$X$ 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.

arXiv commentA few typos are corrected

References in corpus (6)

• 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
• QCD phase diagram: an overview
• Significant in-medium reduction of the mass of eta' mesons in sqrt(s(NN)) = 200 GeV Au+Au collisions

Cited by in corpus (8)

• Significant in-medium eta' mass reduction in sqrt(s(NN))=200 GeV Au+Au collisions at the BNL Relativistic Heavy Ion Collider
• Is Hyperon Polarization in Relativistic Heavy Ion Collisions Connected to Axial U(1) Symmetry Breaking at High Temperature?
• Remarks on the U(1) axial symmetry and the chiral transition in QCD at finite temperature
• Roles of axial anomaly on neutral quark matter with color superconducting phase
• Study of the theta dependence of the vacuum energy density in chiral effective Lagrangian models at zero temperature
• QCD axion and topological susceptibility in chiral effective Lagrangian models at finite temperature
• Study of some local and global $U(1)$ axial condensates in QCD at finite temperature
• Theta dependence of the vacuum energy density in chiral effective Lagrangian models at finite temperature, above $T_c$