Test of the Heavy Top Expansion in the Evaluation of MW and sin^2theta_eff

TL;DR

This study tests the accuracy of the Heavy Top-mass Expansion in calculating the W boson mass and effective weak mixing angle by comparing it with precise numerical evaluations across a wide Higgs mass range, finding very small discrepancies.

Contribution

It provides a detailed validation of the Heavy Top-mass Expansion method against exact two-loop calculations for electroweak precision observables.

Findings

Differences between HTE and exact calculations are less than 0.8 MeV for MW.

Differences are less than 1.2 x 10^-5 for sin^2theta_eff.

HTE is reliable over a wide Higgs mass range.

Abstract

In order to test the accuracy of the Heavy Top-mass Expansion (HTE) employed in recent two-loop calculations of MW and sin^2theta_eff, we consider their contributions to subtracted quantities of the form MW_sub=MW(mh)-MW(mh0), where mh0 is a reference point. The results are compared with those obtained by a precise numerical evaluation of all the two-loop contributions involving both the Higgs boson and a fermion loop. For the choice mh0=65 GeV, and over the large range 65 GeV <mh< 1TeV, we find very small differences between the precise and HTE calculations, amounting to |deltaMW|<0.8 MeV and |delta s^2_eff|<1.2 x 10^-5. Although corrections involving light fermions are necessary for the consistency and test of existent calculations, we also discuss the separate contributions from the top-bottom isodoublet. In this case, the differences are larger, although still small, namely |deltaMW|<1.9 MeV and |delta s^2_eff|< 4.5 x 10^-5.