Relations between vacuum condensates and low energy parameters from a rational approach

TL;DR

This paper introduces a rational approximant method to relate vacuum condensates and low energy parameters in QCD without relying on hadronic inputs, providing analytical relations for phenomenological applications.

Contribution

The paper presents a novel rational approximant approach that maximizes matching to QCD, avoiding hadronic inputs and yielding simple analytical relations between high and low energy parameters.

Findings

Derived relations for vacuum condensates in rac{LR} and rac{VT} correlators.

Provided estimates for d=6 and d=8 condensates.

Analyzed the quark condensate magnetic susceptibility hi_0.

Abstract

Conventional methods to determine non-perturbative parameters in QCD, such as the different variants of QCD sum rules or the minimal hadronic approximation, combine a certain degree of matching to QCD with inputs from hadronic parameters. The latter introduce systematic errors difficult to quantify. In this paper I will apply a method based on rational approximant theory where matching is maximized and no hadronic inputs are used, thereby leading to simple analytical relations between high and low energy parameters. I will be mostly interested in the phenomenological applications to the \Pi_{LR} and \Pi_{VT} correlators, with especial emphasis on quantities like the d=6 and d=8 vacuum condensates in \Pi_{LR} or the quark condensate magnetic susceptibility \chi_0.