Abstract
We study theoretically the decay $\tau^- \to \nu_\tau P^- A$, with $P^-$ a $\pi^-$ or $K^-$ and $A$ an axial-vector resonance $b_1(1235)$, $h_1(1170)$, $h_1(1380)$, $a_1(1260)$, $f_1(1285)$ or any of the two poles of the $K_1(1270)$. The process proceeds through a triangle mechanism where a vector meson pair is first produced from the weak current and then one of the vectors produces two pseudoscalars, one of which reinteracts with the other vector to produce the axial resonance. For the initial weak hadronic production we use a recent formalism to account for the hadronization after the initial quark-antiquark pair produced from the weak current, which explicitly filters G-parity states and obtain easy analytic formulas after working out the angular momentum algebra. The model also takes advantage of the chiral unitary theories to evaluate the vector-pseudoscalar amplitudes, where the axial-vector resonances were obtained as dynamically generated from the VP interaction. We make predictions for invariant mass distribution and branching ratios for the channels considered.
Highlights
The fact that the τ is the only lepton heavy enough to decay into hadrons makes the hadronic τ lepton decays a priceless test of the strong interaction at low energy in the light flavor sector [1,2,3,4]
Even though there are more than 100 hadronic τ decays experimentally reported by the PDG [5], it is clear that not all the possible ones have been observed or whether there is no room for decays beyond the standard model
We have carried out a theoretical study of the τ decay into a pseudoscalar meson plus an axial-vector resonance
Summary
The fact that the τ is the only lepton heavy enough to decay into hadrons makes the hadronic τ lepton decays a priceless test of the strong interaction at low energy in the light flavor sector [1,2,3,4]. With only one free parameter (for regularization of PV loops), this model predicts masses and widths of these axial vector resonances and the full PV scattering amplitudes from where e.g., the coupling of the different resonances to the different PV channels can be obtained Within this model, the τ decay into one pseudoscalar plus one axial-vector resonance requires the production of one pseudoscalar and one PV pair in the hadronization process, since these axial-vector resonances are dynamically generated from the PV interaction. The strength of the formalism in [19] is that it carries on an elaborate calculation of the angular momentum and spin algebra which allows, in the end, to rely upon only one global unknown constant to get all the different channels This unknown factor is obtained in the present work from the experimental value of the τ− → ντKÃK Ã decay. The formalism allows for an explicit filter of G-parity states, of special importance in the present work
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