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In case there are tensor interactions beyond the SM in the low-energy effective Lagrangian, their interference with the SM V-A currents yields a contribution for tau decays into three or more mesons that cannot be included in the famous structure functions introduced by Kühn and Mirkes in their seminal 1992 paper. We present this generalization here, highlighting again the importance of measuring the (generalized) spectral functions, as being model-independent and exploiting maximally the data. This can be particularly relevant for CP and T violation studies with at least three mesons in the final state of the tau decay.

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