2020/10/31 by Ivan Todorov
Physics and Astronomy · #hep-ph #hep-th
paper · pdf · doi:10.1007/jhep04(2021)164
23 pages; new section 5, minor corrections, reference added
arxiv created 2021/02/04 · arxiv updated 2021/05/05
Restricting the ℤ2-graded tensor product of Clifford algebras Cℓ4⊗Cℓ6 to the particle subspace allows a natural definition of the Higgs field Φ, the scalar part of Quillen's superconnection, as an element of Cℓ41. 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 \citeDT20; 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.