  The search for new physics signals in Higgs precision measurements plays a
pivotal role in the High-Luminosity Large Hadron Collider (HL-LHC) and future
colliders programs. The Higgs properties are expected to be measured with great
experimental precision, implying higher-order perturbative computations of the
electroweak parameters from the theoretical side. In particular, the
renormalized Higgs boson mass parameter in the Standard Model shows significant
variation around the electroweak scale, resulting in a lower-bound theoretical
uncertainty that exceeds future collider expectations. A more stable result
under the renormalization group can be computed from a non-zero external
momentum Higgs self-energy, for which available calculations include 3-loop
corrections in the QCD sector. In this work, we present an additional
contribution by estimating the leading non-QCD 3-loop corrections to the mass
of the Higgs boson in the top-Yukawa sector of order $y_t^6$. The
momentum-dependent Higgs self-energy is computed in the tadpole-free scheme for
the Higgs vacuum expectation value in the Landau gauge, and the explicit
dependence upon the Higgs boson and top quark masses is shown. The obtained
result is expressed in dimensional regularization as a superposition of a set
of master integrals with coefficients that are free of poles in four space-time
dimensions, and the corrections are evaluated numerically by the sector
decomposition method.
