Scalar and pseudoscalar correlators in Resonance Chiral Theory

TL;DR

This paper computes scalar and pseudoscalar correlators in Resonance Chiral Theory at next-to-leading order, deriving low-energy constants and analyzing spectral functions to connect high-energy behavior with low-energy phenomenology.

Contribution

It provides a detailed one-loop calculation of correlators in Resonance Chiral Theory, improving the description by adding complex operators and extracting low-energy constants.

Findings

Estimated L_8(mu) = (1.0+- 0.4) 10^{-3}

Predicted C_{38}(mu) = (8+- 5) 10^{-6}

Confirmed positivity of spectral functions for two-meson cuts

Abstract

The SU(3) octet SS-PP correlator and the difference of the singlet and octet scalar correlators are computed within Resonance Chiral Theory. The calculation is carried on up to the one-loop level, i.e., up to next-to-leading order in the 1/Nc expansion. Using the resonance expressions as interpolators between long and short distances, we demand the correlators to follow the high-energy power behavior prescribed by the operator product expansion and extract predictions for the low-energy constants. By adding more and more complicated operators to the hadronic action, our description is progressively improved, producing for the SS-PP correlator the chiral coupling estimates L_8(mu) = (1.0+- 0.4) 10^{-3} and C_{38}(mu) = (8+- 5) 10^{-6} for mu=770 MeV. Some first results for the S1 S1 - S8 S8 correlator are shown, like, for instance, the positivity of the spectral function for two-meson cuts, the high-energy constraints for each separate scalar form-factor and preliminary expressions for the L_6(mu) low-energy constant.