Neutrino and scalar boson mass in algebraic quantum field theory

Abstract

The hypothesis is explored that fermion rest mass is due entirely to self-interaction via virtual excitation of gauge bosons. This requires revising the standard model to treat both chiral projections of a fermion field as SU(2) doublets, which precludes Yukawa coupling to a scalar (Higgs) boson field. The estimated self-interaction mass of the electron neutrino is $0.291\times10^{-5}m_e$. The implied self-interaction mass of the Higgs boson itself is very small, comparable to the neutrino. Because there is no direct coupling to fermions, only to the $Z^0$ gauge boson, this can be reconciled with failure to detect low-mass Higgs bosons. This argument eliminates many undetermined parameters of the standard model, but requires an {\it ad hoc} Lagrangian term to account for neutral current asymmetries. The proposed algebraic formalism is consistent with fermion generations defined by distinct eigenvalues of a self-interaction mass operator.