Three-flavor chiral effective model with four baryonic multiplets within the mirror assignment

In the case of three quark flavors, (pseudo)scalar diquarks transform as antiquarks under chiral transformations. We construct four spin-$1/2$ baryonic multiplets from left- and right-handed quarks as well as left- and right-handed diquarks. The fact that two of these multiplets transform in a “mirror” way allows for chirally invariant mass terms. We then embed these baryonic multiplets into the Lagrangian of the so-called extended linear sigma model, which features (pseudo)scalar and (axial-)vector mesons, as well as glueballs. Reducing the Lagrangian to the two-flavor case, we obtain four doublets of nucleonic states. These mix to produce four experimentally observed states with definite parity: the positive-parity nucleon $N(939)$ and Roper resonance $N(1440)$, as well as the negative-parity resonances $N(1535)$ and $N(1650)$. We determine the parameters of the nucleonic part of the Lagrangian from a fit to masses and decay properties of the aforementioned states. Studying the limit of vanishing quark condensate, we conclude that $N(939)$ and $N(1535)$, as well as $N(1440)$ and $N(1650)$, form pairs of chiral partners.

Figure 1

Masses as a function of ${\phi }_N$ for minimum 1.

Figure 2

Masses as a function of ${\phi }_N$ for minimum 2.

Figure 3

Masses as a function of ${\phi }_N$ for minimum 3.