Abstract
Within the context of an extended Nambu - Jona-Lasinio model, we analyze the role of the axial-vector $a_1(1260)$ and $a_1(1640)$ mesons in the decay $\tau\to\nu_\tau \rho^0\pi^-$. The contributions of pseudoscalar $\pi$ and $\pi (1300)$ states are also considered. The form factors for the decay amplitude are determined in terms of the masses and widths of these states. To describe the radial excited states $\pi (1300)$ and $a_1(1640)$ we introduce two additional parameters which can be estimated theoretically, or fixed from experiment. The decay rate and $\rho\pi$ mass spectrum are calculated.
Highlights
Semihadronic decay modes of the tau lepton remain to present date a topic of interest to theoreticians as well as experimentalists [1]
In the Nambu–Jona-Lasinio (NJL) model a1ð1260Þ is considered to be a member of the basic axial-vector nonet, i.e., a1ð1260Þ is a pure qqstate, with a1ð1640Þ being its first radial excitation
We do not consider here the contributions of the problematic finite terms, but show instead that the decay can be described by the standard effective meson Lagrangian [18,19,20] provided the first radial excitations πð1300Þ and a1ð1640Þ are taken into account
Summary
Semihadronic decay modes of the tau lepton remain to present date a topic of interest to theoreticians as well as experimentalists [1]. One of the first theoretical studies of the role of the a1ð1260Þ axial-vector state in the τ → ντρ0π− decay is presented in Ref. We do not consider here the contributions of the problematic finite terms, but show instead that the decay can be described by the standard effective meson Lagrangian [18,19,20] provided the first radial excitations πð1300Þ and a1ð1640Þ are taken into account. II we describe the relevant meson vertices of the effective Lagrangian, obtain the amplitude of the τ → ντρ0π− decay, and discuss the partial conservation of the axial-vector current (PCAC) This important relation should be fulfilled in the chiral approach.
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