$X$ Meson aka ${\eta }^{\prime }$ and Kobayashi-Maskawa-'t Hooft Six-quark Vertex -- $U(1{)}_A$ Anomaly and Generalized Nambu-Jona-Lasinio Model --

Abstract

In 1970, Kobayashi and Maskawa concluded that an effective six-quark vertex with a determinantal form is necessary in the chiral effective models to account for the large mass of $X$ meson, which is now called the ${\eta }^{\prime }$. The determinantal interaction has an $SU(3{)}_L\otimes SU(3{)}_R$ symmetry but not $U(3{)}_L\otimes U(3{)}_R$, and, hence accounts for the explicit breaking of $U(1{)}_A$ symmetry in quantum chromodynamics (QCD); the vertex was later derived by 't Hooft as an instanton-induced quark interaction. The vertex, which may be called the Kobayashi-Maskawa-'t Hooft (KMT) term, is widely used in quantitative analyses of hadron physics and QCD phase transitions at finite temperature and density. An account is made for the KMT term with recent extensive applications. Described are also personal experiences with Professor Maskawa and Professor Kobayashi,including an encounter with Professor Maskawa when the author first presented his work on the KMT term.

A few typos are corrected

References in corpus (4)

• A low-lying scalar meson nonet in a unitarized meson model
• The K^*_0(800) scalar resonance from Roy-Steiner representations of pi K scattering
• Vector interaction, charge neutrality and multiple chiral critical point structures
• U_A(1) Anomaly in Hot and Dense QCD and the Critical Surface

Cited by in corpus (4)

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• QCD axion and topological susceptibility in chiral effective Lagrangian models at finite temperature
• Theta dependence of the vacuum energy density in chiral effective Lagrangian models at finite temperature, above $T_c$
• Study of some local and global $U(1)$ axial condensates in QCD at finite temperature