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In this note we expand on our previous study of the implications of LEP1 results for future colliders. We extend the effective operator-based analysis of De Rujula et al. to a larger symmetry group, and show at which cost their expectations can be relaxed. Of particular interest to experiment is a rephrasing of our previous results in terms of the Renard et al. parametrization for the gauge boson self-couplings (slightly extended to include $delta g_{gamma}$). We suggest the use of a ($delta g_{gamma}$, $delta g_{Z}$) plot to confront the expectations of various models.
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The available data on the 125 GeV scalar $h$ is analysed to explore the room for new physics in the electroweak symmetry breaking sector. The first part of the study is model-independent, with $h$ couplings to standard model particles scaled by quantities that are taken to be free parameters. At the same time, the additional loop contributions to $h rightarrow gammagamma$ and $h rightarrow Zgamma$, mediated by charged scalar contributions in the extended scalar sector, are treated in terms of gauge-invariant effective operators. Having justified this approach for cases where the concerned scalar masses are a little above the $Z$-boson mass, we fit the existing data to obtain marginalized 1$sigma$ and 2$sigma$ regions in the space of the coefficients of such effective operators, where the limit on the $h rightarrow Zgamma$ branching ratio is used as a constraint. The correlation between, say, the gluon fusion and vector-boson fusion channels, as reflected in a non-diagonal covariance matrix, is taken into account. After thus obtaining model-independent fits, the allowed values of the coefficients are translated into permissible regions of the parameter spaces of several specific models. In this spirit we constrain four different types of two Higgs doublet models, and also models with one or two $Y = 2$ scalar triplets, taking into account the correlatedness of the scale factors in $h$-interactions and the various couplings of charged Higgs states in each extended scenario.
We revisit the effective field theory of the standard model that is extended with sterile neutrinos, $N$. We examine the basis of complete and independent effective operators involving $N$ up to mass dimension seven (dim-7). By employing equations of motion, integration by parts, and Fierz and group identities, we construct relations among operators that were considered independent in the previous literature, and find seven redundant operators at dim-6, sixteen redundant operators and two new operators at dim-7. The correct numbers of operators involving $N$ are, without counting Hermitian conjugates, $16~(Lcap B)+1~(slashed{L}cap B)+2~(slashed{L}capslashed{B})$ at dim-6, and $47~(slashed{L}cap B)+5~(slashed{L}capslashed{B})$ at dim-7. Here $L/B~(slashed L/slashed B)$ stands for lepton/baryon number conservation (violation). We verify our counting by the Hilbert series approach for $n_f$ generations of the standard model fermions and sterile neutrinos. When operators involving different flavors of fermions are counted separately and their Hermitian conjugates are included, we find there are $29~(1614)$ and $80~(4206)$ operators involving sterile neutrinos at dim-6 and dim-7 respectively for $n_f=1~(3)$.
We consider the phenomenological implications of charged scalar extensions of the SM Higgs sector in addition to EFT couplings of this new state to SM matter. We perform a detailed investigation of modifications of loop-induced decays of the 125 GeV Higgs boson, which receives corrections from the propagating charged scalars alongside one-loop EFT operator insertions and demonstrate that the interplay of $Hto gammagamma$ and $Hto Zgamma$ decays can be used to clarify the additional states phenomenology in case a discovery is made in the future. In parallel, EFT interactions of the charged Higgs can lead to a decreased sensitivity to the virtual presence of charged Higgs states, which can significantly weaken the constraints that are naively expected from the precisely measured $Hto gammagamma$ branching ratio. Again $Hto Zgamma$ measurements provide complementary sensitivity that can be exploited in the future.
We consider effective operators describing Dark Matter (DM) interactions with Standard Model fermions. In the non-relativistic limit of the DM field, the operators can be organized according to their mass dimension and their velocity behaviour, i.e. whether they describe s- or p-wave annihilations. The analysis is carried out for self-conjugate DM (real scalar or Majorana fermion). In this case, the helicity suppression at work in the annihilation into fermions is lifted by electroweak bremsstrahlung. We construct and study all dimension-8 operators encoding such an effect. These results are of interest in indirect DM searches.
In recent years, many natural Hamiltonian systems, classical and quantum, with constants of motion of high degree, or symmetry operators of high order, have been found and studied. Most of these Hamiltonians, in the classical case, can be included in the family of extended Hamiltonians, geometrically characterized by the structure of warped manifold of their configuration manifold. For the extended manifolds, the characteristic constants of motion of high degree are polynomial in the momenta of determined form. We consider here a different form of the constants of motion, based on the factorization procedure developed by S. Kuru, J. Negro and others. We show that an important subclass of the extended Hamiltonians admits factorized constants of motion and we determine their expression. The classical constants may be non-polynomial in the momenta, but the factorization procedure allows, in a type of extended Hamiltonians, their quantization via shift and ladder operators, for systems of any finite dimension.
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