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Abstract
In this note we present a new parametrization of the hadronic current for the decay $\tau \to \pi\pi\pi \nu_\tau$ derived from the chiral lagrangian with explicit inclusion of resonances. We have included both scalar, vector and axial-vector resonances. For the first time, the lowest tensor resonance ($f_2(1270)$) is included as well. Both single and double-resonance contributions to the hadronic form factors are taken into account. To satisfy the correct high energy behaviour of the hadronic form factors, constraints on numerical values of the vertex constants are obtained.
Highlights
Hadronic decay modes of τ-lepton gives information about the hadronization mechanism and resonance dynamics in the energy region, where the pQCD methods are not applicable
In the last years substantial progress for the simulation of the process τ → 3πντ was achieved.The progress [1] was related to a new parametrization of the hadronic current based on the Resonance Chiral Lagrangian (RChL) and to the recent availability of the unfolded distributions from preliminary BaBar analysis [2] for all invariant hadronic masses for the three-prong mode
The goal of this note is to outline a consistent model to describe the tau-lepton decys into three pions based on RChL with scalar (JPC = 0++) and tensor resonances (JPC = 2++) and that fulfill the high-energy QCD and low-energy chiral limits for the hadronic form-factors
Summary
Hadronic decay modes of τ-lepton gives information about the hadronization mechanism and resonance dynamics in the energy region, where the pQCD methods are not applicable. In the last years substantial progress for the simulation of the process τ → 3πντ was achieved.The progress [1] was related to a new parametrization of the hadronic current based on the Resonance Chiral Lagrangian (RChL) and to the recent availability of the unfolded distributions from preliminary BaBar analysis [2] for all invariant hadronic masses for the three-prong mode. The lowest-energy scalar resonance was added phenomenologically and, as a result, the corresponding hadronic current does not reproduce the correct chiral low-energy behaviour and the π0π0π− and π−π−π+ amplitudes do not reproduce the isospin relation [3]. The goal of this note is to outline a consistent model to describe the tau-lepton decys into three pions based on RChL with scalar (JPC = 0++) and tensor resonances (JPC = 2++) and that fulfill the high-energy QCD and low-energy chiral limits for the hadronic form-factors.
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