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

Asian School 2011 Non-quark model states Non-quark model states  States with excited gluon Hybrid mesons ( meson + excited glue) Hybrid mesons ( meson + excited glue) Hybrid baryons ( baryon + excited glue) Hybrid baryons ( baryon + excited glue) Glue balls (consitutent glue) Glue balls (consitutent glue)  Multi-quark states Tetraquark, Pentaquark and higher number of quark states Tetraquark, Pentaquark and higher number of quark states  So far there is no conclusive experimental evidence of such a state of such a state  These states are not well understood Quark model fails to explain these states Quark model fails to explain these states  Lack of understanding makes experimental identification difficult.  Lattice QCD calculations can provide crucial information of such a state

Asian School 2011 Mesons, Hybrid Mesons and Glueballs Mesons, Hybrid Mesons and Glueballs

Asian School 2011 Exotic Hadrons Exotic Hadrons   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

Asian School 2011 S = 0, 1 L = 0, 1, 2, 3… Allowed : Forbidden (Exotics) :

Asian School 2011 Example of an Exotic Example of an Exotic  States with quantum number : 1 -+  It is not possible to write an interpolating field for this state with a form :  Possible operators :

Asian School 2011

Paul Eugenio …Lattice 2006

Asian School 2011 Paul Eugenio …Lattice 2006

Asian School 2011

Lattice results for 1 -+ Lattice results for 1 -+ Where is SIGNAL?

Asian School 2011 Decay states Decay states

Asian School 2011 Decay states Decay states

Asian School 2011 Octahedral group and lattice operators Octahedral group and lattice operators Λ J G 1 G 1 G 2 G 2 H 1/2 ⊕ 7/2 ⊕ 9/2 ⊕ 11/2 … 5/2 ⊕ 7/2 ⊕ 11/2 ⊕ 13/2 … 3/2 ⊕ 5/2 ⊕ 7/2 ⊕ 9/2 … Λ J A1 A1 A2 A2 E E T1 T1 T2 T2 A1 A1 A2 A2 E E T1 T1 T2 T2 E 0⊕4⊕6⊕8 …0⊕4⊕6⊕8 …3⊕6⊕7⊕9 …3⊕6⊕7⊕9 …2⊕4⊕5⊕6 …2⊕4⊕5⊕6 …1⊕3⊕4⊕5 …1⊕3⊕4⊕5 …2⊕3⊕4⊕5 …2⊕3⊕4⊕5 …0⊕4⊕6⊕8 …0⊕4⊕6⊕8 …3⊕6⊕7⊕9 …3⊕6⊕7⊕9 …2⊕4⊕5⊕6 …2⊕4⊕5⊕6 …1⊕3⊕4⊕5 …1⊕3⊕4⊕5 …2⊕3⊕4⊕5 …2⊕3⊕4⊕5 … Baryon Meson …R.C. Johnson, Phys. Lett.B 113, 147(1982) Construct operator which transform irreducibly under the symmetries of the lattice

Asian School 2011

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

Asian School 2011 Dudek, Edwards, Mathur, Richards : Phys. Rev. D77, (2008)

Asian School 2011 S. Olsen arXiv: v1 (hep-ex) Renaissance in Charmonium physics

Asian School 2011 Z + (4430 ) Z + (4430 ) Belle, Since charged, it cannot be either charmonium or hybrid So, tetraquark? Molecule? Small Charm state inside a large light quark hadron? Study in baryon is needed. …….M. Voloshyn, arXiv: v2 S-K. Choi et al, PRL 100, ( 2008) Recent Babar data do not support it However, more recent Belle analysis still claims it

Asian School 2011 Dudek et. al

Asian School 2011 Hadron spectrum Collaboration Dudek et. al.

Asian School 2011 Dudek et al, Phys.Rev.Lett.103, (2009)) M π = 700 MeV N f = 3, a s = 0.12 fm, a t -1 = 5.6 GeV, L = 2 fm A more recent calculation

Asian School 2011 Status of exotic and hybrids Status of exotic and hybrids There is suggestive, though not conclusive, evidence of the existence of exotics and hybrid both in light and charm quark sectors. There is suggestive, though not conclusive, evidence of the existence of exotics and hybrid both in light and charm quark sectors. Lattice calculations find evidence of existence of exotics and hybrid at non-realistic quark masses. More detail calculations with controlled systematic and proper understanding of decay channels are necessary. Lattice calculations find evidence of existence of exotics and hybrid at non-realistic quark masses. More detail calculations with controlled systematic and proper understanding of decay channels are necessary.

Asian School 2011 Glueball Glueball A glueball is a purely gluonic bound state. A glueball is a purely gluonic bound state. In the theory of QCD glueball self coupling admits the existence of such a state. Problems in glueball calculations : ٭ Glueballs are heavy – correlation functions die rapidly at ٭ Glueballs are heavy – correlation functions die rapidly at large time separations. large time separations. ٭ Glueball operators have large vacuum fluctuations ٭ Glueball operators have large vacuum fluctuations ٭ Signal to noise ratio is very bad ٭ Signal to noise ratio is very bad

Asian School 2011 Glueball Glueball On Lattice, continuum rotational symmetry becomes discrete cubic symmetry with representation A 1, A 2, E, T 1,T 2 etc. of different quantum numbers. 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/

Asian School 2011 Generalized Wilson loops Gluonic terms required for glueballs and hybrids can be extracted from generalized Wilson loops Gluonic terms required for glueballs and hybrids can be extracted from generalized Wilson loops

Asian School 2011 Y. Chen…N.Mathur.. et al. Phys. Rev. D73, (2006) Exotic Glueball Oddballs! SU(3) Spectrum

Asian School 2011 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) f 0 (980) f 0 (1370) f 0 (1500) a 0 (980) a 0 (1450) a 1 (1230) K 0 * (1430) J PG (I) M (MeV) a 2 (1320) 2 + ¯ (1) f 0 (1710) κ(800)

Asian School 2011 Tetraquark states Tetraquark states  What is a tetraquark state? Large 4 quark component in Fock space in the same way mesons have large 2 quark and baryons have large 3 quark components. Large 4 quark component in Fock space in the same way mesons have large 2 quark and baryons have large 3 quark components.  Why a tetraquark state is relevant? 1. Old reason – There is a mess in light quark scalar sector. Difficult to explain observe spectrum by two quark states. 2. New reason – Some of the newly observed charmonia states may require explanation through tetraquark states.

Asian School 2011 Two quarks VS Four quarks Two quarks VS Four quarks Alfred and Jaffe : Nucl.Phys.B578:367 (2000)

Asian School 2011 Tetraquark and Molecular States Tetraquark and Molecular States Vary r to see if there is any structure in B-S wave function which will have implication to decaying states.

Asian School 2011 σ and κ σ and κ  I. Caprini, G. Colangelo and H. Leutwyler, Phys. Rev. Lett. 96 (2006)  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) ; D. V. Bugg, arXiv: [hep-ph]; J.M. Link et al., FOCUS collaboration, arXiv: [hep-ex]; E.M. Aitala et al., E791 collaboration, Phys. Rev. D73 (2006) ; I. Caprini, Phys. Rev. D77 (2008)

Asian School 2011 ππ four quark operator (I=0) ππ four quark operator (I=0)

Asian School 2011 Two pion state

Asian School 2011 Alford & Jaffe : Nucl.Phys.B578:367 (2000) Alford & Jaffe : Nucl.Phys.B578:367 (2000) m π : 790 and 840 MeV Presence of a bound state is suggestive, but not conclusive

Asian School 2011 Evidence of a tetraquark state? Evidence of a tetraquark state? Scattering states Scattering states (Negative scattering length) length) Scattering states Scattering states Possible BOUND state σ(600)? σ(600)? d u Mathur,…. Liu et. al.. Phys.Rev.D76, (2007)

Asian School 2011 Volume dependence of spectral weights Volume dependence of spectral weights Volume independence suggests the observed state is an one particle state Volume independence suggests the observed state is an one particle state W0W0W0W0 W1W1W1W1 Mathur,…. Liu et. al.. Phys.Rev.D76, (2007)

Asian School 2011 Suganuma et.al : Prog. Theor. Phys. Suppl. 168, 168 (2007) Suganuma et.al : Prog. Theor. Phys. Suppl. 168, 168 (2007)  Quenched, anisotropic clover : a t = fm, L = 2.15fm, m s < m q < 2m s  Only ground state No indication of tetraquark in this mass range

Asian School 2011 M. Loan et. al : Eur.Phys.J.C57, 579 (2008) M. Loan et. al : Eur.Phys.J.C57, 579 (2008) Quenched, anisotropic clover fermions I = 0 I = 2 I = 1

Asian School 2011 Interpolating fields used : Interpolating fields used : Prelovsek,…NM,…et. al, arXiv :

Asian School 2011 Tetraquark States? Tetraquark States? Prelovsek,….NM … et. al arXiv :

Asian School 2011 Tetraquark States? Tetraquark States? Prelovsek,….NM … et. al arXiv :

Asian School 2011 Prelovsek,….NM … et. al arXiv :

Asian School 2011 Prelovsek,….NM … et. al arXiv :

0 ¯ ¯ (1) 1 ¯ + (1) 0 ++ (0)0 + ¯ (1) 1 + ¯ (1) π (137) 0 + (1/2) ρ (770) σ (600) f 0 (980) f 0 (1370) f 0 (1500) a 0 (980) a 0 (1450) a 1 (1230) K 0 * (1430) J PG (I)) M (MeV) a 2 (1320) 2 + ¯ (1) f 0 (1710) κ (800) K π Mesonium? ππ Mesonium u d N. Mathur et. al.. Phys.Rev.D76, (2007)

Asian School 2011 TWQCD : Chiu & Hsieh, PLB646 (2006) 95, PRD73 (2006) Need to calculate scattering states before conclusion  Quenched, overlap fermions for both light and charm  m π > 430 MeV, 0.4m s <m q <m c, a = 0.09 fm, L=1.8 fm, 2.2 fm  Extracted only ground state

Asian School 2011 TWQCD : Chiu & Hsieh, PRD73 (2006) TWQCD : Chiu & Hsieh, PRD73 (2006)  Quenched, overlap fermions for both light and charm  m π > 430 MeV, 0.4m s <m q <m c, a = 0.09 fm, L=1.8 fm, 2.2 fm  Extracted only ground state Need to calculate scattering states before conclusion

Asian School 2011 Liuming Liu : PoS(lat09)099  Staggered sea  Only ground state Change of sign of scattering length indicates possible bound state?

Asian School 2011 How to distinguish various states? How to distinguish various states? Local : Local : Tetraquark : Tetraquark : Molecular : Molecular : Hybrid : Hybrid : Glueball : Glueball : Solve generalized eigenvalue problem including all operators and find contribution from each state Solve generalized eigenvalue problem including all operators and find contribution from each state

Asian School 2011 G. Bali : arXiv:

Asian School 2011 Θ + on the Lattice Θ + on the Lattice NK u u d d u d u d Θ + bound state Θ + bound state m(Θ + ) ~ 1540 MeV Two-particle NK scattering state S-wave : m K + m N ~ 1432 MeV S-wave : m K + m N ~ 1432 MeV P-wave : P-wave : Quark content : Two possible states Two possible states

Asian School 2011 Θ + on the Lattice Θ + on the Lattice NK u u d d u d u d Most of the experiments do not see any evidence of a pentaquark state Almost all detail quenched lattice calculations do not see Θ + any evidence of Θ + pentaquark state

Asian School 2011 Story of Pentaquarks Story of Pentaquarks The 2006 Review 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 Review 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.

Asian School 2011 Future study on lattice Future study on lattice Future calculations with dynamical fermions and realistic quark masses. Future calculations with dynamical fermions and realistic quark masses. Calculations for spin-3/2 pentaquarks as claimed by a lattice study  Phys. ReV D72, (2005). Calculations for spin-3/2 pentaquarks as claimed by a lattice study  Phys. ReV D72, (2005). Study of charm pentaquarks as predicted by models. Study of charm pentaquarks as predicted by models.

Asian School 2011 B H = 16.6±2.1±4.6 MeV NPLQCD, arXiv: v1 H-dibaryon (uuddss) at m π ~ 390 MeV Charmonium-Nucleon bound state Taichi Kawana’s talk Attractive potential Also S. Aoki’s talk

Asian School 2011

PANDA Antiproton Annihilation at Darmstadt at the High Energy Storage Ring at GSI An Experiment at FAIR “Facility of Antiproton and Ion Research" PANDA Antiproton Annihilation at Darmstadt at the High Energy Storage Ring at GSI An Experiment at FAIR “Facility of Antiproton and Ion Research" Special detector, high luminosity (and phase space cooled antiproton beam. Special detector, high luminosity (L~ 2x10 32 cm -2 s -1 ) and phase space cooled antiproton beam. Energy resolution ~50 keV Physics : Physics :  Charonium spectroscopy  Excited Glue (Glueballs and Hybrids)  Charm in Nuclei  Charmonium Hypernuclei  D and D S -Physics  D and D S -Physics  Other Topics The Panda Experiment is collaboration of more then 45 institutes in 15 countries with more than 300 collaborators.

Asian School 2011 Strangeness nuclear physics, hypernuclei, kaonic nuclei Strangeness nuclear physics, hypernuclei, kaonic nuclei Exotic hadron search, Chiral dynamics and meson properties in nuclear medium Exotic hadron search, Chiral dynamics and meson properties in nuclear medium Structure function, hard exclusive processes, spin structure of the nucleon with target polarization Structure function, hard exclusive processes, spin structure of the nucleon with target polarization Hadron physics in neutrino scattering Hadron physics in neutrino scattering Physics Nuclei with strangeness

Asian School 2011

….D. Richards, Extreme scale computing

Asian School 2011 Conclusion Conclusion 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 states may exist in nature and lattice QCD can contribute significantly by predicting masses and quantum numbers.  One need to be careful to distinguish a bound state from a scattering state.  Various laboratories is (will be) searching for these states. states.