Three-loop master integrals for the Higgs boson self-energy with internal top-quarks and W-bosons

TL;DR

This paper computes three-loop master integrals for the Higgs boson self-energy involving top-quarks and W-bosons, expressing them in terms of multiple polylogarithms with a focus on uniform weight and simplified differential equations.

Contribution

It provides a complete set of master integrals for three-loop Higgs self-energy diagrams with internal top-quarks and W-bosons, using uniform weight and rationalized square roots.

Findings

Master integrals expressed in multiple polylogarithms.

Differential equations are in ε-factorized form.

Square roots are rationalized for simplification.

Abstract

We consider the full set of master integrals with internal top-and $W$-propagators contributing to the three-loop Higgs self-energy diagrams of order ${\mathcal O}(\alpha^2 \alpha_s)$. We split the master integrals into a system relevant to the Feynman diagrams proportional to the product of Yukawa couplings $y_b y_t$ and the complement. For both systems we define master integrals of uniform weight, such that the associated differential equation is in $\varepsilon$-factorised form. The occurring square roots are rationalised and all master integrals are expressible in multiple polylogarithms.