Complexification of the Exceptional Jordan Algebra and Its Application to Particle Physics

Recent papers contributed revitalizing the study of the exceptional Jordan algebra $\mathfrak{h}_{3}(\mathbb{O})$ in its relations with the true Standard Model gauge group $\mathrm{G}_{SM}$. The absence of complex representations of $\mathrm{F}_{4}$ does not allow $\Aut\left(\mathfrak{h}_{3}(\mathbb{O})\right)$ to be a candidate for any Grand Unified Theories, but the automorphisms of the complexification of this algebra, i.e., $\mathfrak{h}_{3}^{\mathbb{C}}(\mathbb{O})$, are isomorphic to the compact form of $\mathrm{E}_{6}$ and similar constructions lead to the gauge group of the minimal left-right symmetric extension of the Standard Model.

Asymmetric accidental composite dark matter

The goal of this work is to find the simplest UV completion of Accidental Composite Dark Matter Models (ACDM) that can dynamically generate an asymmetry for the DM candidate, the lightest dark baryon (DCb), and simultaneously annihilate the symmetric component. In this framework the DCb is a bound state of a confining SU(N)DC gauge group, and can interact weakly with the visible sector. The constituents of the DCb can possess non-trivial charges under the Standard Model gauge group. The generation of asymmetry for such candidate is a two-flavor variation of the out-of-equilibrium decay of a heavy scalar, with mass Mϕ ≳ 1010 GeV. Below the scale of the scalars, the models recover accidental stability, or long-livedness, of the DM candidate. The symmetric component is annihilated by residual confined interactions provided that the mass of the DCb mDCb ≲ 75 TeV. We implement the mechanism of asymmetry generation, or a variation of it, in all the original ACDM models, managing to generate the correct asymmetry for DCb of masses in this range. For some of the models found, the stability of the DM candidate is not spoiled even considering generic GUT completions or asymmetry generation mechanisms in the visible sector.

the complexification of the exceptional Jordan algebra and applications to particle physics

Recent papers of Todorov and Dubois-Violette[4] and Krasnov[7] contributed revitalizing the study of the exceptional Jordan algebra h3(O) in its relations with the true Standard Model gauge group GSM. The absence of complex representations of F4 does not allow Aut (h3 (O)) to be a candidate for any Grand Unified Theories, but the group of automorphisms of the complexification of this algebra isisomorphic to the compact form of E6. Following Boyle in [12], it is then easy to show that the gauge group of the minimal left-right symmetric extension of the Standard Model is isomorphic to a proper subgroup of Aut(C⊗h3(O))

Leptoquarks in oblique corrections and Higgs signal strength: status and prospects

Leptoquarks (LQs) are predicted within Grand Unified Theories and are well motivated by the current flavor anomalies. In this article we investigate the impact of scalar LQs on Higgs decays and oblique corrections as complementary observables in the search for them. Taking into account all five LQ representations under the Standard Model gauge group and including the most general mixing among them, we calculate the effects in h → γγ, h → gg, h → Zγ and the Peskin-Takeuchi parameters S, T and U. We find that these observables depend on the same Lagrangian parameters, leading to interesting correlations among them. While the current experimental bounds only yield weak constraints on the model, these correlations can be used to distinguish different LQ representations at future colliders (ILC, CLIC, FCC-ee and FCC-hh), whose discovery potential we are going to discuss.

Super-Weak Force and Neutrino Masses

We consider an anomaly free extension of the standard model gauge group G SM by an abelian group to G SM ⊗ U ( 1 ) Z . The condition of anomaly cancellation is known to fix the Z-charges of the particles, but two. We fix one remaining charge by allowing for all possible Yukawa interactions of the known left-handed neutrinos and new right-handed ones that obtain their masses through interaction with a new scalar field with spontaneously broken vacuum. We discuss some of the possible consequences of the model.

Dark matter and baryogenesis from non-Abelian gauged lepton number

A simple model is constructed based on the gauge symmetry [Formula: see text], with only the leptons transforming nontrivially under [Formula: see text]. The extended symmetry is broken down to the Standard Model gauge group at TeV-scale energies. We show that this model provides a mechanism for baryogenesis via leptogenesis in which the lepton number asymmetry is generated by [Formula: see text] instantons. The theory also contains a dark matter candidate — the [Formula: see text] partner of the right-handed neutrino.

Grassmannian duality and the particle spectrum

Schemes based on anticommuting scalar coordinates, corresponding to properties, lead to generations of particles naturally. The application of Grassmannian duality cuts down the number of states substantially and is vital for constructing sensible Lagrangians anyhow. We apply duality to all of the subgroups within the classification group [Formula: see text], which encompasses the standard model gauge group, and thereby determine the full state inventory; this includes the definite prediction of quarks with charge [Formula: see text] and other exotic states. Assuming universal gravitational coupling to the gauge fields and parity even property curvature, we also obtain [Formula: see text] which is not far from the experimental value around the [Formula: see text] mass.