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Study of the lowest tensor and scalar resonances in the $τ\to πππν_τ$ decay

In this note we present a new parametrization of the hadronic current for the decay $τ\to πππν_τ$ 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.