Higgs Boson Mass Corrections at N3LO in the Top-Yukawa Sector of the Standard Model

The search of new physics signals in the Higgs precision measurements plays a pivotal role in the High-Luminosity Large Hadron Collider (HL-LHC) and the 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 Higgs boson mass parameter in the Standard Model runs over several tens of MeV with a corresponding large theoretical uncertainty. 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 three-loop corrections in the QCD sector. In this work we present an additional contribution, by estimating the leading non-QCD three-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.