Two-loop heavy top corrections to the Z boson partial widths
G. Degrassi, P. Gambino
TL;DR
This paper computes the two-loop electroweak corrections of order $O(g^4 M_t^2 / M_W^2)$ to the Z^0 partial widths within both the $\overline{\rm MS}$ and on-shell frameworks, employing a Heavy Top Expansion to manage the $M_t$-dependent terms. It demonstrates that using on-shell vector-boson masses and renormalization schemes reduces scheme and scale dependence, and it provides analytic expressions and interpolating formulas for $M_W$, $\sin^2\theta_{{\rm eff}}^{lept}$, and $\Gamma_\ell$, enabling efficient inclusion in global fits. The results show modest but non-negligible shifts in leptonic widths (up to ~34 keV) and larger shifts in hadronic widths, with significant impact on indirect Higgs-mass constraints. With direct search data, the 95% C.L. upper bound on the Higgs mass increases to about $M_H \lesssim 345$ GeV, while precision data alone constrain $M_H$ to roughly $<285$ GeV, illustrating the value of higher-order corrections for SM tests and Higgs phenomenology.
Abstract
We present the evaluation of the two-loop O(g^4 mt^2) effects in the partial widths of the Z boson in the MSbar scheme and in two different implementations of the on-shell scheme. We observe a clear reduction of the scheme dependence of the predictions. The renormalization procedure and the Heavy Top Expansion employed in the O(g^4 mt^2) calculations are illustrated in some detail and intermediate results are provided. We discuss the implication of our results on the constraints for the Higgs mass making use of simple interpolating formulas. We find that precision data give mh < 285 GeV at 95% C.L. taking into account the theory uncertainty. Including also the information from direct search experiments we obtain a 95% upper bound mh < 345 GeV.