Ever since I started studying physics, I’ve been hearing about the Higgs boson which is said to be an essential part of the Standard Model. It’s supposed to be responsible for giving other particles their inertial mass. But what I can’t figure out is why this particle is so important to the Standard Model. Surely a particle that is the basis of mass would have something to do with quantum gravity, which is way outside the Standard Model. Wouldn’t all these massive Higgs particles floating around cause some kind of gravitational effect?
Taking the questions slightly reordered:
The short answer is that the Higgs particle is a byproduct of the Higgs mechanism that allows masses to be present in a (non-Abelian) gauge theory, of which the Standard Model (SM) is one example, and that theory still to be renormalisable.
As you may know, renormalisation is a way of extracting sensible answers from some quantum field theories. However, this doesn’t work for almost any field theory one can think of. And that includes any simpler version of the SM, unless this simpler version is one in which all the particles are massless. With the Higgs mechanism in its simplest form, you take this simpler massless version of the SM and add another massless field/particle. This then interacts with the other fields/particles in the model. The trick is that the result of these interactions is that some of the particles types now behave as if they’re massive. So you can think of the SM in either of two ways. It’s a theory that only contains massless particles and these interact together in a specific way. Or it’s a theory in which there are massive particles and these interact in a different way. As a result, it turns out that the SM is renormalisable, despite being able to describe massive particles.
The Higgs particle itself is one of the massive particles in the second way of thinking about the theory.
[As a caveat, when the Higgs mechanism was introduced, this type of renormalisation was the only way of extracting sensible answers. Three decades on, this is no longer so true and so such renormalisability is no longer regarded as quite so special a property of possible field theories.]
Any massive Higgs particles will behave gravitationally just like any other massive particles, at least in general relativity (GR). But free (technically, real) ones are hard to produce - hence they’ve never been observed to date, even at accelerators.
Now you might be worrying how gravity can have any effect on particles in the SM if they’re really massless particles interacting with another massless field. If we can describe the SM in this way - as just containing massless particles - what on earth are the masses that enter into GR? But it’s a fundamental feature of GR that energy interacts with spacetime in the same way as matter. Now the interactions that make it seem as if stuff is massive in the SM involve energy. Essentially, in flipping back and forth between these two ways of thinking about the SM - massless particles that are interacting or massive particles - we’re just changing how we divide between energy and mass. Which GR doesn’t care about. So the particles described by the SM just behave like massive particles as far as GR is concerned.
This is a fair point and one that most physicists would agree with to a greater or lesser extent, albeit in a slightly different form.
For the Higgs mechanism doesn’t really explain the particle masses at all. For instance, take electrons. In the massless version of the SM, these are described by a massless electron field. Throw in the Higgs interactions and this now looks like a massive electron field. But how massive these electrons appear depends entirely on how strongly they interact with Higgs particles. Which the theory doesn’t specify. We just have to set it so that the electron mass comes out as observed. You then have to do the same for every different type of particle. So, issues of renormalisation aside, in a sense all you’ve done is swap a list of particle masses for a list of interaction strengths.
But the SM was never intended to explain everything: it’s always been regarded as a temporary stop-gap, short of a better theory. The swap has still been a suggestive change and there have been endless hypothetical attempts over the last few decades to explain those interaction strengths. Most of these don’t appeal to quantum gravity, but they’ve also usually been stop-gap solutions of one sort or another themselves.
Expecting that it will require a Theory of Everything, incorporating gravity, to sort all this out completely is certainly not silly. The important point thus far is that the SM, including the Higgs mechanism, has been enormously useful in making sense of what data we have. As an interim hack, that’s pretty good going.
What happens if they don’t find the Higgs with the LHC? Just assume a bigger Higgs, or try something new? If the latter, any other viable candidates out there?
The LHC should find any SM Higgs up to about 1 TeV. Standard Model theoretical bounds and electroweak fits to current experimental data put the Higgs mass in the 130 GeV to 190 GeV range, with m[sub]Higgs[/sub]<219 GeV at the 95% confidence level.
If the LHC sees no Higgs, then the current incarnation of the Standard Model is out the window. As you might expect, there are plenty of theorists with their pet formalisms to handle such a scenario, but I haven’t looked at any of these theories in detail. Fortunately, if the LHC sees no Higgs, it should still be able to say a lot about alternate theories (as a missing Higgs could come hand-in-hand with non-SM behaviour in many measurable quantities.)
Excellent treatment, but I think the part that’s missing is the central role of Higgs in spontaneous breaking of gauge symmetries. If the potential function of a field is like a bowl, then the ground state is the center and is symmetric under rotations of the bowl. If it’s shaped like a bowl with a bump in the bottom, the ground state is now at a (“random”) point along the circle where the bump meets the sides of the bowl. Taking the field and expanding its motion as the ground state plus some vibrations and expressing the vibrations as their own field (essentially a change of variables) makes a new set of equations for the interaction of the field and the symmetry generators. The symmetry is broken (by picking a point on the circle) and the generators of the gauge symmetry – which formed a collection of massless fields at the outset – now show up in the new equations with mass terms.
What I’ve never been able to quite grok is how the Higgs is supposed to also “impart” mass to anything but gauge bosons. It’s a fine description of the electroweak interaction, but I can’t see a way of using the same particle to do the same thing for, say, a (1/2,0)+(0,1/2) Dirac field (electron). Does it even make sense to talk in that way, or is the statement “Higgs gives mass to particles” an example of physicists overgeneralizing for the “benefit” of hoi polloi.
Apologies for the horrendous clang of a name being dropped, but Peter Higgs was one of my physics lecturers: I’m afraid I didn’t understand Group Theory nearly as well as the erudite chaps in this thread, but I enjoyed his story of his mechanism appeared “out of nowhere” up a Scottish mountain one day.
Thanks. I actually conciously decided not to mention symmetry breaking. It would have have added to an already long post and I also half-suspect that a concentration on this aspect of the Higgs mechanism in what ricksummon had heard may have been what was confusing. Still, it is crucial and probably should have been mentioned, at least in passing.
The thing to realise is that once you’ve introduced a Higgs doublet to give masses to the gauge bosons all sorts of other gauge invariant terms become allowed. In particular, you can construct such terms that correspond to a fermion-antifermion-Higgs vertex. Include these in the Lagrangian and then the broken version includes a mass term for the fermion. For the details, see pages 9-11 of this lecture by Peskin, for example. Arguably less elegant than for the gauge bosons, but still the same broad idea.
Truth be told, I didn’t get much out of Peter’s undergraduate group theory course when I took it - quite some time ago now - either.
Isn’t Higgs primarily a physicist? Not to slight physicists, but I’m not sure how well I’d grok group theory (much less Lie groups) if I’d first picked it up from a class taught by one rather than a mathematician.
Yes, Higgs’ background is in theoretical physics - that was his Ph.D. from Kings in London and his positions (now emeritus professor) at Edinburgh have always been in the physics department.
As far as I can reconstruct my own gradual physicist’s understanding of group theory, it was only partly from being exposed to Lie groups later on that I came to realise what he might have been on about.
I’ve read of the vector bosons describe as being a superposition of a Higgs particle, and the otherwise massless vector boson (either a B[sup]+[/sup], B[sup]-[/sup], or B[sup]0[/sup]). The combinations give you the W’s and the Z naught, respectively. Hence, I suppose, the analogy: The W[sup]+[/sup] “swallows” a Higgs, and gets its mass. Do the massive fermions (as far as I know, all of them now appear to be), also “swallow” the Higgs to some degree as well? And is the final mass an expression of what percentage of the superposition is, say, the electron, and what percentage is the Higgs, in terms of probabilities?
Even in the gauge boson case it’s not really a mixture of the two, but more a change of variables as I already indicated. I found Rubakov’s Classical Theory of Gauge Fields a great resource, especially since it covers the whole thing from the viewpoint of classical field theory and doesn’t require a lot of mucking about with quantized fields to get the general idea.
Mathocist, sadly for me, I lack your gifts. I wish fervently I’d been born with the “math gene”, but, to be honest, I felt a great sense of triumph the other day just being able to successfully solve an equation describing a four-way-logistic curve for x so I could use non-linear regressions to determine EC values in a pharmacoligic assay for any value y without relying on software to do it for me. This is the sort of exercise that would bore you to tears. But I’ll give it a look. Hopefully I can wrap some part of my brain around some portion of it.
Honestly, I don’t think this material is that difficult given multivariable calculus and a decent presentation. I really wish I could post a sufficient exposition here like I’d throw out if we were at a board, but this board is really insufficient in that regard.