Gravity from Dirac Eigenvalues

We study a formulation of euclidean general relativity in which the dynamical variables are given by a sequence of real numbers $\lambda_{n}$, representing the eigenvalues of the Dirac operator on the curved spacetime. These quantities are diffeomorphism-invariant functions of the metric and they form an infinite set of ``physical observables'' for general relativity. Recent work of Connes and Chamseddine suggests that they can be taken as natural variables for an invariant description of the dynamics of gravity. We compute the Poisson brackets of the $\lambda_{n}$'s, and find that these can be expressed in terms of the propagator of the linearized Einstein equations and the energy-momentum of the eigenspinors. We show that the eigenspinors' energy-momentum is the Jacobian matrix of the change of coordinates from the metric to the $\lambda_{n}$'s. We study a variant of the Connes-Chamseddine spectral action which eliminates a disturbing large cosmological term. We analyze the corresponding equations of motion and find that these are solved if the energy momenta of the eigenspinors scale linearly with the mass. Surprisingly, this scaling law codes Einstein's equations. Finally we study the coupling to a physical fermion field.Comment: An enlarged and improved version which will be pubblished in Mod. Phys. Lett.

Phenomenology of minimal Z' models: from the LHC to the GUT scale

We consider a class of minimal abelian extensions of the Standard Model with an extra neutral gauge boson $Z'$ at the TeV scale. In these scenarios an extended scalar sector and heavy right-handed neutrinos are naturally envisaged. We present some of their striking signatures at the Large Hadron Collider, the most interesting arising from a $Z'$ decaying to heavy neutrino pairs as well as a heavy scalar decaying to two Standard Model Higgses. Using renormalisation group methods, we characterise the high energy behaviours of these extensions and exploit the constraints imposed by the embedding into a wider GUT scenario.Comment: 6 pages, 4 figures. Reference list updated. Contribution to the proceedings of the 8th International Workshop on QCD - Theory and Experiment (QCD@Work 2016), 27-30 Jun 2016. Martina Franca, Ital

Z′Z', Higgses and heavy neutrinos in U(1)′U(1)' models: from the LHC to the GUT scale

We study a class of non-exotic minimal $U(1) '$ extensions of the Standard Model, which includes all scenarios that are anomaly-free with the ordinary fermion content augmented by one Right-Handed neutrino per generation, wherein the new Abelian gauge group is spontaneously broken by the non-zero Vacuum Expectation Value of an additional Higgs singlet field, in turn providing mass to a $Z'$ state. By adopting the $B-L$ example, whose results can be recast into those pertaining to the whole aforementioned class, and allowing for both scalar and gauge mixing, we first extract the surviving parameter space in presence of up-to-date theoretical and experimental constraints. Over the corresponding parameter configurations, we then delineate the high energy behaviour of such constructs in terms of their stability and perturbativity. Finally, we highlight key production and decay channels of the new states entering the spectra of this class of models, i.e., heavy neutrinos, a second Higgs state and the $Z'$, which are amenable to experimental investigation at the Large Hadron Collider. We therefore set the stage to establish a direct link between measurements obtainable at the Electro-Weak scale and the dynamics of the underlying model up to those where a Grand Unification Theory embedding a $U(1)'$ can be realised.Comment: 32 pages, 59 figures, journal versio

Naturalness and Dark Matter Properties of the BLSSM

In this report, we compare the naturalness and Dark Matter (DM) properties of the Minimal Supersymmetric Standard Model (MSSM) and the $B-L$ Supersymmetric Standard Model (BLSSM), with universality in both cases. We do this by adopting standard measures for the quantitative analysis of the Fine-Tuning (FT), at both low (i.e. supersymmetric (SUSY)) and high (i.e. unification) scales. We will see a similar level of FT for both models in these scenarios, with a slightly better FT for the BLSSM at SUSY scales and MSSM at Grand Unification Theory (GUT) scales. When including DM relic constraints, we drastically confine the MSSM's parameter space, whereas we still find a large parameter space available for the non-minimal scenario.Comment: Prepared for proceedings for DIS2017, talk presented by Simon Kin

Prospects for Sneutrino Dark Matter in the BLSSM

The $(B-L)$ Supersymmetric Standard Model (BLSSM) motivates several Dark Matter (DM) candidates beyond the Minimally Supersymmetric Standard Model (MSSM). We assess the comparative naturalness of the two models and discuss the potential detection properties of a particular candidate, the Right-Handed (RH) sneutrino.Comment: Prepared for proceedings for La Thuile 2018, talk by Simon Kin

Sneutrino Dark Matter in the BLSSM

In the framework of the $(B-L)$ Supersymmetric Standard Model (BLSSM), we assess the ability of ground and space based experiments to establish the nature of its prevalent Dark Matter (DM) candidate, the sneutrino, which could either be CP-even or -odd. Firstly, by benchmarking this theory construct against the results obtained by the Planck spacecraft, we extract the portions of the BLSSM parameter space compliant with relic density data. Secondly, we show that, based on current sensitivities of the Fermi Large Area Telescope (FermiLAT) and their future projections, the study of high-energy $\gamma$-ray spectra will eventually enable us to extract evidence of this DM candidate through its annihilations into $W^+W^-$ pairs (in turn emitting photons), in the form of both an integrated flux and a differential energy spectrum which cannot be reconciled with the assumption of DM being fermionic (like, e.g., a neutralino), although it should not be possible to distinguish between the scalar and pseudoscalar hypotheses. Thirdly, we show that, while underground direct detection experiments will have little scope in testing sneutrino DM, the Large Hadron Collider (LHC) may be able to do so in a variety of multi-lepton signatures, with and without accompanying jets (plus missing transverse energy), following data collection during Run 2 and 3.Comment: 16 pages, 8 figure