Strange Quark Mass from Tau Lepton Decays with O(alpha_s^3) Accuracy

TL;DR

This work delivers the first exact ${O}( ext{a}_s^3)$ calculation of the quadratic strange-quark mass correction to the tau decay correlator, enabling full ${O}( ext{a}_s^3)$ precision in extracting $m_s$ from $R_ au$ within CIPT. The agreement of the exact coefficient with PMS/FAC estimates strengthens confidence in predicting the ${O}( ext{a}_s^4)$ term and supports an improved perturbative analysis. By combining the new results with updated $|V_{us}|$ and a refined renormalization-group treatment, the authors obtain $m_s(M_ au) oughly 100$ MeV with reduced theoretical uncertainty, illustrating the impact of higher-order QCD corrections on fundamental SM parameters.

Abstract

The first complete calculation of the quadratic quark mass correction to the correlator of the two currents relevant for the strangeness-changing semihadronic tau-decay rate is presented including its real part at the four-loop level. This allows to perform the extraction of the strange quark mass m_s from the decay width of the tau-lepton with full O(alpha_s^3) accuracy. In agreement with previous estimates the newly computed alpha_s^3 term proves to be rather large. This justifies inclusion of the similarly estimated alpha_s^4 term in phenomenological analysis. Combined with an updated value of V_{us} and an ``'improved'' version of the renormalization group improvement of the perturbative series this leads to an increase of the central value of m_s by about 20 % and a partial reduction of the theoretical uncertainty by about 50 %.