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  1. Simulations of light scalar mesons on the lattice and related difficulties Scadron 70, IST Lisbon, Portugal (February 2008) Sasa Prelovsek( University of Ljubljana and Jozef Stefan Institute some of the results presented obtained in my collaboration with RBC, MILC and BGR lattice collaborations (C. Dawson, K. Orginos, T. Izubuchi, A. Soni, C. Bernard, C. Detar, Z. Fu, C. Lang, C. Gattringer, L. Glozman, D. Mohler, ..) Scadron70, February 2008

  2. f0(1710) f0(1500) a0(1450) K0*(1430) f0(1370) a2(1320) a1(1230) a0(980) f0(980) M (MeV) ρ(770) K0*(800) σ(600) π(137) JPG(I)) 1+ ¯(1) 0¯ ¯(1) 2+ ¯(1) 0+¯(1) 0++(0) 0+(1/2) 1¯+(1) Scadron70, February 2008

  3. Determination of sigma pole from experiment using Roy equations and theoretical input on pi-pi scattering Scadron70, February 2008

  4. Outline Extracting scalar meson masses from lattice simulations: a0:dynamical quenched formulations with various unphysical approx. - tetraquark interpolators One of the main difficulties to determine scalar masses: bound states are accompanied by scattering states in lattice correlators Scadron70, February 2008

  5. a0 JP=0+ I=1 t=0 t C(t)= JP=0+ I=1 point-point correlator ma0 from scalar correlator Scadron70, February 2008

  6. dominates if ma0from scalar correlator JP=0+ ,I=1 : Scadron70, February 2008

  7. extracting hadron masses from lattice correlator Scadron70, February 2008

  8. Resolving this puzzle: S.P. [PRD 73, 2006]: Prediction for withStaggered ChPT Taste breaking effects of staggered fermions allow at finite lattice spacing ? Lattice simulations of a0 with u,d,s dynamical quarks • dynamical staggered u,d,s quarks [MILC] u,d,s close to physical masses MILC 2001 [PRD64] similar observation UKCD Irving et al. [Pos LAT05:027] Scadron70, February 2008

  9. Simulation of a0 and f0 correlators with dynamical staggered u,d,s quarksC. Bernard, C. Detar, S.P., Z. Fu[PRD76] point-point scalar correlators Staggered ChPT Staggered ChPT describes I=0,1 point-point scalar correlators well (with no free parameters) Extracted uncertain due to large unphysical scattering contribution Scadron70, February 2008

  10. a0 with u,d dynamical quarks t=0 t I=1 3 flavor QCD: p h, KK, p h’ 2 flavor QCD ( p,h’ ):p h’ 2 flavor QCD with m0=inf. : none Scadron70, February 2008

  11. a0 with dynamical u,d : a0(980) or a0(1450) ? Scadron70, February 2008

  12. u d quenched a0: a0(980) or a0(1450) ? Quenched ChPT prediction Bardeen et al. [2001] scattering states: S.P. et al [RBC] 2003 Scadron70, February 2008

  13. scalar mesons: Important scattering state in all lattice formulations (even quenched) Scattering state subtracted (to my knowledge) only in quenched simulation of K.F.Liu, N.Mathur et al. [hep-ph/0607110], PRD: m=1.41 +/- 0.12 GeV s Scadron70, February 2008

  14. scattering states vs. bound states • Quenched: no sea quarks, Bardeen et al [2001] • Staggered: staggered sea and valence quarks, S.P. [2006], PRD • Partially quenched: S.P. et al. [2004], PRD • Mixed:staggered sea and chiral valence qcuarks; S.P. et al. [2006], PRD • Twisted mass:Abdel-Rehim et al., ETM coll. • prediction for scattering state to point-point a0 correlator fromcorresponding ChPT: • volume dependence: scattering state: resonant state: small volume dependence • various boundary conditions on quark fields • variational method with a number of interpolators Scadron70, February 2008

  15. I=0 scalar mesons • disconnected quark contributions • mixing with glueballs • sizable dependence on lattice spacing Scadron70, February 2008

  16. Tetraquark simulations of light scalars:all quenched • K.-F.Liu, N. Mathur et al. (Kentucky), hep-ph/0607110, PRD, 2006 - -small u,d quark masses (good chiral properties) - quenched -volume dependence of spectral weight to distinguish between resonance (W~L0) and pp scattering (W~1/L3): Scadron70, February 2008

  17. Two Pion Energy Shift Scadron70, February 2008

  18. Tetraquark simulations of light scalars • Alford & Jaffe, 2000 relation for scattering at finite volume (Luscher 1986) - exotic channel, I=2 of SU(2)flavor - interpreted as repulsive pp scattering - non-exotic channel, I=0 of SU(2) - interpreted as repulsive pp scattering + possible tetraquark resonance Scadron70, February 2008

  19. Tetraquark simulations of light scalars • Suganuma et al. , 2007 - quenched - hybrid boundary coditions - result: The lowest state found is pp scattering, No indication of tetraquark found for Scadron70, February 2008

  20. Recent reviews: Craig McNeile: Lattice approach to light scalars, 0710.2470 [hep-lat] Hard Hadron spectroscopy, Lattice 2007, 0710.0985 [hep-lat] Summary • determining scalar meson spectra on the lattice is not a simple problem final concusions not ready yet • effect of the scattering states has to be disentangeled ! • “vague” conclusions for the time beeing: - a0: simulations with dynamical u,d seem to indicate that the lightest state that couples to is perhaps closer to a0(980) than to a0(1450) -kappa: dynamical simulation which dissentangles pK stattering state missing - sigma: two indications for light sigma, which take into account pp scattering: * K.F. Liu et al., tetraquark, quenched: msigma~600 MeV * SCALAR Coll, , dynamical: msigma~mrho Scadron70, February 2008