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Pattern of Light Scalar Mesons a 0 (1450) and K 0 *(1430) on the Lattice Tetraquark Mesonium – Sigma (600) on the Lattice Pattern of Scalar Mesons and Glueball χ QCD Collaboration : A. Alexandru, Y. Chen, S.J. Dong, T. Draper, I. Horvath, B. Joo,

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Presentation Transcript
slide1

Pattern of Light Scalar Mesons

  • a0 (1450) and K0*(1430) on the Lattice
  • Tetraquark Mesonium – Sigma (600) on the Lattice
  • Pattern of Scalar Mesons and Glueball

χQCDCollaboration:

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

Chiral07, Osaka, Nov. 15, 2007

tetraquark mesoniums

q1

q2

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?

slide3

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)

why a 0 980 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.
  • γ γ width of a0(980) and f0(980) are much smaller than expected of states.
  • Large indicates

in f0(980), but cannot be in I=1 a0(980). How to explain the mass degeneracy then?

is a 0 1450 the state
Isa0(1450) the state?
  • Why is it higher than a1 (1230) and a2(1320)?
  • Why is it almost degenerate with K0*(1430)?
  • Why is it higher than a0(980) ?
slide6

f0(1710)?

f0(1370)

σ(600)

f0(980)

f0(1500)

Julian Alps, Slovenia 2007

masses of n and in quenched lattice calculation
Masses of N, ρ, and π inQuenched Lattice Calculation
  • 163 x 28 quenched lattice, Iwasaki action with a = 0.200(3) fm
  • Overlap fermion
  • Critical slowing down is gentle
  • Smallest mπ~ 180 MeV
  • mπL > 3
is a 0 1450 0 a two quark state
Is a0 (1450) (0++) a two quark state?

Correlation

function

for

Scalar

channel

Ground state : πηghost state.

First excited state : a0

slide10

ms

Our results shows scalar mass around 1400-1500 MeV, suggesting

a0(1450)is a two quark state.

what is the nature of 600

Two-pion exchange potential:

Chembto, Durso, Riska; Stony Brook, Paris, …

σ (500): Johnson and Teller

σ enhancement of Δ I = ½ rule

What is the nature of σ (600)?
slide12

Without a σ pole

σ

With a σ pole

The σ in D+→π¯π+π+

Mσ= 478 ± 2423± 17MeV Γσ= 324 ± 4240 ± 21 MeV

E.M. Aitala et. al. Phys. Rev. Lett. 86, 770, (2001)

slide13

J/ψ—> ωπ+π-

M. Ablikim et al. (BES), Phys. Lett. B598, 149 (2004)

Mσ= 541 ± 39 MeV, Γσ= 504 ± 84 MeV

slide14

ZQZXZW

ZQZXZW

CCL

Caprini, Colangelo, & Leutwyler

Zhou, Qin, Zhang, Xiao, Zheng & Wu

M. Pennington

Charm 2006

 : I = 0, J = 0

0.4

complex s-plane

0.2

CERN-Munich

2

0

Im s (GeV )

E791

-0.2

BES

-0.4

0

0.2

0.4

0.6

0.8

1.0

-0.2

2

Re s (GeV )

slide16

|T|2 in continuum

W on lattice

E

E

?

L

L

E

E

slide19

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.

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 dependence22
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

W0

W1

Volume independence suggests the observed state is an one particle state

slide24

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)

Kπ Mesonium

ππMesonium

π(137)

JPG(I))

1+ ¯(1)

0¯ ¯(1)

2+ ¯(1)

0+¯(1)

0++(0)

0+(1/2)

1¯+(1)

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)

slide27

SU(3) Breaking and f0(1370), f0(1500), f0 (1710) mixing

H.Y. Cheng, C.K. Chua, and K.F. Liu, PR D74, 094005 (2006) hep-ph/0607206

  • 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

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 !

SU(3) breaking effect is weak and can be treated perturbatively

slide28

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

slide29

: 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

  • 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))
summary
Summary
  • Plenty of tetraquark mesonium candidates
  • σ(600) is very likely to be a tetraquark mesonium.
  • f0(1710) could be a fairly pure glueball.
  • Pattern of light scalar mesons may be repeated in the heavy-light sectors (?)