Sigma meson in QCD sum rules using a two quark current with derivatives

TL;DR

This paper investigates the sigma meson using QCD sum rules with a derivative two-quark current, finding a mass around 550 MeV consistent with the sigma meson, contrasting with previous non-derivative current results.

Contribution

It introduces a derivative-based interpolating current in QCD sum rules to better match the sigma meson's properties, providing a novel approach to its mass estimation.

Findings

Derivative current yields a sigma mass around 550 MeV.

Non-derivative current estimates the mass around 1 GeV.

The derivative approach aligns better with experimental sigma properties.

Abstract

We study the $\sigma$ meson in QCD sum rules using a two quark interpolating field with derivatives. In the constituent quark model, the $\sigma$ meson is composed of a quark and an antiquark in the relative p-wave state and is thus expected to have a larger overlap with an interpolating field that measures the derivative of the relative quark wave-function. While the sum rule with a current without derivatives gives a pole mass of around 1 GeV, the present sum rule with a derivative current gives a mass of around 550 MeV and a width of 400 MeV, that could be identified with the $\sigma$ meson.