Neutrino and scalar boson mass in algebraic quantum field theory

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× 10−5me. 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 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 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. For Europhysics Letters The standard model revisited. – The standard model(SM) [1,2], based on conventional quantum field theory [3], explains qualitatively and in many cases quantitatively almost all established experimental data for elementary particles and fields other than gravity. A striking exception is neutrino mass, empirically small but nonzero [4]. Although nonvanishing neutrino mass appears to be empirically established, the electroweak theory of Weinberg and Salam [1, 2, 5] constrains neutrino mass to vanish by excluding right-handed chiral neutrino fields. SM assumes left-chiral fermion projections to be SU(2) doublets, while right-chiral projections are SU(2) singlets. Equivalently, chiral projectors modify gauge boson Feynman vertices. The theory is assumed to descend by successive symmetry-breaking from a renormalizable grand-unified theory (GUT) of higher symmetry. This excludes bare fermion mass, so that bare fermion fields are chiral eigenstates. Hence chiral projection operators do not affect the parental GUT. Their introduction in SM justifies fermion mass generation by Yukawa coupling of fermion fields to the SU(2) doublet Higgs scalar boson. Such coupling terms in the Lagrangian are invariants only for fermion current densities constructed from an SU(2) doublet field and a distinct SU(2) singlet field [6]. Since neutrino mass requires some modification of the theory, it is of interest to see whether the large number of arbitrary parameters required by SM might be reduced, without invoking unknown new physics or departing from quantum field theory. Both chiral projections of fermion fields are assumed here to be SU(2) doublets, eliminatng inequivalent field projections. This assumption excludes Higgs-fermion Yukawa coupling terms from the Lagrangian, because they cannot be SU(2) invariants. In accord with the logical principle of ‘Occam’s razor’, removing chiral projection operators eliminates arbitrary mass parameters. This can be done without affecting the success of SM electroweak theory for processes involving only leptons. The very small mass of neutrinos makes chiral projection redundant. The modified theory can be reconciled with neutral current asymmetries by inserting into the Lagrangian density an ad hoc term that does not add arbitrary parameters. Self-interaction mass results from virtual emission and reabsorption of gauge field quanta [3, 7–9]. Depending on the same operators as spontaneous emission, these processes cannot be eliminated without selective chiral projections. Otherwise, it is inconsistent to postulate neutrino mass exactly zero [10]. For lepton/neutrino processes with intermediate charged W± gauge bosons it will be shown here that chiral projectors can be omitted without affecting the established V-A phenomenology. This justifies a calculation of the electron-neutrino self-interaction mass consistent with current empirical data. An interacting massless bare fermion is dressed by vir-