Next-to-leading order perturbative contributions in the QCD sum rules for mesonic two-point correlation functions with unequal quark masses

TL;DR

This paper calculates next-to-leading order spectral densities for mesonic two-point correlation functions with unequal quark masses, using dimensional regularization and the optical theorem, providing analytical expressions useful for QCD sum rules and phenomenology.

Contribution

It introduces a detailed calculation of NLO contributions to spectral densities for mesonic correlators with unequal quark masses, expanding the tools available for QCD sum rule analyses.

Findings

Derived analytical expressions for spectral densities at NLO

Applicable to various mesonic channels and phenomenological analyses

Provides technical details for regularization and calculation methods

Abstract

In this article, we assume that the two quarks have unequal masses and calculate the next-to-leading order contributions to the spectral densities of the mesonic two-point correlation functions of the vector, axialvector, scalar and pseudoscalar currents. We take dimensional regularization to regularize both the ultraviolet and infrared divergences, and use optical theorem to obtain the spectral densities directly, furthermore, we present some necessary technical details for readers convenience. The analytical expressions are applicable in many phenomenological analysis besides the QCD sum rules.