New Results on the Hadronic Tau Decay Determination of $\alpha_s$

Finite energy sum rule (FESR) analyses of non-strange hadronic $\tau$ decay data provide one of the most precise determinations of the strong coupling constant, $\alpha_s$. Over the last two years, analyses of the relevant current-current two-point functions based on the recently derived 5-loop result for the relevant $D=0$ OPE contributions have reached a nominal precision of order $1\%$, and brought the resulting determination of $\alpha_s(M_Z^2)$ into excellent agreement with independent lattice results. An outstanding issue for the FESR analyses is the possibility of residual ``duality violation'', i.e. of contributions associated with the breakdown of the OPE in the vicinity of the timelike real invariant-squared-mass axis. In this talk I discuss recent work to investigate and quantify these effects and present results for the impact of such contributions on the determination of $\alpha_s$, as well as on the determination of the $D=6$ condensates appearing in the OPE representation of the non-strange vector minus axial vector correlator difference, which condensates are relevant to determining the chiral limit values of the $K\rightarrow\pi\pi$ matrix elements of the electroweak penguin operators in the Standard Model.The reported analysis also provides a new determination of the gluon condensate.