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) Sasa Prelovsek Lattice 05

Outline motivation challenges present simulation and its results previous lattice simulations Sasa Prelovsek Lattice 05

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, .....] Sasa Prelovsek Lattice 05

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

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: Sasa Prelovsek Lattice 05

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 Sasa Prelovsek Lattice 05

Simulation Chirally Improved Fermins [BGR Coll.] a=0.148 fm, V=163x32, 123x24 ms with 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 Sasa Prelovsek Lattice 05

Results for I=0 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 Sasa Prelovsek Lattice 05

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! Sasa Prelovsek Lattice 05

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

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

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 Sasa Prelovsek Lattice 05

Summary of our results for I=0,1/2,1 ? Sasa Prelovsek Lattice 05

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) Sasa Prelovsek Lattice 05

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 Sasa Prelovsek Lattice 05

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 Sasa Prelovsek Lattice 05

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 Sasa Prelovsek Lattice 05

Concusion and outlook the Kentucky group fond indication that 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) Sasa Prelovsek Lattice 05