New results on $\alpha_s$ from hadronic $\tau$ decay

We describe recent developments in the determination of the strong coupling from finite energy sum rule (FESR) analyses of non-strange spectral distributions measured in hadronic 𝜏 decay, focusing, in particular, on the consequences of a newly discovered redundancy in the “truncated OPE” version of these analyses. Such analyses employ OPE fits to weighted spectral integrals involving multiple weights at a single upper integration limit, $𝑠_0$ , with a number of the non- perturbative contributions in principle present removed by hand. We show that (i) contrary to conventional understanding, $\alpha_s$ in these analyses is obtained from fits which retain only perturbative contributions to FESRs of a subset of spectral integrals involving weights of the highest (rather than lowest) degrees entering the analysis, and (ii) the non-perturbative condensates nominally determined in the full analysis are obtained in a redundant manner, leading to potentially very large systematic uncertainties due to amplifications of any residual non-perturbative contamination of the results for $\alpha_s$ produced by the perturbative tOPE truncation in the FESRs which determine $\alpha_s$ . Finally, we show that alternate multi-weight, multi-$𝑠_0$ FESR analyses do not suffer from these redundancy issues and, through their use of multiple $𝑠_0$ , provide non-trivial additional constraints on the theory representations employed.