A modified gravity model coupled to a Dirac field in 2D space–times with quadratic nonmetricity and curvature

After summarizing the basic concepts for the exterior algebra, we first discuss the gauge structure of the bundle over base manifold for deciding the form of the gravitational sector of the total Lagrangian in any dimensions. Then we couple minimally a Dirac spinor field to our gravitational Lagrangian 2-form which is quadratic in the nonmetricity and both linear and quadratic in the curvature in two dimensions. Subsequently, we obtain field equations by varying the total Lagrangian with respect to the independent variables. Finally, we find some classes of solutions of the vacuum theory and then a solution of the Dirac equation in a specific background and analyze them.

Solving the electron and muon $$g-2$$ anomalies in $$Z'$$ models

We consider simultaneous explanations of the electron and muon $$g-2$$ g - 2 anomalies through a single $$Z'$$ Z ′ of a $$U(1)'$$ U ( 1 ) ′ extension to the Standard Model (SM). We first perform a model-independent analysis of the viable flavour-dependent $$Z'$$ Z ′ couplings to leptons, which are subject to various strict experimental constraints. We show that only a narrow region of parameter space with an MeV-scale $$Z'$$ Z ′ can account for the two anomalies. Following the conclusions of this analysis, we then explore the ability of different classes of $$Z'$$ Z ′ models to realise these couplings, including the SM$$+U(1)'$$ + U ( 1 ) ′ , the N-Higgs Doublet Model$$+U(1)'$$ + U ( 1 ) ′ , and a Froggatt–Nielsen style scenario. In each case, the necessary combination of couplings cannot be obtained, owing to additional relations between the $$Z'$$ Z ′ couplings to charged leptons and neutrinos induced by the gauge structure, and to the stringency of neutrino scattering bounds. Hence, we conclude that no $$U(1)'$$ U ( 1 ) ′ extension can resolve both anomalies unless other new fields are also introduced. While most of our study assumes the Caesium $$(g-2)_e$$ ( g - 2 ) e measurement, our findings in fact also hold in the case of the Rubidium measurement, despite the tension between the two.

Solutions of Integral Equations via Fixed-Point Results on Orthogonal Gauge Structure

The main outcome of this paper is to introduce the notion of orthogonal gauge spaces and to present some related fixed-point results. As an application of our results, we obtain existence theorems for integral equations.

Symplectic realization of two interacting spin-two fields in three dimensions

We constructed a symplectic realization of the dynamic structure of two interacting spin-two fields in three dimensions. A significant simplification refers to the treatment of constraints: instead of performing a Hamiltonian analysis à la Dirac, we worked out a method that only uses properties of the pre-symplectic two-form matrix and its corresponding zero-modes to investigate the nature of constraints and the gauge structure of the theory. For instance, we demonstrate that the contraction of the zero-modes with the potential gradient, yields explicit expressions for the whole set of constraints on the dynamics of the theory, including the symmetrization condition and an explicit relationship between the coupling and cosmological constants. This way, we further identify the necessary conditions for the existence of a unique non-linear candidate for a partially massless theory, using only the expression for the interaction parameters of the model. In the case of gauge structure, the transformation laws for the entire set of dynamical variables are more straightforwardly derived from the structure of the remaining zero-modes; in this sense, the zero-modes must be viewed as the generators of the corresponding gauge transformations. Thereafter, we use an appropriate gauge-fixing procedure, the time gauge, to compute both the quantization brackets and the functional measure on the path integral associated with our model. Finally, we confirm that three-dimensional bi-gravity has two physical degrees of freedom per space point. With the above, we provide a new perspective for a better understanding of the dynamical structure of theories of interacting spin-two fields, which does not require the constraints to be catalogued as first- and second-class ones as in the case of Dirac’s standard method.

Jet substructure from dark sector showers

We examine the robustness of collider phenomenology predictions for a dark sector scenario with QCD-like properties. Pair production of dark quarks at the LHC can result in a wide variety of signatures, depending on the details of the new physics model. A particularly challenging signal results when prompt production induces a parton shower that yields a high multiplicity of collimated dark hadrons with subsequent decays to Standard Model hadrons. The final states contain jets whose substructure encodes their non-QCD origin. This is a relatively subtle signature of strongly coupled beyond the Standard Model dynamics, and thus it is crucial that analyses incorporate systematic errors to account for the approximations that are being made when modeling the signal. We estimate theoretical uncertainties for a canonical substructure observable designed to be sensitive to the gauge structure of the underlying object, the two-point energy correlator $$ {e}_2^{\left(\beta \right)} $$ e 2 β , by computing envelopes between resummed analytic distributions and numerical results from Pythia. We explore the separability against the QCD background as the confinement scale, number of colors, number of flavors, and dark quark masses are varied. Additionally, we investigate the uncertainties inherent to modeling dark sector hadronization. Simple estimates are provided that quantify one’s ability to distinguish these dark sector jets from the overwhelming QCD background. Such a search would benefit from theory advances to improve the predictions, and the increase in statistics using the data to be collected at the high luminosity LHC.

Gauge Structure of Teleparallel Gravity

During the conference Teleparallel Universes in Salamanca, we became aware of a recent paper [M. Fontanini, E. Huguet, and M. Le Delliou, Phys. Rev. D 2019, 99, 064006] in which some criticisms on the interpretation of teleparallel gravity as a gauge theory for the translation group were put forward. This triggered a discussion about the arguments on which those criticisms were based, whose output is described in the present paper. The main conclusion is that to a great extent, those arguments are incorrect, and lack mathematical and physical support.

Quaternionic Formalism for Non-Abelian Gauge Theory of Dyons and Gravito-Dyons

Starting with the Quaternion formulation of SU (2 )× U (1)gauge theory of dyons and gravitodyons, it is shown that the formulation characterizes the abelian and non-Abelian gauge structure of dyons and gravito-dyons in terms of purely real and imaginary units of quaternion.

Quaternionic Formalism for Non-Abelian Gauge Theory of Dyons and Gravito-Dyons

Starting with the Quaternion formulation of SU (2 )× U (1)gauge theory of dyons and gravitodyons, it is shown that the formulation characterizes the abelian and non-Abelian gauge structure of dyons and gravito-dyons in terms of purely real and imaginary units of quaternion.