Classic Calculations of Static Properties of the Nucleons reexamined

TL;DR

This paper reexamines classic QCD sum rule calculations of nucleon properties, demonstrating that using a polynomial kernel improves stability and accuracy, aligning results with experimental data.

Contribution

It introduces a polynomial kernel approach to stabilize QCD sum rule calculations of nucleon properties, reducing arbitrariness and improving agreement with experiments.

Findings

Polynomial kernel stabilizes sum rule calculations.

Results align with experimental values.

Dependence on four-quark condensate value is confirmed.

Abstract

Classic calculations of the magnetic moments mu_p and mu_n of the nucleons using the traditional exponential kernel show instability with respect to variations of the Borel mass as well as arbitrariness with respect to the choice of the onset of perturbative QCD. The use of a polynomial kernel, the coefficients of which are determined by the masses of the nucleon resonances stabilizes the calculation and provides much better damping of the unknown contribution of the nucleon continuum. The method is also applied to the evaluation of the coupling gA of proton to the axial current and to the strong part of the neutron-proton mass difference Delta M_np. All these quantities depend sensitively on the value of the 4-quark condensate < 0 | qqqq | 0 > and the value < 0 | qqqq | 0 > ~ 1.5< 0 | qq | 0 >^2 reproduces the experimental results.