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mitchell porter

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

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

Ivan Todorov

*[Submitted on 29 Oct 2020]*

We postulate that the exactly conserved weak hypercharge Y gives rise 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; 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 field normalizations 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.

I haven't had time to study this paper yet. But a few curiosities:

It talks about Clifford algebras. But in fact it builds on work due to Michel Dubois-Violette, who comes from noncommutative geometry but who somehow uses the 27-dimensional exceptional Jordan algebra as the noncommutative space in his physics model.

It talks about superalgebras. But it looks like the concept of "super" here can't be the usual one from particle physics. Indeed, I suspect that the author is really talking about a "Z2-graded algebra" rather than a true "superalgebra" (both algebras have "even" and "odd" objects, but only in the true superalgebra are the odd objects fermionic).

The main thing I wish to understand, is how the author obtains the Weinberg angle and W/Higgs mass ratio. But one probably needs to grasp the overall theoretical framework too, to really understand.