O(αα_s) correction to the pole mass of the t-quark within the Standard Model

TL;DR

This paper computes the two-loop mixed electroweak–QCD correction $O(\alpha\alpha_s)$ to the relation between the pole mass and the $\overline{\rm MS}$ mass of the top quark in the Standard Model, in the diagonal CKM and massless $b$-quark limit. Using a systematic two-loop on-shell self-energy calculation, Tarasov reduction to a small set of master integrals, and explicit analytic evaluations of those masters, the authors provide a complete expression for the pole–MS mass relation and the top-quark width, including a careful treatment of tadpole contributions to ensure RG invariance. They also derive the corresponding two-loop MS–OS renormalization constants and present a semi-numerical assessment showing that the $O(\alpha\alpha_s)$ term is phenomenologically relevant, especially for larger Higgs masses. The work delivers new analytic master integrals and demonstrates the practical impact of mixed EW/QCD corrections on precision top-quark mass determinations.

Abstract

We have calculated the O(αα_s) contributions to the relationship between the MS-mass and the pole of the t-quark propagator in the Standard Model in the limit of a diagonal CKM matrix and for a massless b-quark. Analytical results for the so far unknown master-integrals appearing in the calculation are also given.

Figures (4)

• Figure 1: The two--loop one--particle irreducible diagrams contributing to the pole mass of a quark. $\phi_0$ and $\phi$ are the neutral and the charged pseudo--Goldstone bosons, respectively. The number of diagrams is 24.
• Figure 2: The two--loop tadpole type diagrams which should be included for manifest gauge and renormalization group invariance.
• Figure 3: The master diagrams arising in this two--loop calculation. Bold, thin and dashed lines correspond to off--shell massive, on--shell massive and to massless propagators, respectively.
• Figure 4: Electroweak $O(\alpha \alpha_s)$ correction to $M_t/m_t(m_t)-1$ [left] and $m_t(M_t)/M_t-1$ [right], in comparison with $O(\alpha_s^2)$ and $O(\alpha_s^3)$ QCD corrections as a function of the Higgs boson mass $M_H$.