Superselection of the weak hypercharge and the algebra of the Standard Model

Abstract

Restricting the ${\mathbb{Z}}_2$-graded tensor product of Clifford algebras $C{\ell }_4\hat{\otimes }C{\ell }_6$ to the particle subspace allows a natural definition of the Higgs field $\Phi$, the scalar part of Quillen's superconnection, as an element of $C{\ell }_4^1$. We emphasize the role of the exactly conserved weak hypercharge Y, promoted here to a superselection rule for both observables and gauge transformations. This yields a change of the definition of the particle subspace adopted in recent work with Michel Dubois-Violette \cite{DT20}; here we exclude the zero eigensubspace of Y consisting of the sterile (anti)neutrinos which are allowed to mix. One thus modifies the Lie superalgebra generated by the Higgs field. Equating the normalizations of $\Phi$ in the lepton and the quark subalgebras we obtain a relation between the masses of the W boson and the Higgs that fits the experimental values within one percent accuracy.

23 pages; new section 5, minor corrections, reference added

References in corpus (4)

• A spectral geometry for the Standard Model without the fermion doubling
• Superconnection in the spin factor approach to particle physics
• Chirality, a new key for the definition of the connection and curvature of a Lie-Kac super-algebra
• Scalar anomaly cancellation reveals the hidden superalgebraic structure of the quantum chiral SU(2/1) model of leptons and quarks

Cited by in corpus (4)

• Subgroups of Clifford algebras
• Octonion Internal Space Algebra for the Standard Model
• Algebraic realisation of three fermion generations with $S_3$ family and unbroken gauge symmetry from $\mathbb{C}\ell (8)$
• An Algebraic Roadmap of Particle Theories, Part I: General construction