Physics : Charonium spectroscopyCharonium spectroscopy Excited GlueExcited Glue

(Glueballs and Hybrids)(Glueballs and Hybrids) Charm in NucleiCharm in Nuclei Charmonium HypernucleiCharmonium Hypernuclei D and DD and DSS-Physics-Physics Other TopicsOther Topics

The Panda Experiment is collaboration of more then 45 institutes in 15 countries with more than 300

collaborators.

http://www-panda.gsi.de


Strangeness nuclear physics, Strangeness nuclear physics, hypernuclei, kaonic nucleihypernuclei, kaonic nuclei

Exotic hadron search, Chiral Exotic hadron search, Chiral dynamics and meson properties dynamics and meson properties in nuclear mediumin nuclear medium

Structure function, hard Structure function, hard exclusive processes, spin exclusive processes, spin structure of the nucleon with structure of the nucleon with target polarizationtarget polarization

Hadron physics in neutrino Hadron physics in neutrino scatteringscattering

Physics

Nuclei with strangeness



….D. Richards, Extreme scale computing


ConclusionConclusion

Lattice QCD is entering an era where it can make significant contributions in nuclear and particle physics.

Exotic and Multiquark (>3) states :Exotic and Multiquark (>3) states : Exotic and Multiquark states may exist in nature and Exotic and Multiquark states may exist in nature and

lattice QCD can contribute significantly by predicting lattice QCD can contribute significantly by predicting masses and quantum numbers.masses and quantum numbers.

One need to be careful to distinguish a bound state One need to be careful to distinguish a bound state from a scattering statefrom a scattering state..

Various laboratories is (will be) searching for theseVarious laboratories is (will be) searching for these

states.states.

Documents

Nilmani Mathur Department of Theoretical Physics, TIFR, INDIA Hadron spectrum : Excited States, Multiquarks and Exotics Hadron spectrum : Excited States,