τ vector and axial-vector spectral functions in the extended linear sigma model

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The extended linear sigma model describes the vacuum phenomenology of scalar, pseudoscalar, vector and axial-vector mesons at energies ≃ 1 GeV. We combine the chiral U(2)ₗ× U(2)ᵣ symmetry of this model with a local SU(2)ₗ× U(1)Y symmetry and obtain a gauge invariant effective description for electroweak interaction of hadrons in the vacuum. Vector and axial-vector spectral functions can be described well by two intermediate resonances ρ and a₁. They are implemented into this model as chiral partners and yield the predominant contributions to both spectral functions. However, the contributions that arise from the non-resonant decay channels of the weak charged W bosons are essential for reproducing the lineshapes of the spectral functions.