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Searching for light scalar tetraquarks on the lattice

Searching for light scalar tetraquarks on the lattice. Bled, september 2008 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. motivation

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Searching for light scalar tetraquarks on the lattice

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  1. Searching for light scalar tetraquarks on the lattice Bled, september 2008 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) Bled 2008

  2. Outline • motivation • challenges • present simulation and its results • previous lattice simulations Bled 2008

  3. Puzzle of light scalar mesons: Model independent determination of poles from exp: sigma: Leutwyler & Caprini 2006 kappa: Descotes-Genon & Moussallam2006 Bled 2008

  4. Tetraquark with diquark anti-diquark structure Jaffe 1977 Jaffe & Wilczek PRL 2003 Jaffe, “Exotica”, 2004 The most titly bound diquark is SCALAR (“GOOD”) diquark SCALAR (“GOOD”) anti-diquark : nonet of SCALAR and color singlet states: Bled 2008

  5. Arguments in favor of tetraquark interpretation • L=1 quark-antiquark mesons expected to be above 1GeV: scalar mesons, axial mesons, tensor mesons • observed m(I=1)>m(I=1/2) for states below and above 1 GeV not possible to explain with pure quark-antiquark states. This ordering is natural in tetraquark picture. - states below 1 GeV could be “pure” tetraquarks - states above 1 GeV could be lin. combinations of (mixing via t’Hooft vertex): t’Hooft, Maiani, Polosa, Isidori, Riquer 2008 • a0(980) strongly couples to KK: Bled 2008

  6. Related observations in favor of tetraquarks:observed X,Y,Z states with charm quarks Experiment: Belle, BaBar, BES, Cleo .... Possible interpreations: tetraquarks [Maiani, Polosa, ...] Bled 2008

  7. Present simulation: searching tetraquarks below 1GeV (s,k,a0,f0) Calculation of the correlator on the lattice: a=0.15 fm, V=163 32 , 123 24 - discard disconnected diagrams - quenched approximation(we needed two different volumes and different shapes of interpolators) above two approximations (used in all previous tetraquark simulations) allow definite quark assignment, no mixing Bled 2008

  8. Present simulation: - Chirally Improved quarks (BGR Coll.) : ms: physical value mu,d : mp= 340, 470, 570 MeV - we study I=0,1/2,1; all previous simulations only I=0 Bled 2008

  9. Challenge is analysis of correlator: 0 t I flavor of source/sink scattering states 0 [ud][ud] sigma p p 1/2 [ud][ds] kappa K p 1 [us][ds] a0 K K, p h to distinguish one-particle (tetraquark) state and scattering states in C(t) Bled 2008

  10. How to distinguish tetraquark from scattering? • we distinguish one-particle and scattering states by considering: • En • volume dependence of wn • properties of scattering: • property of (one-particle) tetraquark: Bled 2008

  11. How to extract several states ? • Ground state: straight forward! • Excited states: challenge! - fitting two exponentials is VERY unstable; fitting more is impossible - All previous tetraquark simulations calculated only a single correlator Bled 2008

  12. Extracting several states: variational method In each flavour channel 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) Bled 2008

  13. Results for I=0 Bled 2008

  14. 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! Bled 2008

  15. I=0 ground state as tower of pp Bled 2008

  16. Results for I=0: ground state k Bled 2008

  17. Results for I=1/2 similar conclusions as in I=0 channel Bled 2008

  18. 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 Bled 2008

  19. Summary of our results for I=0,1/2,1 Bled 2008

  20. 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 Bled 2008

  21. Still hopes for finding tetraquarks! There may still exist possibility for finding tetraquarks on lattice: • at mpi<340 MeV Kentucky group found I=0 tetraquark only for mpi<300 MeV • with larger/different operator basis My current simulations: - mpi=180-400 MeV, overlap fermions, quenched, I=1/2,1, variational method, with Kentucky group - mpi~300 MeV, domain wall fermions, dynamical u,d,s quarks variational method, using RBC/UKQCD propagators Bled 2008

  22. Intermezzo: puzzling meff Effect of finite T on PP state: Bled 2008

  23. 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 Bled 2008

  24. 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 Bled 2008

  25. 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 Bled 2008

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