Decays \(\tau \rightarrow f_0(\pi ,K) \nu _\tau \) and \(\tau \rightarrow 3 \pi \nu _\tau \) accounting for the contribution of \(f_0(500)\)

In the \(U(3) \times U(3)\) quark NJL model, \(\tau \) lepton decays with the production of scalar mesons \(f_0(\pi ,K)\) and neutrinos are studied, where \(f_0=f_0(500), f_0(980)\). It is shown that these decays mainly occur via contact channels and channels with axial-vector mesons \(a_1(1260)\), \(K_1(1270)\) and \(K_1(1400)\). All mesons are considered as quark-antiquark states in this case. The obtained results can be considered as predictions for future experiments. The obtained estimates for the branching fractions of the \(\tau \rightarrow \pi ^-2\pi ^0 \nu _\tau \) decay taking into account the contributions of the \(\rho \pi \) and \(f_0(500)\pi \) states are in satisfactory agreement with experimental data.