Quadratic Mass Corrections of Order $α_s^3 m_q^2/s$ to the Decay Rate of Z- and W- Bosons

TL;DR

The work presents analytic, higher-order quadratic mass corrections ${\cal O}(\alpha_s^3 m_q^2/s)$ to the absorptive part of non-diagonal axial-vector current correlators, enabling precise ${\cal O}(\alpha_s^3 m_q^2/M_W^2)$ and related corrections to $Z$ and $W$ hadronic decay widths. It employs a renormalization-group framework, using known polarization functions, anomalous dimensions up to ${\cal O}(\alpha_s^3)$, and Ward identities to predict logarithmic structures and determine the non-singlet mass corrections for non-diagonal currents. The main contributions include explicit expressions for $R^{V}_2$ and $R^{A}_2$ in terms of quark masses, $\alpha_s$, and $n_f$, plus their incorporation into the hadronic decay rates, providing practical corrections for precision electroweak phenomenology. The results also corroborate consistency with the diagonal-vector case and rely on cross-checks with the MINCER program.

Abstract

We analytically compute quadratic mass corrections of order $α_s^3 m_q^2/s$ to the absorptive part of the (non-diagonal) correlator of two axial vector currents. This allows us to find the correction of order $α_s^3 m_q^2/M^2_W$ to the $Γ(W -->hadrons)$ as well as similar corrections to $Γ(Z -->hadrons)$.