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

Abstract

Abstract Restricting the ℤ2-graded tensor product of Clifford algebras $$ C{\mathrm{\ell}}_4\hat{\otimes}C{\mathrm{\ell}}_6 $$ C ℓ 4 ⊗ ̂ C ℓ 6 to the particle subspace allows a natural definition of the Higgs field Φ, the scalar part of Quillen’s superconnection, as an element of $$ C{\mathrm{\ell}}_4^1 $$ C ℓ 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 [13]; 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 Φ 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.