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The interview continues with the following questions.
William: According to your paper, xSM predicts four distinct Higgs bosons, all of them lighter than the electron. How is it possible that these particles, of which two are expected to bear electric charge, have gone undetected?
Stig: 'It isn't possible! The charged particles should have turned up in various experiments long ago. Since they haven't been seen, the conclusion must be that'”contrary to what I state in the paper'”only one kind of Higgs boson exists.'
'Still, the information contained in the muon-electron mass ratio cannot be misinterpreted: First, the Higgs boson is employed as mass carrier when two pion pairs are formed from the last two electron pairs. An instant later, three more spinless bosons'”each carrying the same mass as the original Higgs'”are employed in building the proton-antiproton pair from the last pion pair. Consequently, the question is: What happened to the three 'Higgs triplets' once they had accomplished their mission?'
'It turns out that there is no need to resort to exotic new physics for finding the answer. The explanation lies much nearer at hand'”in the standard model itself. Thus, page 271 in Appendix E of Martinus Veltman's book Diagrammatica: The Path to Feynman Diagrams (1994) provides the answer. The Higgs triplets today appear in the form of Higgs ghosts (φ0, φ+, and φ−). This means that at a very early stage of the universe, four unique kinds of spinless bosons existed momentarily; but today only the original Higgs boson exists as a physical particle, while the Higgs triplets have reappeared as unreal 'ghost' particles that do not affect physical processes. See my separate article on 'Neutrino and Higgs masses' (Higgs.pdf), in which I'm now adding a section discussing Higgs ghosts (page 7).'
William: So, what are these Higgs ghosts? The Higgs boson has recently received much publicity, but I cannot remember reading about 'Higgs ghosts.'
Stig: 'Gerardus 't Hooft and Veltman turned the model for weak interactions into a logically consistent and mathematically tractable theory'”a work that rendered them the 1999 Nobel Prize in Physics for 'elucidating the quantum structure of electroweak interactions in physics.''
'In appendix E of Diagrammatica, Veltman lists 92 Feynman-graph vertices. The listing contains nine vertices describing lepton couplings, among them one with a Higgs boson and three with Higgs ghosts.'
'On page 249 in his book, Veltman notes:
Then, he goes on to explain:
This means that the Higgs ghosts are unphysical 'particles' that only play an algebraic role in electroweak calculations. In other words, their impact on physical processes is zero. Consequently, the historical role assigned to the phi bosons is very limited: they appear momentarily, suck mass from virtual leptons, deposit it at the quarks, and disappear. The spin-0 φ bosons (which should not be confused with the composite spin-1 φ meson) may be looked upon as a kind of stillborn triplets delivered by the leptons. The only directly observable physical effect caused by the brief appearance of these 'Higgs triplets' is a negative correction to the tauon-muon and muon-electron mass ratios.'
'If you haven't heard about Higgs ghosts, you are in good company, since I guess that few physicists are aware of them. The reason for this ignorance is that ghost particles are not needed in practical calculations. This is explained, for instance, by P.D.B. Collins, A.D. Martin, and E.J. Squires on page 47 in their book on Particle Physics and Cosmology (which is Ref. [20] in my paper):
Page five continues Part 3 of a three-part interview about the xSM theory.
