{"id":91,"date":"2008-11-16T14:55:33","date_gmt":"2008-11-16T14:55:33","guid":{"rendered":"http:\/\/spinor.info\/weblog\/?page_id=91"},"modified":"2022-05-06T16:23:51","modified_gmt":"2022-05-06T20:23:51","slug":"finite-electroweak-theory","status":"publish","type":"page","link":"https:\/\/spinor.info\/weblog\/?page_id=91","title":{"rendered":"Finite Electroweak Theory"},"content":{"rendered":"

The Standard Model (SM) of particle physics is an amazing theory. It accounts for all the known families of particles that make up matter, and all their interactions. It even provides a mechanism that allows particles to gain mass. Yet the theory has some shortcomings.<\/p>\n

For starters, it has a large number of free parameters. It is one thing to provide a mechanism to generate mass, it is another thing to predict the magnitude of those masses. This, the theory does not do. Individual particle masses, along with other parameters such as coupling constants, are not predicted, but determined through observation.<\/p>\n

But these are just minor problems, relatively speaking. There are two much bigger ones.<\/p>\n

First, the theory is based on the assumption that neutrinos are massless. But they aren’t. Or, at the very least, there is some mechanism beyond the SM that converts neutrinos of different flavors into one another, because we observed them do just that. What’s wrong with giving neutrinos masses, just like we give masses to charged leptons and quarks? Trouble is, neutrinos are ultra light. The corresponding dimensionless quantity in the model would have to be a very small number. People are suspicious of dimensionless quantities in a physical theory that are very far from unity. But we need either such a quantity or a new feature in the SM to account for neutrino oscillations.<\/p>\n

Second, the theory cannot account for quantum gravity, because spin-2 gravity with its dimensioned coupling constant is notoriously nonrenormalizable.<\/p>\n

One particular possibility to address these problems is a theory, developed by Moffat and others in 1991 and onwards, which addresses the problem in a somewhat unusual way. Its main feature is a non-local regularization scheme that guarantees that the theory remains finite.<\/p>\n

The cornerstone of the SM is the Higgs particle, which really does two things. First, it offers a mechanism through spontaneous symmetry breaking that allows particles to gain mass. Second, it produces exactly the right terms needed to ensure that when we calculate the probability amplitude of some physical processes, we get finite answers. But it is an oddball particle. It is the only spin-0 scalar particle in the theory. The self-interactions of the Higgs boson are a source of additional trouble.<\/p>\n

One of the original motivations for Moffat’s theory was the desire to do away with the Higgs boson. The existence of the Higgs has since been confirmed (representing another spectacular triumph for the Standard Model) but other problems remain, so Moffat’s theory remains relevant.<\/p>\n

The theory reproduces the SM at low energies, but predicts deviations at energy levels that may be reachable by present-day instruments. This is important… too many theories nowadays rely on postulates that can never, ever, be confronted with experiment!<\/p>\n

The basic steps of building the finite electroweak theory (FEW) are as follows.<\/p>\n