Towards Order alpha_s^4 Accuracy in tau-decays

TL;DR

This work advances precision in tau-decay perturbative QCD by computing the leading large-$n_f$ contributions at $\mathcal{O}(\alpha_s^4)$ for key correlator functions, testing optimization schemes (FAC and PMS) against these results, and propagating the implications to full fixed-order and contour-improved tau-decay predictions. The authors extend the analysis to $\mathcal{O}(\alpha_s^5)$ estimates and examine massless and quadratic mass corrections, exploiting the new results to refine determinations of $\alpha_s$ and explore $m_s$ extraction from Cabibbo-suppressed decays. They find that while the massless sector benefits from reduced theoretical uncertainties and improved convergence, a persistent scheme difference of about $\delta\alpha_s(M_\tau) \approx 0.02$ remains between fixed-order and contour-improved approaches, even after including $\mathcal{O}(\alpha_s^4)$ and estimated $\mathcal{O}(\alpha_s^5)$ terms. For the $m_s^2$-dependent part, the spin-1 contribution shows more robust perturbative behavior than the spin-0 part, suggesting cautious optimism for $m_s$ determinations from tau decays with improved higher-order inputs.

Abstract

Recently computed terms of orders O(α_s^4 n_f^2) in the perturbative series for the tau decay rate, and similar (new) strange quark mass corrections, are used to discuss the validity of various optimization schemes. The results are then employed to arrive at improved predictions for the complete terms order O(α_s^4) and O(α_s^5) in the massless limit as well as for terms due to the strange quark mass. Phenomenological implications are presented.