Power corrections to alpha_s(M_\tau),|V_{us}| and m_s

TL;DR

This paper re-evaluates power corrections in tau-decay for alpha_s, |V_{us}|, and m_s, highlighting the limitations of tau-decay for gluon condensate extraction and confirming precise alpha_s determinations consistent with electroweak data.

Contribution

It provides a critical comparison of tau-decay and QCD sum rules for power corrections, introduces the impact of non-standard corrections, and refines alpha_s and other parameter estimates.

Findings

Tau-decay is not ideal for gluon condensate extraction due to suppression.

Results confirm deviation from vacuum saturation for four-quark condensates.

Alpha_s(M_tau) and alpha_s(M_Z) are determined with high precision, aligning with electroweak fits.

Abstract

We re-examine recent determinations of power corrections from tau-decay and confront the results with the existing ones from QCD spectral sum rules (QSSR). We conclude that contrary to the QSSR analysis, which lead to <alpha_s G^2>=(6.8+-1.3)10^{-2} GeV^4, tau-decay is not a good place for extracting the gluon condensate due to its extra alpha_s^2 coefficient which suppresses its contribution in this process. Results from e^+e^- sum rules and tau-decay: rho alpha_s<uu>^2= (4.5+-0.3)10^{-4}GeV^6, where rho=3.0+-0.2 confirm the deviation from the vacuum saturation estimate of the four-quark condensate."Non-standard" power corrections (direct instantons, duality violation and tachyonic gluon mass) beyond the SVZ-expansion, partially cancel out in the V+A hadronic tau-decay channel, which gives at order alpha_s^4: alpha_s(M_tau)=0.3249(29)_{ex}(75)_{th} leading to als(M_Z)|_tau=0.1192 (4)_{ex}(9)_{th},in remarkable agreement with (but more accurate than) alpha_s(M_Z)|_Z=0.1191(27)obtained at the same alpha_s^4 order from the Z-width and the global fit of electroweak data. Finally, the role of the tachyonic gluon mass in the determinations of |V_{us}|from tau-decay and of m_s from tau-decay, e^+e^- and (pseudo)scalar channels is emphasized.