Eur. Phys. J. A (2023) 59: 271
https://doi.org/10.1140/epja/s10050-023-01190-6

Regular Article - Theoretical Physics

U(5) Nambu–Jona–Lasinio model with flavor dependent coupling constants: pseudoscalar and scalar mesons masses

¹ Instituto de Física, Federal University of Goias, Av. Esperança, s/n, 74690-900, Goiânia, GO, Brazil
² Instituto Federal de Goiás, R. 75, n.46, 74055-110, Goiânia, GO, Brazil

^b fbraghin.ufg@gmail.com

Received: 13 May 2023
Accepted: 4 November 2023
Published online: 20 November 2023

Abstract

By considering the background field method we calculate one-loop polarization corrections to the coupling constant of the flavor-U(5) Nambu-Jona-Lasinio (NJL) model with degenerate up and down quarks. They break flavor and chiral symmetries and they can be written as $G_{\mathit{ij}}^{\mathrm{\Gamma }}(\overline{\psi }{\lambda }_i\mathrm{\Gamma }\psi )(\overline{\psi }{\lambda }_j\mathrm{\Gamma }\psi )$, for the scalar and pseudoscalar channels ($\mathrm{\Gamma }=I,i{\gamma }_5$) and $i,j=0,1,...,N_f^2-1$. These coupling constants do not introduce further free parameters in the model which amount to five, six or seven in total. Their contributions to different observables are computed: quark-antiquark scalar condensates, masses of quark-antiquark meson states (pseudoscalar and scalar) and pseudoscalar meson weak decay constants. The non-covariant three dimensional regularization scheme is employed leading to an unique interpretation for light and heavy quarks cutoffs. Besides that, flavor dependence of cutoffs is implemented in an unambiguous way. It turns out that only two UV cutoffs (${\mathrm{\Lambda }}_f$) are best suitable, one for the light ($f\equiv l=u,s$) and one for the heavy quarks ($f\equiv h=c,b$), although an unique flavor independent cutoff also provides similar results. A quantum mixing due to the representations of the flavor group leads to different interactions for the quarks and for the meson states, respectively denoted by $G_{\mathit{ff}}$ and $G_{\mathit{ij}}$. This quantum mixing effect is responsible for a lowering of quark effective masses and a slight improvement of predictions of observables. A quite surprisingly good description of most of the all the 25-plet pseudoscalar meson masses (within nearly $5\%$) and most of the scalar meson masses (within nearly 10%) is obtained. However, the usual problems to describe the correct mass hierarchy of some light scalar mesons still remain. The NJL-seem to overestimate the heavy quark condensates at the usual mean field level usually adopted for the NJL-model. In spite of the good description of the meson masses, the pseudoscalar meson weak decay constants cannot be described by the NJL model with relativistic heavy quark propagators without further interactions or effects.