τ − →K − η (′) ν τ decays in Chiral Perturbation Theory with resonances

Abstract

Abstract:We have studied the τ − → K − η ( ) ν τ decays within Chiral Perturbation Theory including resonances as explicit degrees of freedom. We have considered three different form factors according to treatment of final-state interactions. In increasing degree of soundness: Breit-Wigner, exponential resummation and dispersive representation. We find that although the first one fails in accounting for the data on the Kη mode, the other two approaches provide good fits to them which are sensitive to the K (1410) pole parameters, that are determined to be M K = 1330 +27 −41 MeV and Γ K = 217 +68 −122 MeV. These values are competitive with the standard determination from τ − → (Kπ) − ν τ decays. The corresponding predictions for the τ − → K − η ν τ channel respect the current upper bound and hint to the discovery of this decay mode in the near future.

Combined analysis of the decays $\tau \to KS \pi^- \nu_\tau$ and $\tau \to K^- \eta \nu_\tau$

“…This may be compared to the averages by the Particle Data Group, 5 Still, including them in the fits would just increase the χ 2 with only irrelevant changes in the fit parameters. 6 Contrary to our previous analysis [18], in the present study we have not included the BaBar data [19].…”

“…A more detailed derivation of the differential distribution in the Kη case can be found in ref. [18]. Regarding the global normalisation, in the following we will employ |V us f [42], from a global fit to K 3 data, and…”

“…In ref. [18], we showed that a simple Breit-Wigner parametrisation of the dominating vector form factor lead to a rather poor description of the data, while more elaborated approaches based on Chiral Perturbation Theory (χP T ) [28][29][30] including resonances as dynamical fields [31,32] and resumming final-state interactions (FSI) encoded in the chiral loop functions provided very good agreement with data. Since the K − η currents are presently modelled in TAUOLA [33,34] (the standard Monte Carlo generator for τ lepton decays) relying on phase space, our form factors will enrich the Resonance Chiral Lagrangian-based currents [35,36] in the library (along these lines, the inclusion of the dispersive treatment for the Kπ system is also in progress).…”

“…This observation was one of the motivations for the analysis of ref. [18], where it was first shown that the considered decays were competitive to the τ − → (Kπ) − ν τ decays for the extraction of the K * (1410) meson parameters. This was made possible thanks to BaBar [19] and Belle [20] data of the K − η spectrum which improved drastically the pioneering CLEO [21] and ALEPH [22] measurements.…”

“…[37,38], thereby resumming FSI which is crucial to describe the considered decay spectra. Our previous analysis of the τ − → K − ην τ decays [18] disfavoured strongly the use of Breit-Wigner functions, both from the theoretical and phenomenological perspective. In section 3, we describe our fits in detail and present the corresponding results for all parameters.…”