Sigma meson contribution in the D I=1/2 rule

1. Takumi Doi (Univ. of Kentucky) Sigma meson contribution in the DI=1/2 rule In collaboration with T.Draper (Univ. of Kentucky) K.-F.Liu (Univ. of Kentucky) N.Mathur (JLAB) J.-B. Zhang (Zhejiang Univ.) Lattice 2007

2. Outline • The long-standing puzzle in the Scalar mesons • s(600), k (800), a0(980), a0(1450), etc. • The lattice QCD study for the scalar mesons • Study of the spectrum • Standard q-qbar meson or tetraquark ? • The volume dependence study to extract the nature of the signal •  s as a tetraquark mesonium • The role of s meson in K  2p decay Lattice 2007

3. 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)

4. Puzzle in scalar mesons • Too many states compared to the other channels • Strange meson is lighter than non-stranged mesons ?? • Some have very broad width, others have narrow width •  s(600), k(800), f0(980), a0(980) may be tetraquark states R.L.Jaffe (1977) Diquark model, molecular model etc. Lattice 2007

5. Two-pion exchange potential: Chembto, Durso, Riska; Stony Brook, Paris, … The controversial state: σ meson σ (500): Johnson and Teller N-N potential Lattice 2007

6. J/ψ—> ωπ+π- s M. Ablikim et al. (BES), Phys. Lett. B598, 149 (2004) Mσ= 541 ± 39 MeV, Γσ= 504 ± 84 MeV Lattice 2007

7. Simulation Parameters • Overlap fermion with quenched approx. • Iwasaki gauge action • a = 0.200(3)fm (a-1 = 1GeV) (beta=2.264) • V=163X28  L3 = (3.2fm)3 • mp >= 180 MeV, mp L > 3 • About 200-300 configurations Exact chiral symmetry ! N.Mathur et al.( cQCD collab.), hep-lat/0607110 Lattice 2007

8. Eliminate h’p ghost state for a0 study ms Our results shows scalar mass around 1400-1500 MeV, suggesting a0(1450) is a two quark state. N.Mathur et al.( cQCD collab.), hep-lat/0607110 Lattice 2007

9. ππfour quark operator (I=0) Disconnected diagrams are found to be small  neglected at this moment Lattice 2007

10. Scattering states Possible BOUND state σ(600)? Scattering states (Negative scattering length) Further study is needed to check the volume dependence of the observed states.

11. Volume dependence to distinguish one/two particle state • Spectral weight on the lattice • Normalization for the particle • If the signal is one particle state: • If the signal is two particle state: • Physical meaning: O(1/V) corresponds to the encounter possibility of two particles Lattice 2007

12. Volume dependence of spectral weights 3D-Volume 123 vs. 163 W0 W1 Volume independence suggests the observed state is an one particle state N.Mathur et al.( cQCD collab.), hep-lat/0607110 Lattice 2007

13. The role of Sigma meson in Physics • K2p decay • D I = 1/2 rule • Sigma can enhance the I=0 channel only Usual lattice formulation K p, K vac. + chPT No s consideration ! T.N.Pham, Phys.Rev.D33 (1986) 1499 (However, T.Yamazaki at lat06, direct K 2p for I=2) T.Morozumi, C.S.Lim, A.I.Sanda, PRL65 (1990) 404 Lattice 2007

14. Hw s, 2p K0 Strategy • 3pt correlator G(t) • Almost no energy-momentum mismatch • (m(K)=m(s)=500MeV) Coulomb wall t For the contribution to physical K2p, one needs additional s  2p, for which one may use experimental information Lattice 2007

15. Results • The correlator is found to be very noisy • Further work is necessary to extract the quantitative signal O2 O6 s ? s ? K K Hw Wall src Hw Wall src Lattice 2007

16. Summary/Outlook • We have investigated the scalar mesons with overlap fermion at the quenched level with mp > 180MeV • a0(1450) is two quark state • s(600) is likely to be a tetraquark state • 3D-Volume dependence study is essential • Dynamical quark effect, disconnected diagram study is desirable for future study • The existence of s meson may have substantial impact: • The enhancement of I=0 for K2p decay, which may solve the D I=1/2 rule • Need further calculation to extract the quantitative results Lattice 2007