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A lattice study of light scalar tetraquarks with I=0, 1/2, 1

A lattice study of light scalar tetraquarks with I=0, 1/2, 1. Lattice 08, Williamsburg Sasa Prelovsek University of Ljubljana sasa.prelovsek@ijs.si Lattice data from collaboration with Bern-Graz-Regensburg Coll. (BGR) (Daniel Mohler, Christian Lang, Christof Gattringer). Outline.

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A lattice study of light scalar tetraquarks with I=0, 1/2, 1

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  1. A lattice study of light scalar tetraquarks with I=0, 1/2, 1 Lattice 08, Williamsburg Sasa Prelovsek University of Ljubljana sasa.prelovsek@ijs.si Lattice data from collaboration with Bern-Graz-Regensburg Coll. (BGR) (Daniel Mohler, Christian Lang, Christof Gattringer) Lattice 05

  2. Outline • motivation • challenges • present simulation and its results • previous lattice simulations Lattice 05

  3. ? Puzzle of light scalar mesons: I=1/2 I=1 I=1 I=0 I=1/2 0++ nonet with inverted spectrum Interpolators used: diquark anti-diquark [Jaffe, Maiani, t’Hooft, .....] Lattice 05

  4. I flavor of source/sink scattering states 0 udud p p 1/2 udds K p 1 usds K K, p h Challenge of the simulation: to distinguish one-particle (tetraquark) state and scattering states in C(t) Lattice 05

  5. How to distinguish tetraquark from scattering? • we distinguish one-particle and scattering states by considering: • En • volume dependence of wn • properties of scattering: k Mathur et al. Kentucky (2006) • property of (one-particle) tetraquark: Lattice 05

  6. Lattice simulations of tetraquarks Previous studies (briefly reviewed at the end): [BGR Coll, PRD 73 (2006)] • only I=0 channel (Jaffe studied also I=2) • all consider a single correlator Present study: • a whole flavour pattern: I=0, 1/2, 1 • 3x3 correlation matrix evaluated: 3 different smearings at source and the sink: spatially symmetric Jacobi smearing on quarks: narrow (n) & wide (w) anti-diquark diquark variational method Lattice 05

  7. Simulation • Chirally Improved Fermins [BGR Coll.] a=0.148 fm, V=163x32, 123x24 mswith physical mass; mu,d correspond to mpi= 340-570 MeV • As in all previous studies we: • use quenched approximation: • discard single and double annihilation contractions There is a good excuse to use these two approximations as we are interested in state with 4 valence quarks: these two approximations discard Lattice 05

  8. E0 close to shifted 2mp • E1,2>2 GeV: to heavy correspond to s(600), f0(980) • meff of ground state not flat • p(1)p(-1) does not have its own eigenvalue • tower of p(k)p(-k) present in the ground state eigenvalue Results for I=0 Lattice 05

  9. Results for I=0: ground state if all tree sources behave close to point-like: then three eigenvalues of 3x3 matrix are: the whole tower of scattering states comes in a single eigenvalue! Lattice 05

  10. k parameters of fit: mpi, w Results for I=0: ground state we can not exclude weakly coupling lighter state at large t Lattice 05

  11. Results for I=1/2 similar conclusions as in I=0 channel parameters of fit: mpi, w Lattice 05

  12. Results for I=1 analysis of ground state is more complicated: two towers of scattering states KK, pi etass: conventional fit of mass at large t Lattice 05

  13. ? Summary of our results for I=0,1/2,1 Lattice 05

  14. Summary of our results for I=0,1/2,1 • excited states: to heavy to correspond to light tetraquark candidates: I was not looking for interpretation of these states (they may be also some excited scattering states) • ground state: effective mass and volume dependence of spectral weights roughly consistent with tower of scattering states we find no evidence for light tetraquark at mpi=340-570 MeV • slight fall of meff at large times: we can not completely exclude possibility of very light weakly coupling tetraquark; requires further study with larger time extent and larger operator basis • there may still exist possibility for tetraquarks at mpi<340 MeV (Kentucky group found I=0 tetraquark only for mpi<300 MeV) Lattice 05

  15. Previous tetraquark simulations • all quenched, all discard annihilation contr. • study only I=0 channel (Jaffe studies also exotic I=2 channel) • all consider single correlator I=0 • Alford & Jaffe, 2000 • pp interpolator • one relatively heavy quark mass • different L • only ground state explored • conclusion: shift does not completely agree with FULL (!) scattering prediction: possible indication of tetraquark Lattice 05

  16. Previous tetraquark simulations: • Suganuma, Tsumura, Ishii, Okiharu , 2007 0707.3309 [hep-lat] • diquark antidiquark interpolator • conventional and hybrid boundary conditions • only ground state studied • conclusion: ground state corresponds to scattering Lattice 05

  17. Previous tetraquark simulations: • N. Mathur, K.F. Liu et al. (Kentucky, XQCD Collaboration) [hep-ph/0607110, PRD, 2006] • pp interpolator • range of very small quark masses (overlap fermions) • two volumes • three lowest states explored: sequential Bayes method • conclusion: indication for tetraquark around sigma mass for mpi<300 MeV Lattice 05

  18. Concusion and outlook • I did not find indication for tetraquarks in I=0, ½, 1 channels at mpi>300 MeV. • There are still hope to find tetraquark on the lattice !! • Prompts for tetraquark search with dynamical simulation, light quark masses, preferably on various volumes and using variational method !! • the Kentucky group fond indication that s(600) is tetraqurk at mpi<300 MeV • our ground state in I=1 channel seems to be slightly below the scattering state (at lightest quark mass) Lattice 05

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