A Rational Approach to Resonance Saturation in large-Nc QCD

Abstract

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.

23 pages, 2 figures

References in corpus (9)

• Towards a consistent estimate of the chiral low-energy constants
• Emerging Holography
• Large-Nc QCD and Pade Approximant Theory
• Towards understanding Regge trajectories in holographic QCD
• On the relation between low-energy constants and resonance saturation
• Vanishing chiral couplings in the large-N_C resonance theory
• The $B_K$ Kaon Parameter in the Chiral Limit
• QCD condensates of dimension D=6 and D=8 from hadronic tau-decays
• K_l3 form factor with N_f=2+1 dynamical domain wall fermions: A progress report

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