ykis06 K F Liu

Slide1: 

σ(600) and Pattern of Scalar Mesons from Lattice QCD a0 (1450) on the Lattice Tetraquark Mesonium – Sigma (600) on the Lattice Pattern of Scalar Mesons and Glueball χQCD Collaboration: A. Alexandru, Y. Chen, S.J. Dong, T. Draper, I. Horvath, B. Joo, F .X. Lee, K.F. Liu, N. Mathur, T. Streuer, S. Tamhankar, H.Thacker, J.B. Zhang YKIS06 Kyoto, Nov. 24, 2006

Slide2: 

QCD Vacuum

Slide3: 

Creation Operator QCD Vacuum

Slide4: 

Creation Operator QCD Vacuum ?? Pentaquark Tetraquark ??

Slide5: 

Le Taureau of Pablo Picasso (1945) Dynamical chiral fermion Quenched approximation with Chiral symmetry, and light quark masses 5th stage 11th stage

Masses of N, ρ, and π: 

Masses of N, ρ, and π 163 x 28 quenched lattice, Iwasaki action with a = 0.200(3) fm Overlap fermion Critical slowing down is gentle Smallest mπ ~ 180 MeV mπ L > 3

Quenched Artifacts: 

Quenched Artifacts Chiral log in mπ2 x

Evidence of η’N GHOST State in S11 (1535) Channel: 

Evidence of η’N GHOST State in S11 (1535) Channel - - - - η η W > 0 W<0

Tetraquark Mesoniums: 

Tetraquark Mesoniums QCD allows a state with more than three quarks Four quarks : Two quarks + two anti-quarks Like molecular state? Like di-quark anti-diquark state?

Slide10: 

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

Why a0(980) is not a state?: 

Why a0(980) is not a state? The corresponding K0 would be ~ 1100 MeV which is 300 MeV away from both and . Cannot explain why a0(980) and f0(980) are narrow while σ(600) and κ(800) are broad. Large indicates in f0(980), but cannot be in I=1 a0(980). How to explain the mass degeneracy then?

Is a0 (1450) (0++) a two quark state?: 

Is a0 (1450) (0++) a two quark state? Ground state : π η ghost state. First excited state : a0 Correlation function for Scalar channel

Slide13: 

Our results shows scalar mass around 1400-1500 MeV, suggesting a0(1450) is a two quark state. ms

What is the nature of σ (600)?: 

What is the nature of σ (600)?

Slide15: 

The σ in D+→ π¯π+π+ σ Without a σ pole With a σ pole Mσ= 478 ± 2423 ± 17MeV Γσ = 324 ± 4240 ± 21 MeV E.M. Aitala et. al. Phys. Rev. Lett. 86, 770, (2001)

Slide16: 

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

Slide17: 

Recent calculation of ππ scattering amplitude by solving the Roy equation [Caprini, Calangelo, and Leutwyler (hep-ph/0512364)] yields a pole at

Slide18: 

ππ four quark operator (I=0)

K. Rummukainen and S. Gottlieb, NP B450, 397 (1995): 

K. Rummukainen and S. Gottlieb, NP B450, 397 (1995)

Slide22: 

Lüscher formula

Scattering Length and energy shift: 

Scattering Length and energy shift Threshold energy shift on the finite lattice :

Slide24: 

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

Scattering state and its volume dependence : 

Scattering state and its volume dependence Normalization condition requires : Two point function : Lattice For one particle bound state spectral weight (W) will NOT be explicitly dependent on lattice volume

Scattering state and its volume dependence : 

Scattering state and its volume dependence Normalization condition requires : Two point function : Lattice For two particle scattering state spectral weight (W) WILL be explicitly dependent on lattice volume

Volume dependence of spectral weights: 

Volume dependence of spectral weights Volume independence suggests the observed state is an one particle state W0 W1

Slide28: 

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

Mixing of : 

Mixing of First order approximation: exact SU(3) x is annihilation diagram

Mixing of with Glueball: 

Mixing of with Glueball First order approximation: exact SU(3)

Slide31: 

SU(3) Breaking and f0(1370), f0(1500), f0 (1710) mixing For SU(3) octet f0(1500),  = -2  R1=0.21 vs. 0.2460.026 (expt) R2=0 vs. 0.1450.027 (expt) LQCD [Lee, Weingarten]  y= 4331 MeV, y/ys=1.1980.072 y and x are of the same order of magnitude ! Need SU(3) breaking in mass matrix to lift degeneracy of a0(1450) and f0(1500) Need SU(3) breaking in decay amplitudes to accommodate observed strong decays SU(3) breaking effect is weak and can be treated perturbatively H.Y. Cheng, C.K. Chua, and K.F. Liu, hep-ph/0607206

Slide32: 

Consider two different cases of chiral suppression in G→PP: (i) (ii) In absence of chiral suppression (i.e. g=gKK=g), the predicted f0(1710) width is too small (< 1 MeV)  importance of chiral suppression in GPP decay

Slide33: 

MS-MU  25 MeV is consistent with LQCD result  near degeneracy of a0(1450), K0*(1430), f0(1500) (J/f0(1710)) = 4.1 ( J/ f0(1710)) versus 6.62.7(expt) no large doubly OZI is needed (J/ f0(1710)) >> (J/f0(1500)) : primarily a glueball : tend to be an SU(3) octet : SU(3) singlet + glueball content ( 13%) MU=1474 MeV, MS=1498 MeV, MG=1666 MeV

Scalar Mesons and Glueball: 

Scalar Mesons and Glueball glueball

Summary: 

Summary Plenty of tetraquark mesonium candidates σ(600) is very likely to be a tetraquark mesonium. One needs to identify both the scattering and bound states and discern their nature, e.g. via volume study of the spectral weights. Pattern of light scalar mesons may be repeated in the heavy-light sectors (?)

Hadron Mass and Decay Constant: 

Hadron Mass and Decay Constant The two-point Green’s function decays exponentially at large separation of time Mass M= Ep(p=0), decay constant ~ Φ

Slide37: 

Constituent Quark Scaling Anisotropy in Au + Au at = 200 GeV (STAR) Meson n=2 and Baryon n=3 grouping Some deviation due to internal hadron structure

Slide38: 

Azimuthal anisotropy in Au + Au collisions with = 200 GeV (STAR collaboration)