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We review some results obtained in the context of the Collaborative Research Center/Transregio~9. In particular we discuss three-loop corrections to the Higgs boson mass in the Minimal Supersymmetric Standard Model, higher order corrections to Higgs boson production, and the calculations of renormalization group functions and decoupling constants.
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In this paper we present the complete two-loop vertex corrections to scalar and pseudo-scalar Higgs boson production for general colour factors for the gauge group ${rm SU(N)}$ in the limit where the top quark mass gets infinite. We derive a general formula for the vertex correction which holds for conserved and non conserved operators. For the conserved operator we take the electromagnetic vertex correction as an example whereas for the non conserved operators we take the two vertex corrections above. Our observations for the structure of the pole terms $1/epsilon^4$, $1/epsilon^3$ and $1/epsilon^2$ in two loop order are the same as made earlier in the literature for electromagnetism. However we also elucidate the origin of the second order single pole term which is equal to the second order singular part of the anomalous dimension plus a universal function which is the same for the quark and the gluon. [3mm]
Effective field theories are useful tools to search for physics beyond the Standard Model (SM). However, effective theories can lead to non-unitary behavior with fastly growing amplitudes. This unphysical behavior may lead to large sensitivity to SM deviations, making necessary a unitarization of the amplitudes prior to a comparison with experiment. In the present work, we focus on all the processes entering the two-Higgs production by longitudinal $WW$ scattering: we perform a full one-loop calculation of all relevant processes, we determine the necessary counterterms in the on-shell scheme, and we study how the full inclusion of the gauge degrees of freedom modifies the previously computed masses and widths of the dynamical resonances arising from the unitarization process in the vector-isovector channel. Altogether, we are able to provide the technical tools that are needed to study the low-energy couplings in the Higgs effective theory under the requirements of unitarity and causality.
A weakly interacting boson-fermion mixture model was investigated using Wisonian renormalization group analysis. This model includes one boson-boson interaction term and one boson-fermion interaction term. The scaling dimensions of the two interaction coupling constants were calculated as 2-D at tree level and the Gell-Mann-Low equations were derived at one-loop level. We find that in the Gell-Mann-Low equations the contributions from the fermion loops go to zero as the length scale approaches infinity. After ignoring the fermion loop contributions two fixed points were found in 3 dimensional case. One is the Gaussian fixed point and the other one is Wilson-Fisher fixed point. We find that the boson-fermion interaction decouples at the Wilson-Fisher fixed point. We also observe that under RG transformation the boson-fermion interaction coupling constant runs to negative infinity with a small negative initial value, which indicates a boson-fermion pairing instability. Furthermore, the possibility of emergent supersymmetry in this model was discussed.
Reaching a theoretical accuracy in the prediction of the lightest MSSM Higgs-boson mass, M_h, at the level of the current experimental precision requires the inclusion of momentum-dependent contributions at the two-loop level. Recently two groups presented the two-loop QCD momentum-dependent corrections to Mh [1,2], using a hybrid on-shell--DRbar scheme, with apparently different results. We show that the differences can be traced back to a different renormalization of the top-quark mass, and that the claim in [2] of an inconsistency in [1] is incorrect. We furthermore compare consistently the results for M_h obtained with the top-quark mass renormalized on-shell and DRbar. The latter calculation has been added to the FeynHiggs package and can be used to estimate missing higher-order corrections beyond the two-loop level.
Motivated by models for neutrino masses and lepton mixing, we consider the renormalization of the lepton sector of a general multi-Higgs-doublet Standard Model with an arbitrary number of right-handed neutrino singlets. We propose to make the theory finite by $overline{mbox{MS}}$ renormalization of the parameters of the unbroken theory. However, using a general $R_xi$ gauge, in the explicit one-loop computations of one-point and two-point functions it becomes clear that---in addition---a renormalization of the vacuum expectation values (VEVs) is necessary. Moreover, in order to ensure vanishing one-point functions of the physical scalar mass eigenfields, finite shifts of the tree-level VEVs, induced by the finite parts of the tadpole diagrams, are required. As a consequence of our renormalization scheme, physical masses are functions of the renormalized parameters and VEVs and thus derived quantities. Applying our scheme to one-loop corrections of lepton masses, we perform a thorough discussion of finiteness and $xi$-independence. In the latter context, the tadpole contributions figure prominently.
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