| Abstract [eng] |
Research into elementary particles and their interactions is based on quantum field theory (QFT), whose most successful model is the Standard Model (SM). It has correctly predicted the properties of many particles, the most recent of which is the Higgs boson. Nevertheless, the SM cannot explain several phenomena, such as the origin of neutrino masses, the existence of dark matter, gravity, and others. For this reason, particle physicists are developing extensions of the Standard Model in order to account for these discrepancies. This work delves into one such extension — the Grimus–Neufeld model (GNM). The Grimus–Neufeld model adds an additional Higgs doublet, making it a two-Higgs-doublet model (2HDM), as well as a Majorana fermion, which is used to explain the smallness of neutrino masses. Our hypothesis is that by renormalizing the Higgs–fermion interaction and fixing the counterterms of the particle propagators that compose it, we can derive the counterterm for the Yukawa coupling. This is motivated by the fact that the Yukawa sector describes the interactions between the Higgs boson and fermions — by deriving the Feynman rules for the counterterms of the Higgs–fermion interaction, also known as the three-point function, we observe that it is a combination of the counterterms of the fermion and Higgs propagators, also called two-point functions, together with the Yukawa counterterm. We then apply the SD scheme, which has already been used for the renormalization of the two-point functions in the GNM. The Yukawa counterterm is thus obtained by computing higher-order perturbations, otherwise known as one-loop corrections, and using the field counterterms of the two-point functions to remove UV divergences. The Yukawa counterterm is verified using its relation to the mass counterterms of the two-point functions. This is grounded in the relationship between the Yukawa couplings and the fermion masses through the Dirac mass term in the Lagrangian, which arises due to spontaneous symmetry breaking and the Higgs mechanism. The aim of this work was to determine whether the SD scheme can be applied to the renormalization of the Yukawa sector in the SM part of the GNM. Direct calculations revealed a structural similarity between the Yukawa counterterms derived from the interaction vertex and from the mass relation, but also uncovered discrepancies. The Yukawa counterterm derived via the mass relation contains mass terms of higher order than those present in the interaction counterterm, and the mass relation expression includes the Higgs boson mass in the majority of its terms. Furthermore, the terms involving the CKM matrix differ by a factor of one-half between the two expressions. However, the QCD contributions are identical in both expressions. It is likely that these discrepancies arose due to incomplete renormalization — the renormalization of the vacuum expectation value was not included, and a fully consistent renormalization requires that all mutually related parameters be renormalized simultaneously. Nevertheless, the result obtained indicates that the procedure presented in this work is a promising method for the renormalization of the Yukawa sector in the GNM, and that further derivations and calculations could confirm this relation. |
