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Lattice QCD searches for tetraquarks / mesonic molecules (light scalar mesons & XYZ)

Lattice QCD searches for tetraquarks / mesonic molecules (light scalar mesons & XYZ). Excited QCD 2010, Slovakia Sasa Prelovsek University of Ljubljana and Jozef Stefan Institute, Slovenia [sasa.prelovsek@ijs.si] In collaboration with: C.B. Lang, Keh-Fei Liu, N. Mathur ,

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Lattice QCD searches for tetraquarks / mesonic molecules (light scalar mesons & XYZ)

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  1. Lattice QCD searches for tetraquarks / mesonic molecules (light scalar mesons & XYZ) Excited QCD 2010, Slovakia SasaPrelovsek University of Ljubljana and Jozef Stefan Institute, Slovenia [sasa.prelovsek@ijs.si] In collaboration with: C.B. Lang, Keh-Fei Liu, N. Mathur, D. Mohler, M. Limmer and T. Draper Lattice 09

  2. examples Subject of study • Some of observed resonances • hidden charm states X,Y,Z • scalars s(600), k(800), a0(980), f0(980) • are candidates for exotic states like • Presented lattice criteria do no distinguish between tetraquarks / molecules: • when saying “tetraquarks” I have in mind both types. Conveying present status of lattice QCD simulations concerning whether tetraquarks exist. Lattice 09

  3. Correlator and physical states n • Compute correlation function in lattice QCD using interpolators • with desired JPC and flavor • Which physical • states n contribute? • Two-particle scattering states • have discrete spectrum Lattice 09

  4. Task: is there any state in addition to tower of scattering states? One-particle (tetraquark) state vs. Two-particle (scattering) state illustration Essential to look for few excited states in addition to the ground state ! Resonances have been sucessfully extracted in simulations of toy models: Sasaki&Yamazaki (2006) Lang & Gattringer (1993) Lattice 09

  5. Finding physical states n: • Easy to extract ground state E1 : • many lattice simulation determine only ground state from a single correlator • Essential to extract few excited states in addition to ground state • Multi-exponential fits to extract several En are unstable • Generalized eigenvalue problem allows determination of [Luscher, Wolf] [Blossier, Sommer, Mendes…] Lattice 09

  6. Recent simulation: is s(600)tetraquark ?[S.P., K.F. Liu, Lang, Mohler, Limmer, Draper, Mathur, arXiv: 0910.2749]first dynamical simulation aimed at tetraquarks tetraquarkscattering st. interpolators attractive I=0 s =udud ? p p 5: repulsive I=2 no resonance expected pp 3: To extract states with four valence quarks: we omit disconn.contractions in I=0,1/2 (as all previous lattice sim.) p(1)p(-1) p(1)p(-1) Such s would have strong tetraquark component, but it can also have qq component. Needs confirmation from independent simulation ! p(0)p(0) p(0)p(0) & s ? Lattice 09

  7. Recent simulations: is k(800)tetraquark ?[S.P., Liu, Lang, Mohler, Limmer, Draper, Mathur, arXiv: 0910.2749] tetraquarkscattering st. interpolators attractive I=1/2 k =udud ? Kp 5: repulsive I=3/2 no resonance expectedKp 3: K(1)p(-1) K(1)p(-1) Such k would have strong tetraquark component, but it can also have qq component . Needs confirmation! K(0)p(0) & k ? K(0)p(0) Lattice 09

  8. [Niu, Liu, Shen, Gong, PRD80 (2009) Mathur et al., PRD76( 2007) S.P. & Mohler, PRD 79 (2009)] Available lattice methods to distinguish: - one-particle (tetraquark) states - two-particle (scattering) states Trivial to derive for two non-interacting particles L-dependence of <Oi |n> Lattice 09

  9. Available lattice methods to distinguish (cont.): - one-particle (tetraquark) states - two-particle (scattering) states [S.P. & Mohler, PRD 79 (2009)] One-particle Two-particles B) Time -dependence of correlators at finite T Lattice 09

  10. [Sasaki, Yamazaki (2006) Liuming Liu, PoS(lat09) 099] Available lattice methods to distinguish (cont.): - one-particle (tetraquark) states - two-particle (scattering) states a mu/d Energy shifts precise simulations can determine Bound state Scattering state (attractive) Lattice 09

  11. Previous simulations: is stetraquark? • Kentucky coll, [Mathur et al, PRD76 (2007)] • quenched , overlap fermions • Single I=0 interpolator • three states with sequential Bayes method; • needs confirmation using eigenvalue method p(1)p(-1) s ? p(0)p(0) Lattice 09

  12. Previous simulations: is stetraquark?These simulations extract only the ground state • Suganuma et al. (2007) • quenched • extract ground state from one interpolator • conventional and non-conventional (hybrid) boundary conditions • ground state is scattering • no observation for tetraquark for • Alford & Jaffe (2000): slight indication for tetraquark • Loan et al.[Loan, Luo, Lam: 0809.5121, 0907.3609] , Scadron70, February 2008

  13. Hidden charm: XYZAll these simulations extract only the ground state • X(3872), Y(4260), …. [T.-W. Chiu & T.-H. Hsieh, 2005-2007 ] • quenched , overlap fermions, relativistic charm • 0.4 ms < mq < mc, mp>430 MeV • a=0.09 fm, L=1.8 fm, 2.2 fm • Ground state from single correlators Lattice 09

  14. Is X(3872) tetraquark/molecule ? • X(3872): JPC=1++ • [Chiu & Hsieh, • PLB646 (2006) 95,PRD73 (2006) 111503] possible issue: scattering should be found at the same energies, before tetraquarks can be trusted Discovered by CDF in 2009 Lattice 09

  15. Is Y(4260) tetraquark/molecule ? • JPC=1-- states • [Chiu & Hsieh, PRD73 (2006) 094510] possible issue: near by scattering states should be found, before tetraquarks can be trusted Lattice 09

  16. [Luscher 1986, 1991, Sasaki, Yamazaki :PRD74, 114507] Liuming Liu, PoS(lat09) 099] Available lattice methods to distinguish (again): - one-particle (tetraquark) states - two-particle (scattering) states a mu/d Energy shifts Only precise simulations can determine them Bound state Scattering state (attractive) Lattice 09

  17. Is X(3872) tetraquark/molecule ? • X(3872) [Liuming Liu, PoS(lat09)099 ] • dynamical , staggered sea • extract ground state from single correlator Many scattering lenghts determined by Liu (not with purpose of looking for tetraquarks) [see also Yokokawa et al, PRD74(2006)034504] a mp Change of sign in a: possible indication for bound state related to X(3872) Lattice 09

  18. Is Z+(4430) tetraquark/molecule ? • Z+(4430) [Meng et al., PRD80 (2009) 034503] • JPC unknown • near to D* D1 threshold: m(D*) + m(D1)= 4430 MeV • suspected to be D* D1 molecule • 1- 1+ • ground state energy determined from correlator • attractive interaction , but no change in sign of scattering lenght • authors suspect that interaction is no strong enough for bound state Lattice 09

  19. Conclusions • Do light scalar mesons s and k have tetraquark component? • We find two light states in I=0 and I=1/2 channels. One is the scattering state, while the other state may be candidate for s or k with strong tetraquark component. Confirmation is needed before firm conclusion! • Ultimate study would need to take into account mixing • and the interpolators have to cover all these Fock components. Then one could determine the fraction of physical states in terms of various Fock components. • Are some of hidden charm states XYZ tetraquarks/molecules? • There is some indication for tetraquark/molecular structure of • X(3872), Y(4260), Y(4140) from the lattice, but much more work is needed. • Few excited states would have to be extracted in addition to the ground state to make • reliable identification for tetraquark/molecular states. Lattice 09

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