1. Chiral Condensates of the LR-Correlator and Large-NC QCD Samuel FRIOT
in collaboration with D. GREYNAT and E de RAFAEL

2. The LR-Correlator
with
OPE in the chiral limit

3. Large-NC QCD [E. de Rafael EURIDICE ’03]
Green’s functions are meromorphic functions of :
If the OPE in QCD gives
then
by Cauchy’s formula, we have
Here
Therefore

4. 1 vector V and 1 axial A 2 unknown parameters
 M H A
1 vector V and 1 axial A
with
 M H A + V’
2 vectors V, V’ 1 axial A and 1 zero 
2 unknown parameters

5. MHA + V’   
with 
with 

6. MHA   
with 
with 

7. Results of the fits Constraints Values of the parameters: z -2 -1
Values of the parameters:  z -2 -1
Values of the parameters:

8. Predictions Chiral Condensates: Matrix Elements: [Knecht et al. ’01] 

9. Results MHA MHA+V’ - 9.5  3 - 8.6  2.6 +16.2  5 +13.3  4 M7 M8 NDR
Regularization
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

10. M7 M8 - 9.5  3 Aleph -7.7  0.8 +11  1 Opal -6.0  0.6 Davier et al.
NDR HV
MHA+V’  =2.45
- 8.6  2.6
+13.3  4
0.12  0.04
0.62  0.19
2.12  0.64
2.15  0.64
MHA
- 9.5  3
+16.2  5
0.11  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  9.0
0.24  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
 =5.3
=10.5
Narison
0.17  0.05
1.4  0.3

11. A Preliminary Analysis-1
Ioffe et al.

12. A Preliminary Analysis -2
Compatibility Constraints from and
Davier et al.
YES NO
Ioffe et al.
Bijnens et al.
Cirigliano et al.
Rojo-Latorre M7 M8
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]

13. CP-PACS -CollaborationM7 M8
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  0.04
0.18  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 Results
0.35  0.07
1.4  0.4