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Register a new userIntroducing tools to test Higgs interactions via $WW$ scattering I: one-loop calculations and renormalization in the HEFT
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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.
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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.
In the standard model (SM), the $rho$ parameter is equal to 1 and the ratio $lambda_{WZ}$ of Higgs $to ZZ$ and Higgs $to WW$ is also equal to 1 at the tree level. When going beyond the SM with more than one types of Higgs representations these quantities may be different from the SM predictions which can provide crucial information about new physics. There may also exist a certain charged Higgs $h^+$ decays into a $W^+$ and a $Z$. Imposing a custodial symmetry can force the parameter $rho$ to be equal to 1 with certain predictions for $lambda_{WZ}$ and $h^+ to W^+Z$. However, imposing $rho =1$ without custodial symmetry may have different predictions. We show how differences arise and how to use experimental data to obtain information about the underlying physics in a model with the SM plus a real and a complex $SU(2)_L$ triplets.
A detailed study of Higgs interference effects at the one-loop level in the 1-Higgs-Singlet extension of the Standard Model (1HSM) is presented for the WW and tt decay modes with fully leptonic WW decay. We explore interference effects for benchmark points with a heavy Higgs mass that significantly exceeds 2*m_t. In the WW channel, the Higgs signal and the interfering continuum background are loop induced. In the tt channel, which features a tree-level background, we also calculate the interference with the one-loop background, which, due to the appearance of the absorptive part, is found to dominate the normalisation and shape of differential Higgs distributions and should therefore be considered in experimental analyses. The commonly used geometric average K-factor approximation K_interference ~ (K_Higgs*K_background)^(1/2) is not appropriate. We calculate with massive top and bottom quarks. Our 1HSM and SM implementation in Sherpa+OpenLoops is publicly available and can be used as parton-level integrator or event generator.
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.
We study the self energies of all particles which appear in a lattice regularization of supersymmetric QCD (${cal N}=1$). We compute, perturbatively to one-loop, the relevant two-point Greens functions using both the dimensional and the lattice regularizations. Our lattice formulation employs the Wilson fermion acrion for the gluino and quark fields. The gauge group that we consider is $SU(N_c)$ while the number of colors, $N_c$ and the number of flavors, $N_f$, are kept as generic parameters. We have also searched for relations among the propagators which are computed from our one-loop results. We have obtained analytic expressions for the renormalization functions of the quark field ($Z_psi$), gluon field ($Z_u$), gluino field ($Z_lambda$) and squark field ($Z_{A_pm}$). We present here results from dimensional regularization, relegating to a forthcoming publication our results along with a more complete list of references. Part of the lattice study regards also the renormalization of quark bilinear operators which, unlike the non-supersymmetric case, exhibit a rich pattern of operator mixing at the quantum level.
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