New picture on the mesons mass relations

TL;DR

The paper challenges the traditional GMO/ideal‑mixing description of the pseudoscalar nonet by arguing that η and η′ masses and mixing cannot be captured within that framework. It proposes a second‑order phase transition in a chiral SU(3)×SU(3) setting, leading to a new mass‑mixing matrix that yields simple, testable relations m_{η′}^2 = 4 m_K^2 − 3 m_π^2 and m_η^2 = m_K^2 + 3 m_π^2, along with an η–η′ mixing angle near −19.5°. Building a Euclidean SL(3,C)–invariant field theory for a nonet of scalars and fermions, the authors derive one‑loop corrections and map the scalar sector onto the pseudoscalar nonet, successfully reproducing the observed η–η′ mass matrix M_Δ^2 and quark contents. The work suggests a deep link between spontaneous symmetry breaking dynamics and meson spectroscopy, offering an alternative to instanton‑based explanations and pointing toward broader implications for confinement and flavor structure in QCD.

Abstract

This work is divided in two parts. In the first three sections we review the meson physics phenomenology, highlighting the history of the pseudoscalar multiplet mass spectra research. Then we propose a new approach for the mass mixing problem exclusively based on a second order phase transition principle. This development leads to new relations among the masses of the mesons in this nonet, which present a nice agreement with measurements. Also the quark constitutions and the mixing angle problem are correctly addressed. Then, after describing the spontaneous symmetry breaking process coming from this phenomenological analysis, we establish a field theory with the necessary elements that could reproduce theoretically such results. This is done in the second part of this work. In the end, our quantum analysis of this field theory shows a compatibility with the phenomenology, which allows for further exploration along this path.