1. Sasa PrelovsekLattice 091 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, D. Mohler, M. Limmer and T. Draper

2. Subject of study Sasa PrelovsekLattice 092 Some of observed resonances hidden charm states X,Y,Z scalars s (600 ), k (800 ), a 0 (980 ), f 0 (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. examples

3. Compute correlation function in lattice QCD using interpolators with desired J PC and flavor Which physical states n contribute? Two-particle scattering states have discrete spectrum Correlator and physical states n Sasa PrelovsekLattice 093

4. Task: is there any state in addition to tower of scattering states? Sasa PrelovsekLattice 094 One-particle (tetraquark) state vs.Two-particle (scattering) state illustration Resonances have been sucessfully extracted in simulations of toy models: Sasaki&Yamazaki (2006) Lang & Gattringer (1993) Essential to look for few excited states in addition to the ground state !

5. Easy to extract ground state E 1 : 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 E n are unstable Generalized eigenvalue problem allows determination of Finding physical states n: Sasa PrelovsekLattice 095 [Luscher, Wolf] [Blossier, Sommer, Mendes…]

6. Sasa PrelovsekLattice 096 tetraquark scattering st. interpolators attractive I=0 s = udud ? p p 5: repulsive I=2 no resonance expected pp 3: Recent simulation: is s(600) tetraquark ? 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 To extract states with four valence quarks: we omit disconn.contractions in I=0,1/2 (as all previous lattice sim.) p(0)p(0) & s ? p(1)p(-1) Such s would have strong tetraquark component, but it can also have qq component. Needs confirmation from independent simulation ! p(1)p(-1) p(0)p(0)

7. Sasa PrelovsekLattice 097 tetraquark scattering st. interpolators attractive I=1/2 k = udud ? K p 5: repulsive I=3/2 no resonance expected Kp 3: Recent simulations: is k(800) tetraquark ? Recent simulations: is k(800) tetraquark ? [S.P., Liu, Lang, Mohler, Limmer, Draper, Mathur, arXiv: 0910.2749] Such k would have strong tetraquark component, but it can also have qq component. Needs confirmation! K(1)p(-1) K(0)p(0) & k ? K(1)p(-1) K(0)p(0)

8. Available lattice methods to distinguish: Available lattice methods to distinguish: - one-particle (tetraquark) states - two-particle (scattering) states A)L -dependence of A)L -dependence of Sasa PrelovsekLattice 098 [Niu, Liu, Shen, Gong, PRD80 (2009) Mathur et al., PRD76( 2007) S.P. & Mohler, PRD 79 (2009)] Trivial to derive for two non- interacting particles

9. Available lattice methods to distinguish (cont.): Available lattice methods to distinguish (cont.): - one-particle (tetraquark) states - two-particle (scattering) states B) Time -dependence of correlators at finite T Sasa PrelovsekLattice 099 [ S.P. & Mohler, PRD 79 (2009)] One- particle Two- particles

10. Available lattice methods to distinguish (cont.): Available lattice methods to distinguish (cont.): - one-particle (tetraquark) states - two-particle (scattering) states C)Energy shifts precise simulations can determine Sasa PrelovsekLattice 0910 [Sasaki, Yamazaki (2006) Liuming Liu, PoS(lat09) 099 ] a m u/d Bound state Scattering state (attractive)

11. Sasa PrelovsekLattice 0911  Kentucky coll, [Mathur et al, PRD76 (2007)] o quenched, overlap fermions o Single I=0 interpolator o three states with sequential Bayes method; needs confirmation using eigenvalue method Previous simulations: is s tetraquark? s ? p(0)p(0) p(1)p(-1)

12. Sasa PrelovsekScadron70, February 200812 Previous simulations: is s tetraquark? These simulations extract only the ground state  Suganuma et al. (2007) o quenched o extract ground state from one interpolator o conventional and non-conventional (hybrid) boundary conditions o ground state is scattering o no observation for tetraquark for  Alford & Jaffe (2000): slight indication for tetraquark  Loan et al. [Loan, Luo, Lam: 0809.5121, 0907.3609],

13. Hidden charm: XYZ All these simulations extract only the ground state Sasa PrelovsekLattice 0913  X(3872), Y(4260), …. [T.-W. Chiu & T.-H. Hsieh, 2005-2007 ] o quenched, overlap fermions, relativistic charm o 0.4 m s 430 M eV o a=0.09 fm, L=1.8 fm, 2.2 fm o Ground state from single correlators

14. Is X(3872) tetraquark/molecule ? Sasa PrelovsekLattice 0914 possible issue: scattering should be found at the same energies, before tetraquarks can be trusted  X(3872): J PC =1 ++ [Chiu & Hsieh, PLB646 (2006) 95, PRD73 (2006) 111503 ] Discovered by CDF in 2009

15. Is Y(4260) tetraquark/molecule ? Is Y(4260) tetraquark/molecule ? Sasa PrelovsekLattice 0915  J PC =1 -- states [Chiu & Hsieh, PRD73 (2006) 094510] possible issue: near by scattering states should be found, before tetraquarks can be trusted

16. Available lattice methods to distinguish (again): Available lattice methods to distinguish (again): - one-particle (tetraquark) states - two-particle (scattering) states C)Energy shifts Only precise simulations can determine them Sasa PrelovsekLattice 0916 [Luscher 1986, 1991, Sasaki, Yamazaki :PRD74, 114507] Liuming Liu, PoS(lat09) 099 ] a m u/d Bound state Scattering state (attractive)

17. Is X(3872) tetraquark/molecule ? Is X(3872) tetraquark/molecule ? Sasa PrelovsekLattice 0917  X(3872) [Liuming Liu, PoS(lat09)099 ] o dynamical, staggered sea o extract ground state from single correlator a m p Change of sign in a: possible indication for bound state related to X(3872) Many scattering lenghts determined by Liu (not with purpose of looking for tetraquarks) [see also Yokokawa et al, PRD74(2006)034504]

18. Is Z+(4430) tetraquark/molecule ? Is Z+(4430) tetraquark/molecule ? Sasa PrelovsekLattice 0918  Z+(4430) [Meng et al., PRD80 (2009) 034503] o J PC unknown o near to D* D 1 threshold: m(D*) + m(D1)= 4430 MeV o suspected to be D* D 1 molecule 1- 1+ o ground state energy determined from correlator o attractive interaction, but no change in sign of scattering lenght o authors suspect that interaction is no strong enough for bound state

19. Sasa PrelovsekLattice 0919 Conclusions o 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. o 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.