Chiral Condensates of the LR-Correlator and Large-NC QCD Samuel FRIOT

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Presentation transcript:

Chiral Condensates of 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

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

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

MHA + V’    with  with 

MHA    with  with 

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

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

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

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 -12 +7-11  =5.3 =10.5 Narison 0.17  0.05 1.4  0.3

A Preliminary Analysis-1 Ioffe et al.

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]

CP-PACS -Collaboration M7 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