Anticrossing in the η-η′ complex

Abstract

The Dyson-Schwinger approach to mesons as quark-antiquark bound states produces a very satisfactory description of the whole light pseudoscalar nonet, both at zero and at finite temperatures [1]. Especially interesting is the temperature behavior of the η-η′ complex, where results for masses differ very greatly for various possible relationships between the chiral restoration temperature and the temperature of melting of the topological susceptibility χ. Namely, χ is connected with the quantity β in the η-η′ mass matrix as χ = β (2 +X ²)f ²_π /6, where $X = f_\pi /f_{s\bar s}$ . For example, in certain regimes, the “mass” of η _NS , namely $M_{\eta _{NS} }$, for some temperatures becomes larger than $M_{\eta _{NS} }$, the “mass” of η _S [1]; that is, $M_{\eta _{NS} }$ and can $M_{\eta _{NS} }$ can cross.