Comparing the broken $U3 \times U3$ linear sigma model with experiment

Abstract

The linear \(\sigma\) model with broken \(U3 \times U3\) is compared with data of the lightest scalar and pseudoscalar mesons. When 5 of the 6 parameters are fixed by the pseudoscalar masses and decay constants, one finds that, already at the tree level, one has a reasonable description for the 4 scalar masses, describing mixing and up to 8 trilinear couplings of lightest scalars, taken as \(a_0(980), f_0(980), \sigma(\approx 500)\) and \(K^*_0(1430)\). This clearly indicates that these scalars are the chiral partners of the \(\pi, \eta, \eta ', K\), and this strongly suggests that they, like the latter, are (unitarized) \(q \bar q\) states.