TY - JOUR

T1 - A rational approach to resonance saturation in large-Nc QCD

AU - Masjuan, Pere

AU - Peris, Santiago

PY - 2007/5/1

Y1 - 2007/5/1

N2 - We point out that resonance saturation in QCD can be understood in the large-Nc limit from the mathematical theory of Pade Approximants to meromorphic functions. These approximants are rational functions which encompass any saturation with a finite number of resonances as a particular example, explaining several results which have appeared in the literature. We review the main properties of Pade Approximants with the help of a toy model for the VV-AA two-point correlator, paying particular attention to the relationship among the Chiral Expansion, the Operator Product Expansion and the resonance spectrum. In passing, we also comment on an old proposal made by Migdal in 1977 which has recently attracted much attention in the context of AdS/QCD models. Finally, we apply the simplest Pade Approximant to the VV-AA correlator in the real case of QCD. The general conclusion is that a rational approximant may reliably describe a Green's function in the Euclidean, but the same is not true in the Minkowski regime due to the appearance of unphysical poles and/or residues. © SISSA 2007.

AB - We point out that resonance saturation in QCD can be understood in the large-Nc limit from the mathematical theory of Pade Approximants to meromorphic functions. These approximants are rational functions which encompass any saturation with a finite number of resonances as a particular example, explaining several results which have appeared in the literature. We review the main properties of Pade Approximants with the help of a toy model for the VV-AA two-point correlator, paying particular attention to the relationship among the Chiral Expansion, the Operator Product Expansion and the resonance spectrum. In passing, we also comment on an old proposal made by Migdal in 1977 which has recently attracted much attention in the context of AdS/QCD models. Finally, we apply the simplest Pade Approximant to the VV-AA correlator in the real case of QCD. The general conclusion is that a rational approximant may reliably describe a Green's function in the Euclidean, but the same is not true in the Minkowski regime due to the appearance of unphysical poles and/or residues. © SISSA 2007.

KW - 1/N expansion

KW - Chiral lagrangians

KW - QCD

U2 - 10.1088/1126-6708/2007/05/040

DO - 10.1088/1126-6708/2007/05/040

M3 - Article

SN - 1126-6708

VL - 2007

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 5

M1 - 040

ER -