U(3)⊗U(3) symmetry model with isospin breaking

Abstract

Mesonic and baryonic interactions are studied in a model of chiral U(3)\ensuremath{\bigotimes}U(3) symmetry. The scalar and pseudoscalar mesons are assumed to belong to the (3,${3}^{*}$)\ensuremath{\bigoplus}(${3}^{*}$,3) representation. Nonets of vector and axial-vector fields are introduced as gauge fields. The baryons are assumed to transform as the (3,${3}^{*}$)\ensuremath{\bigoplus}(${3}^{*}$,3) representation. Explicit and spontaneous symmetry breakings are introduced and masses and various couplings are obtained. Most of the parameters are fixed by using some particle masses as input. We find that the Lagrangian is approximately invariant under SU(2)\ensuremath{\bigotimes}SU(2) while for the vacuum SU(3) is a better symmetry than SU(2)\ensuremath{\bigotimes}SU(2). The scalar-meson masses are predicted to be ${m}_{S \ensuremath{\pi}}=949$ MeV, ${m}_{{S}_{K}}=1025$ MeV, ${m}_{S \ensuremath{\eta}}=1068$ MeV, and ${m}_{S {\ensuremath{\eta}}^{\ensuremath{'}}}=694$ MeV. The $V\ensuremath{\rightarrow}\mathrm{PP}$, $A\ensuremath{\rightarrow}\mathrm{VP}$, $S\ensuremath{\rightarrow}\mathrm{PP}$, and the three-body decay models $A\ensuremath{\rightarrow}3P$ are calculated, which compare well with the experiments. The meson-meson scattering lengths and effective ranges are calculated and compared with experiments and the current-algebra results. The mesonic decay constants and the ${K}_{l3}$ form factors are calculated, and we have $\frac{{F}_{K}}{{F}_{\ensuremath{\pi}}}=1.04$, $\frac{{F}_{{S}_{K}}}{{F}_{\ensuremath{\pi}}}=\ensuremath{-}1.04$, ${f}_{+}(0)=0.99$, $\ensuremath{\xi}=\ensuremath{-}0.24$, ${\ensuremath{\lambda}}_{+}=0.021$, and ${\ensuremath{\lambda}}_{\ensuremath{-}}=\ensuremath{-}0.022$. The $\mathrm{BBP}$ coupling constants and some of the meson-baryon scattering lengths, however, do not agree with the experiments. The nonelectromagnetic isospin-violating effects are studied and it is found that a single value of a parameter characterizing the strength of these interactions does not explain the following three results: (i) the electromagnetic mass differences of pseudoscalar mesons, (ii) the $\ensuremath{\eta}\ensuremath{\rightarrow}3\ensuremath{\pi}$ decay parameters, and (iii) the baryon electromagnetic mass differences.