Chiral Condensatesof the LR-Correlator

and Large-NC QCD

Samuel FRIOT

in collaboration with D. GREYNAT and E de RAFAEL

The LR-Correlator

with

OPE in the chiral limit

Green’s functions are meromorphic functions of :

Large-NC QCD [E. de Rafael EURIDICE ’03]

then

by Cauchy’s formula, we have

Here

Therefore

If the OPE in QCD gives

M H A

M H A + V’

1 vector V and 1 axial A

with

2 vectors V, V’ 1 axial A and 1 zero

2 unknown parameters

MHA + V’

with

with

MHA

with

with

Results of the fitsConstraints

Values of the parameters:

z0-1-2

z0-1-2

Values of the parameters:

Predictions

Chiral Condensates:

Matrix Elements:

[Knecht et al. ’01]

MHA MHA+V’

- 9.5 3 - 8.6 2.6

+16.2 5 +13.3 4

Regularization NDR HV NDR HV

M7 0.11 0.03 0.67 0.2 0.12

0.04 0.62

0.19

M8 2.3 0.7 2.5 0.8 2.12 0.64 2.15

0.64

Results

M7 M8

NDR HV NDR HV

MHA+V’ =2.45- 8.6

2.6+13.3

40.12 0.04

0.62

0.19 2.12 0.64

2.15 0.64

MHA - 9.5 3+16.2

50.11 0.03

0.67 0.20 2.3 0.7 2.5 0.8

Aleph-7.7

0.8+11 1

Opal-6.0

0.6+7.5

1.3

Davier et al. -6.4

1.6+8.7

2.4

=3.3 =2.8

Ioffe et al.-6.8

2.1+7 4

=3.1 =3.4

Bijnens et al. -3.2

2.0-12.4

9.00.24 0.03

0.37 0.08

1.2 0.8 1.3 0.8

=6.6 =12.1

Cirigliano et al.

-4.45 0.7

-6.2 3.2

0.22 0.05

1.5 0.3

=4.7 =7.7

Rojo-Latorre-4 2 -12 +7

-11

=5.3 =10.5

Narison0.17 0.05

1.4 0.3

A Preliminary Analysis-1 Ioffe et

al.

A Preliminary Analysis -2

Davier et al. YES NO

Ioffe et al. YES YES

Bijnens et al. NO NOCirigliano et

al. NO NO

Rojo-Latorre NO NOM7 M8

NDR HV NDR HV

Bijnens et al.0.24 0.03 0.37 0.08 1.2 0.8 1.3 0.8

[0.94, 2.65] [1.06, 3.01] [0.48, 1.52] [0.52,1.64]

Cirigliano et al.

0.22 0.05 1.5 0.3

[1.70, 2.31] [0.95, 1.30]

Compatibility Constraints from and

M7 M8

NDR HV NDR HV

MHA+V’ =2.45 0.12 0.04 0.62 0.19 2.12 0.64 2.15 0.64

MHA 0.11 0.03 0.67 0.20 2.3 0.7 2.5 0.8

Bhattacharya et al. 0.32 0.06 1.2 0.2

Donini et al.0.11

0.040.18 0.06 0.51 0.1 0.62 0.12

RBC - Collaboration 0.27 0.03 1.1 0.2

CP-PACS -Collaboration 0.24 0.03 1.0 0.2

Garron et al.

Preliminary Results0.35 0.07 1.4 0.4