  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.
