Gell-Mann-Okubo Mass Formula Revisited

TL;DR

This paper revisits the Gell-Mann-Okubo mass formula by applying Regge phenomenology to derive a new mass-mixing relation for mesons, achieving high accuracy in predicting meson masses across different sectors.

Contribution

It introduces a novel mass-mixing formula derived from Regge phenomenology for SU(4) meson multiplets, improving mass predictions for vector, tensor, and pseudoscalar mesons.

Findings

The new formula accurately predicts vector and tensor meson masses within ~1%.

It derives a pseudoscalar meson mass relation with better than 1% accuracy.

The formula accounts for nonet mixing angles consistent with experimental data.

Abstract

We show that the application of Regge phenomenology to SU(4) meson multiplets leads to a new Gell-Mann-Okubo mass-mixing formula in the SU(3) sector, 3m_1^2 + (cos theta)^2 m_0^2 + (sin theta)^2 m_{0'}^2 + sqrt{2} sin(2theta) (m_0^2 - m_{0'}^2) = 4m_{1/2}^2, where m_1,m_{1/2},m_0,m_{0'} are the masses of the isovector, isodoublet, isoscalar mostly octet and isoscalar mostly singlet states, respectively, and theta is the nonet mixing angle. For an ideally mixed nonet, theta = arctan(1/sqrt{2}), this formula reduces to 2m_0^2 + 3m_1^2 = 4m_{1/2}^2 + m_{0'}^2 which holds with an accuracy of ~1% for vector and tensor mesons. For pseudoscalar mesons, with the eta-eta' mixing angle -arctan[1/(2sqrt{2})] ~ -19.5^o, in agreement with experiment, it leads to the relation 4m_K^2 = 3m_pi^2 + m_{eta'}^2 which holds to an accuracy of better than 1% for the measured pseudoscalar meson masses.