τ− → π−π0ντ and e+e− → π+π− Processes in the Chiral Nambu—Jona-Lasinio Model Including the Interaction of Pions in the Final State

Low-energy interactions of mesons with participation of the first radially excited states in $U(3) \times U(3)$ NJL model

“…The calculation result of the process τ → ππν τ in the framework of the NJL model is 30% lower than the experimental value [74]. The discrepancy of the theoretical and experimental results indicates the need of taking into account additional effects such as the interactions of mesons in the final state.…”

“…Those interactions in the final state for the process τ → ππν τ can be represented as a triangle shown in Figure 20. This triangle can be described with the integral of the following form [74]:…”

“…The third term in the squared brackets describes the diagram with the intermediate ω meson. By the known dependence of the cross-section of this process on the energy of the colliding leptons, one can fix the cut-off parameter of the meson loop Λ ππ = 740 MeV [74]. The appropriate diagram is shown in Fig.…”

“…By using the obtained value of Λ ππ , the branching fraction of the decay τ → ππν τ has been calculated [74]:…”

Calculation of the width of the decay $τ\to K^{-} K^{0} ν_τ$ in the extended NJL model with estimation of the contribution of the kaon final state interaction

“…In the recent works considering tau lepton decays into two pseudoscalar mesons [1,2,3], it was shown that in the description of these processes in the framework of the Nambu-Jona-Lasinio model (NJL) [4,5] the meson interaction in the final state plays an important role. Especially, this concerns the processes with the produced light pions.…”