Weinberg sum rules at NLO in 1/Nc

TL;DR

This paper investigates the impact of renormalization schemes on the Weinberg sum rules at next-to-leading order in 1/Nc within Resonance Chiral Theory, highlighting scheme-dependent uncertainties and constraints from short-distance behavior.

Contribution

It provides a detailed one-loop calculation of the SS-PP correlator and derives new constraints from short-distance conditions, clarifying scheme dependence in NLO corrections.

Findings

Short-distance constraints depend on the renormalization scheme.

Some logarithmic terms are absent at high energies, affecting constraints.

Scheme choice influences the size of uncertainties in the sum rules.

Abstract

We study the relevance of different renormalization schemes in Resonance Chiral Theory. The SS-PP correlator is explicitly computed at the one-loop level. Demanding the operator product expansion behaviour at short distances produces a new set of constraints, as some logarithmic terms are absent at high energies. Likewise, the loops induce subleading corrections in 1/Nc to the leading-order constraints, the Weinberg sum rules. We find that the short-distance conditions from a minimally subtracted scheme generate large uncertainties which, alternatively, can be largely simplified in other schemes.