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Nilmani Mathur Department of Theoretical Physics, TIFR, INDIA

Delve into non-quark model states, excited gluons, and multi-quark systems like tetraquarks and pentaquarks in theoretical physics. Gain insights into the exotic realm of hybrid mesons, hybrid baryons, and glueballs through lattice QCD calculations. Navigate the complexities of understanding and identifying these elusive states, including the challenges and implications they present.

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Nilmani Mathur Department of Theoretical Physics, TIFR, INDIA

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  1. Hadron spectrum : Excited States, Multiquarks and Exotics NilmaniMathur Department of Theoretical Physics, TIFR, INDIA

  2. Non-quark model states States with excited gluon Hybrid mesons ( meson + excited glue) Hybrid baryons ( baryon + excited glue) Glue balls (consitutent glue) Multi-quark states Tetraquark, Pentaquark and higher number of quark states So far there is no conclusive experimental evidence of such a state These states are not well understood 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

  3. Mesons, Hybrid Mesons and Glueballs

  4. 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 : Aufbau principleof 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

  5. Allowed : Forbidden(Exotics) : S = 0, 1 L = 0, 1, 2, 3…

  6. 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 :

  7. Paul Eugenio …Lattice 2006

  8. Paul Eugenio …Lattice 2006

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

  10. Decay states

  11. Decay states

  12. Octahedral group and lattice operators Construct operator which transform irreducibly under the symmetries of the lattice Baryon Meson …R.C. Johnson, Phys. Lett.B 113, 147(1982)

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

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

  15. Renaissance in Charmonium physics S. Olsen arXiv:0801.1153v1 (hep-ex)

  16. 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:0711.4556v2 Z+(4430) Belle, S-K. Choi et al, PRL 100, 142001 (2008) Recent Babar data do not support it However, more recent Belle analysis still claims it

  17. Dudek et. al

  18. Hadron spectrum Collaboration Dudek et. al.

  19. A more recent calculation Mπ= 700 MeV Nf = 3, as = 0.12 fm, at-1 = 5.6 GeV, L = 2 fm Dudek et al, Phys.Rev.Lett.103, 262001 (2009))

  20. 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. • 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.

  21. Glueball 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 large time separations. ٭Glueball operators have large vacuum fluctuations ٭Signal to noise ratio is very bad

  22. Glueball On Lattice, continuum rotational symmetry becomes discrete cubic symmetry with representationA1, A2 , E, T1 ,T2etc.of different quantum numbers. Typical gluon operators : Moringstar and Peardon …. hep-lat/9901004 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.

  23. Generalized Wilson loops Gluonic terms required for glueballs and hybrids can be extracted from generalized Wilson loops

  24. SU(3) Spectrum Exotic Glueball Oddballs! Y. Chen…N.Mathur.. et al. Phys. Rev. D73, 014516 (2006)

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

  26. f0(1710) f0(1500) a0(1450) K0*(1430) f0(1370) a2(1320) a1(1230) a0(980) f0(980) M (MeV) ρ(770) κ(800) σ(600) π(137) JPG(I) 1+ ¯(1) 0¯ ¯(1) 2+ ¯(1) 0+¯(1) 0++(0) 0+(1/2) 1¯+(1)

  27. 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. • Why a tetraquark state is relevant? • Old reason – There is a mess in light quark scalar sector. Difficult to explain observe spectrum by two quark states. • New reason – Some of the newly observed charmonia states may require explanation through tetraquark states.

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

  29. 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.

  30. σandκ • 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.

  31. ππfour quark operator (I=0)

  32. Two pion state

  33. Alford & Jaffe : Nucl.Phys.B578:367 (2000) mπ : 790 and 840 MeV Presence of a bound state is suggestive, but not conclusive

  34. Mathur,…. Liu et. al.. Phys.Rev.D76, 114505 (2007) d u Scattering states Possible BOUND state σ(600)? Scattering states (Negative scattering length) Evidence of a tetraquark state?

  35. Mathur,…. Liu et. al.. Phys.Rev.D76, 114505 (2007) Volume dependence of spectral weights W0 W1 Volume independence suggests the observed state is an one particle state

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

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

  38. Prelovsek,…NM,…et. al, arXiv : 1005.0948 Interpolating fields used :

  39. TetraquarkStates? Prelovsek,….NM … et. al arXiv : 1005.0948

  40. Tetraquark States? Prelovsek,….NM … et. al arXiv : 1005.0948

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

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

  43. f0(1710) f0(1500) a0(1450) N. Mathur et. al.. Phys.Rev.D76, 114505 (2007) K0*(1430) f0(1370) a2(1320) a1(1230) a0(980) f0(980) M (MeV) κ(800) ρ(770) σ(600) Kπ Mesonium? ππMesonium d u π(137) JPG(I)) 1+ ¯(1) 0¯ ¯(1) 2+ ¯(1) 0+¯(1) 0++(0) 0+(1/2) 1¯+(1)

  44. TWQCD :Chiu & Hsieh, PLB646 (2006) 95, PRD73 (2006) 111503 • 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

  45. TWQCD :Chiu & Hsieh, PRD73 (2006) 094510 • 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

  46. Liuming Liu : PoS(lat09)099 • Staggered sea • Only ground state Change of sign of scattering length indicates possible bound state?

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

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