First, please pardon the ignorance behind this question. I know a fair amount of
ID: 1379443 • Letter: F
Question
First, please pardon the ignorance behind this question. I know a fair amount of math but almost no physics.
I'm hoping someone can give me a brief "big picture" explanation of how physicists were able to predict the existence of the Higgs boson. Here's a (perhaps completely wrong) example of the level of explanation I'm hoping for:
"Consider the following group [insert precise specification of a particular group here]. This group is know to have precisely [insert number here] irreducible representations. All but one of these representations corresponds to a previously-observed particle via a correspondence in which the property [insert mathematical property of representation here] corresponds to the property [insert physical property of particle here]. The Higgs Boson is the particle that corresponds to the remaining representation."
If I happen to have hit on the right story, I'd like someone to fill in the blanks. If, as is more likely, I've concocted a completely wrong story, I'd like someone to give me a more accurate story at about the same level of sophistication. Thanks!
Explanation / Answer
No, it doesn't work like that. The Higgs boson doesn't complete a set of particles that we had some theoretical reason to expect to exist. (Other particles have been predicted in roughly that way, e.g. the charm and top quarks.) So in the sense I believe you're thinking about it, physicists had no reason to predict the existence of the Higgs boson.
Where it actually comes from is the fact that particles have mass. The Lagrangian (if you're not familiar with what a Lagrangian is, let me know, I'll edit in an explanation) of the standard model is supposed to be invariant under the gauge group SU(3)
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