Second-class current effects from isospin breaking in $\tau \to \omega \pi \nu_\tau$

Second-class weak currents can in the standard model be induced by chiral-symmetry breaking. In the specific case of the decay $\ensuremath{\tau}\ensuremath{\rightarrow}\ensuremath{\omega}\ensuremath{\pi}{\ensuremath{\nu}}_{\ensuremath{\tau}}$, dominated by the first-class vector current with the $\ensuremath{\rho}$ quantum numbers, such effects would manifest themselves by small axial vector (or, generally, nonvector) contributions to the decay rate. We present an attempt to estimate such effects, based on a vector and axial-vector dominance model of the relevant matrix elements supplemented by $\ensuremath{\omega}\mathrm{\text{\ensuremath{-}}}\ensuremath{\rho}$ mixing. We also give an indication on the amplitude directly mediated by ${b}_{1}(1235)\ensuremath{\rightarrow}\ensuremath{\omega}\ensuremath{\pi}$, in principle also allowed in the standard model by isotopic spin violation.