Speaker
Description
The inclusion of isospin-breaking corrections is necessary for high precision measurements of hadronic observables. One such observable with phenomenological relevance is the tau decay-rate, which is connected to the CKM-matrix elements. The isospin-symmetry is broken by both the interaction of the quarks with the photon and their mass differences. In the following we would like to present one possible approach that we plan to follow in order to improve upon the currently available iso-symmetric calculations. The breaking of the symmetry and the inclusion of the additional photon field poses new challenges. The first of these is the renormalization of the effective electro-weak Hamiltonian that mediates the decay. The initially large $5\times 5$ mixing can be reduced by employing Wilson averages for the valence OS twisted-mass fermions. This enables us to reasonably compute the relevant 4-point function, for which the effective mixing pattern is reduced to just $2\times 2$. We plan to calculate the renormalization constants using flowed probe operators at finite flow time, see L. Holan's talk for more information. Furthermore, to include electromagnetic effects we use $C^*$ boundary conditions, which allows us to treat QED fully non-perturbatively in a finite volume. The final challenge is to obtain the real time-decay rate or spectral density from the euclidean data. We plan to address this ill-posed inverse Laplace transform with the HLT-method.