Terms Of Effective Operators Research Articles

The see-saw portal at future Higgs factories: the role of dimension six operators

We study an extension of the Standard Model with electroweak scale right-handed singlet fermions N that induces neutrino masses, plus a generic new physics sector at a higher scale Λ. The latter is parametrized in terms of effective operators in the language of the νSMEFT. We study its phenomenology considering operators up to d = 6, where additional production and decay modes for N are present in addition to those arising from the mixing with the active neutrinos. We focus on the production with four-Fermi operators and we identify the most relevant additional decay modes to be N → νγ and N → 3f. We assess the sensitivity of future Higgs factories on the νSMEFT in regions of the parameter space where the new states decay promptly, displaced or are stable on detector lengths. We show that new physics scale up to 5–60 TeV can be explored, depending on the collider considered.

The Gauge-Higgs legacy of the LHC run II

We present a global analysis of the Higgs and electroweak sector based on LHC Run II and electroweak precision observables. We show which measurements provide the leading constraints on Higgs-related operators, and how the achieved LHC precision makes it necessary to combine rate measurements with electroweak precision observables. The SFitter framework allows us to include kinematic distributions beyond pre-defined ATLAS and CMS observables, independently study correlations, and avoid Gaussian assumptions for theory uncertainties. These Run II results are a step towards a precision physics program at the LHC, interpreted in terms of effective operators.

Magnetic dipole transitions in crystals

The magnetic dipole transitions in rare earth ions in crystals are described in terms of a model based on the fourth order perturbation theory. An analysis of the perturbing influence of crystal field potential and spin-orbit interaction is made. In addition to intra-shell interactions, inter-shell interactions that include the influence of the excited configurations are analysed. The transition amplitude is defined in terms of effective operators expressed by double unit tensor operators. The radial integrals of all effective operators are defined within the perturbed function approach, therefore the complete radial basis sets of one-electron states of given symmetry are taken into account. Conclusions mainly focus on the possible importance of magnetic dipole transitions in the description of electric dipole 0 ⟷ 0 transition due to the so-called borrowing mechanism.

Judd—Ofelt theory: past, present and future

The original Judd-Ofelt theory is briefly presented in the terms of effective operators defined in the traditional form that has been used for many years for the interpretation of the f spectra of rare earths. The semi-empirical approach of the Judd-Ofelt theory that defines the one-particle parametrization scheme is modified here. The unit tensor operators that act within the orbital space are replaced by double tensor operators acting within the spin-orbital space. This extension enables one to include the impact of the relativistic effects upon the transition amplitude. At the same time it leads to a generalization of the theoretical approach to f ↔ f transitions, especially in the case of those that are not described by the standard scheme.

Theoretical description of the spectroscopic properties of rare earth ions in crystals

In this article the present state of knowledge of the theory of one- and two-photon processes observed in rare earth ions in crystals is presented. The conclusions are based on the results of ab initio calculations performed for various ions across the lanthanide series. The model applied for the calculations is based on the Rayleigh–Schrödinger perturbation theory, and the amplitude of a certain electric dipole transition is expressed in terms of effective operators. The radial integrals of the effective operators are defined by the perturbed functions that contain the perturbing influence of single excitations from the 4f shell to all one-electron states of a given symmetry, discrete and continuum. In this approach the interactions between the 4f N and the excited configurations via the crystal field potential, the electron correlation operator and the spin–orbit interaction operator are discussed; it is believed that the presented theory contains the most important physical mechanisms responsible for the f↔f electric dipole transitions. Two alternative formulations of the theory of one-photon electric dipole transitions are presented. Consequently, the transition amplitude is defined within the standard theory based on the length formula and within a new approach which is based on the velocity form of the electric dipole radiation operator.

A systematic view of optical absorption spectra in the actinide series

In recent years sufficient new spectra of actinides in their numerous valence states have been measured to encourage a broader scale analysis effort than has been attempted in the past. Theoretical modelling in terms of effective operators has also undergone development. Well-established electronic structure parameters for the trivalent actinides are being used as a basis for estimating parameters in other valence states and relationships to atomic spectra are being extended. Recent contributions to our understanding of the spectra of 4+ actinides have been particularly revealing and supportive of a developing general effort to progress beyond a preoccupation with modelling structure to consideration of the much broader area of structure-bonding relationships. We summarize here both the developments in modelling electronic structure and the interpretation of apparent trends in bonding.

Reduced Matrix Elements of Tensor Operators

Reduced matrix elements of a tensorial product of n tensor operators in the basis of N-particle angular-momentum eigenstates are expanded into a sum of products of n 1-particle reduced matrix elements and a single (N + n)-particle recoupling coefficient. Application of the formula is illustrated by specific examples. The method leaves the coupling schemes of N-particle states undisturbed, which allows summation over intermediate states in a product of matrix elements to be made for any number of factors. A formula is given for the sum of products of two matrix elements and the extension to a greater number of matrix elements is illustrated by an example which is reduced to a form suitable for numerical evaluation. Such summations over products of matrix elements occur in the perturbation theory of configuration interaction and have hitherto been discussed in terms of effective operators. The connection of the method used here with the effective-operator approach is demonstrated.

Magnetic Parameters for the Configurationf3

The energy-level schemes of several atomic configurations ${f}^{3}$ are analyzed in terms of effective operators. These include all possible Hermitian two-electron scalar operators and six three-body spin-independent scalar operators. This collection of operators allows for spin-spin and spin-other-orbit interactions as well as for the most important effects of configuration interaction. Several alterations and extensions are suggested for the terms of Pr III $4{f}^{3}$. The positions of the free-ion levels of Nd IV $4{f}^{3}$ and Er IV $4{f}^{11}$ are inferred from the crystal spectra of ${\mathrm{Nd}}^{3+}$ in La${\mathrm{Cl}}_{3}$, and analyses with restricted sets of operators are carried out.