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