Strangeness content of the pion in the U(3) Nambu–Jona–Lasinio model

Abstract

Abstract The Nambu–Jona–Lasinio model is considered with flavor-dependent coupling constants G i j ( ψ ¯ λ i ψ ) ( ψ ¯ λ j ψ ) + ( ψ ¯ i γ 5 λ i ψ ) ( ψ ¯ i γ 5 λ j ψ ) for i , j = 0 , 1 … N f 2 − 1 , and N f = 3. A self-consistent calculation of quark effective masses and coupling constants is performed, making the strange quark effective mass vary considerably. Quantum mechanical mixings between up, down and strange constituent quarks yield a strangeness content (s-content) of the light u and d quark constituent and of the pion. Different types of estimates for the strangeness contribution for the pion mass are provided. Mixing-type interactions, G i≠j , induce light meson mixings, and estimates for the π 0 − η and η − η′ mixings are provided. The η − π 0 mixing is argued to be an indication of the s-content of the pion.