# Higgs Particle

What is a Higgs Particle?

Staff Emeritus
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A Higgs particle is the quantum of the hypothetical Higgs field which supports the theoretical Higgs mechanism for giving mass to particles.

Originally the electroweak theory had four bosons, or force carrier particles, and the theory said they were all massless. Now one of the particles was the photon, and it was already considered massless, so that was OK. But the other three particles were known as carriers of the weak force, and thirty years of experiments (at that time in the 1960s) showed that they had to have mass. So if the mass didn't come out of the gauge theory, where would it come from?

Several people thought up the answer, and the one who got noticed was Peter Higgs. Suppose there was a simple field with a curious property. Most fields have their minimum strength at zero energy. But suppose this field had its minimum strength at some positive energy. Then {..do a lot of math..} interacting with the quantum of that field (the Higgs particle) would slow another particle down. Make it act like it had MASS.

So that is the current idea on how the massive particles in the standard model get that way. By interacting with the quantum of a field with that odd property.

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The way it was briefly explained to me was as follows:

If you had something without any mass, even the smallest impulse could accelerate it up to the speed of light, (a photon for example, has some momentum but so little of it that you wouldn't notice one hitting you). You have heard of friction, that is a force that resists motion, now imagine a "force" that resists acceleration, this "force" is attributed to Higgs particles.
If you wave your arm around in the air, it's pretty easy. But Higgs particles can be thought of as treacle, try waving your arm around in some treacle and I imagine that it would be quite hard.

Of course this brakes down when you consider that treacle resists all motion and Higgs particles are selective on what they act on. But still it's a nice analogy to begin with.

marcus
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http://hepwww.ph.qmw.ac.uk/epp/higgs.html [Broken]

David Miller a physicist at University college London responded to the UK science ministry "Waldegrave Higgs challenge" by inventing an explanation of the Higgs field using Margaret Thatcher and a cocktail party as a metaphor.

this is an example of humor in the British Isles. In fact it is
a rather good example. It was an admirable idea to hold an
"explaining contest" in the first place. the prize for the best
brief intuitive explanation of the higgs mechanism was
to be dinner at a good restaurant.

this link will give the top 4 or 5 explanations of which I believe
David Miller's to be by far the best.

However treacle is very good.

Originally posted by lavalamp
The way it was briefly explained to me was as follows:

If you had something without any mass, even the smallest impulse could accelerate it up to the speed of light, (a photon for example, has some momentum but so little of it that you wouldn't notice one hitting you). You have heard of friction, that is a force that resists motion, now imagine a "force" that resists acceleration, this "force" is attributed to Higgs particles.
If you wave your arm around in the air, it's pretty easy. But Higgs particles can be thought of as treacle, try waving your arm around in some treacle and I imagine that it would be quite hard.

Of course this brakes down when you consider that treacle resists all motion and Higgs particles are selective on what they act on. But still it's a nice analogy to begin with.

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The Higgs particle (so far only the neutral scalar member) is included in a forward term in the electro-weak Lagrangian, but only with a flavor-diagonal coupling. Just remember that the Z particle and photon can be taken as an admixture of the originally proposed W~3 and B particle fields that couple to isospin and weak hypercharge respectively. The Z particle naturally gains a mass upon symmetry breaking, giving you a massless photon field A and the massive weak neutral current Z. The W+ and W- are alot simpler, just complex combinations of W~1 and W~2 such that W+ = W~1 - iW~2 and W- = W~1 + iW~2. The Higgs should also assign masses to the various quarks and leptons, as well as having an effect on the masses of the gauge bosons.

Well I'm glad that's been cleared up?!?

Staff Emeritus
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Originally posted by mormonator_rm
The Higgs particle (so far only the neutral scalar member) is included in a forward term in the electro-weak Lagrangian, but only with a flavor-diagonal coupling. Just remember that the Z particle and photon can be taken as an admixture of the originally proposed W~3 and B particle fields that couple to isospin and weak hypercharge respectively. The Z particle naturally gains a mass upon symmetry breaking, giving you a massless photon field A and the massive weak neutral current Z. The W+ and W- are alot simpler, just complex combinations of W~1 and W~2 such that W+ = W~1 - iW~2 and W- = W~1 + iW~2. The Higgs should also assign masses to the various quarks and leptons, as well as having an effect on the masses of the gauge bosons.

I believe "flavor-diagonal" means not changing flavor? What flavor are we refering to in this electrowerak contex?

flavor diagonal

That is correct. Any interaction with a Higgs field should not change the flavor of the particle, i.e. it should not change any of the Iz, S, C, B, or T quantum numbers, which represent the isospin (characteristic of up and down quarks) and the flavors of the heavier quarks (strangeness, charm, bottom, top). So none of the quark types should change in the process, and the isospin will not be changed either.

Hi:

Is there any theory that may explain why particles have mass if the higgs boson isn't found? and what does that theory says..?

blechman
Hi:

Is there any theory that may explain why particles have mass if the higgs boson isn't found? and what does that theory says..?

The key point is that the electroweak theory is spontaneously broken, and this is what allows things to get a mass (otherwise masses would violate gauge invariance). The simplest, most obvious way to do this is to propose the existence of a scalar field that breaks the symmetry. This is the Higgs.

However, there's no reason why nature had to be so simple-minded (Occam's Razor never impressed me!). So there are many more complicated ways that could explain how electroweak symmetry is broken.

The most obvious choice (I'll tell you why in a minute) is that a fermion-fermion pair form a "condensate" - that is, the two fermions pair up into a spin-0 state (has to be, otherwise it would break Lorentz invariance) and then pick up a vacuum expectation value. This is the basic idea behind the theories of "technicolor" theories. Unfortunately, careful measurements of the standard model parameters have all but ruled out these kinds of theories except in some rather contrived circumstances, and even I have to acknowedge Occam's Razor sooner or later! The reason why I said that "technicolor" is the most "obvious" choice is because it happens elsewhere: that's how superconductors work! The electrons pair up (called a "Cooper pair") and acquire a vacuum expectation value, thus creating superconductivity. In fact, before Cooper (and Bardeen and Schrieffer) figured out that this was happening, there was another theory by the famous Russians Landau and Ginzberg, who proposed.... that's right: a scalar field that gets a vev!

So you see, history has a way of repeating itself. Just to emphasize the point: sometimes particle physicists would say that we are living in "an electroweak superconductor!"

To wrap up your question: lots of people are trying to come up with ways to break electroweak theory without a Higgs scalar field (or at least not the simplest model) - sometimes you need more scalars, sometimes extra dimensions, sometimes fermions, the list goes on. But the key is in the breaking of electroweak gauge symmetry - all of our data to this point fits in extremely well with the notion of an electroweak gauge theory (Glashow-Weinberg-Salam). If masses are to come about, this symmetry must be broken. Whether by a dumb scalar, fermion penpals, or something more exotic... who's to say?

blechman
Putting aside the issue of mass for a moment: I should also mention that there IS something waiting for us out there! If there is no Higgs at all, then we have a prediction that at energies around a TeV, the W and Z bosons become strongly coupled (like the gluons of QCD) and something dramatic will occur when we probe at those energies with the LHC. So I think I am safe in saying that no matter what happens: the LHC will find something. Either a Higgs boson, something else that is doing the Higgs boson's job (see above), or something really whacky with strong couplings (perhaps new composite particles of some kind, along the same line as hadrons in QCD).

ADDED: this last possibility is unlikely, though, since cosmic rays probe at energies even higher than TeV and they don't seem to produce such new particles. But you never know... Last edited:
Haelfix
As was oft mentioned at the recent Planck conference, if you abandon Occams razor, you can sadly evade most of those no lose theorems with a host of hidden sector fantasies.

Very depressing, but hopefully completely incorrect.

The reason why I said that "technicolor" is the most "obvious" choice is because it happens elsewhere: that's how superconductors work!
I always thought the quark condensate $$<\bar{q}q>$$ order parameter for the dynamical breaking of chiral symmetry constitues another motivation, but maybe I am oversimplifying.

If the Higgs particle is a gauge boson, what force is it carrying? Is mass/inertia a fundamental force? Is the Higgs force anything like the fundamental forces? I looked up http://en.wikipedia.org/wiki/Higgs_mechanism#Superconductivity" and it said that the force is like superconductivity, but I got lost in the technicality. Are there virtual Higgs particles like virtual photons that mediate the force?

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malawi_glenn
Homework Helper
It is not a force since it is scalar, forces have direction.

If the Higgs particle is a gauge boson, what force is it carrying? Is mass/inertia a fundamental force? Is the Higgs force anything like the fundamental forces? I looked up http://en.wikipedia.org/wiki/Higgs_mechanism#Superconductivity" and it said that the force is like superconductivity, but I got lost in the technicality. Are there virtual Higgs particles like virtual photons that mediate the force?
I've just learned Higgs mechanism in my particle physics course.
Please allow me trying to present my understanding.(Please correct me if I got wrong)
Higgs particle is not a gauge boson. Instead, it is a scalar doublet introduced to break the $$U(1)\times SU(2)$$ symmetry by using so called spontaneously symmetry breaking process, i.e. the ground state of the theory breaks the symmetry of the Lagrangian.
From experiments, we know that weak interaction is a short-ranged interaction so that it is mediated by massive bosons, however, we cannot add the mass term by hand into the Lagrangian, because if we do this way, we would not only break the gauge symmetry but also make the theory unrenormalizable. One solution for this situation is spontaneous symmetry breaking(SSB). We introduce a scalar field to accomplish SSB, it is Higgs boson.
Higgs field also accounts for the masses of the gauge bosons and fermions. They would eat the Higgs particle and turn into masses. The Higgs boson is not the fundamental matter particles(quarks, leptons...) nor the gauge bosons.
So I guess it would not interact through the four fundamental interactions.

BTW, I have also some questions about Higgs mechanism. Is there anyone can explain what is the "hierarchy problem"?
And, what is "little Higgs theory?" Thanks!

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Haelfix
"BTW, I have also some questions about Higgs mechanism. Is there anyone can explain what is the "hierarchy problem"? And, what is "little Higgs theory?" Thanks! "

Try wikipedia first, and then maybe ask specifics. The latter is a bit of an advanced topic and requires some machinery to fully explain beyond a cursory handwavey exposition.

The Hierarchy problem can be phrased in many ways, amongst them 'why is gravity or the GUT scale so high relative to the mass of the Higgs'. Its probably the most serious theoretical problem in all of particle physics today, and we eagerly await the LHC to help us resolve it.

blechman
Let me respond in bulk:

I always thought the quark condensate $$<\bar{q}q>$$ order parameter for the dynamical breaking of chiral symmetry constitues another motivation, but maybe I am oversimplifying.

absolutely! yet another great example! there are lots of others in physics - and despite Einstein's maxim of "You should never repeat a good joke!" I think repetition of concepts suggests something. but that's just me... If the Higgs particle is a gauge boson, what force is it carrying? Is mass/inertia a fundamental force? Is the Higgs force anything like the fundamental forces? I looked up http://en.wikipedia.org/wiki/Higgs_mechanism#Superconductivity" and it said that the force is like superconductivity, but I got lost in the technicality. Are there virtual Higgs particles like virtual photons that mediate the force?

It is not a force since it is scalar, forces have direction.

Er.... what about pions, mediating the strong nuclear force in nuclear physics? Yes, bosons can be thought of as mediating forces, and the massive Higgs would generate a "Yukawa Potential" between the fermions (hence "yukawa couplings" in the SM!!). However, I think this "force" is interpreted as part of the "weak nuclear force" since the relevant Feynman diagrams are the same as if you exchanged a Z-boson. People with more experience with nonrelativistic potentials can perhaps give a better explanation than this...

I've just learned Higgs mechanism in my particle physics course.
Please allow me trying to present my understanding.(Please correct me if I got wrong)
Higgs particle is not a gauge boson. Instead, it is a scalar doublet introduced to break the $$U(1)\times SU(2)$$ symmetry by using so called spontaneously symmetry breaking process, i.e. the ground state of the theory breaks the symmetry of the Lagrangian.
From experiments, we know that weak interaction is a short-ranged interaction so that it is mediated by massive bosons, however, we cannot add the mass term by hand into the Lagrangian, because if we do this way, we would not only break the gauge symmetry but also make the theory unrenormalizable.

These are the same statement: if you violate gauge invariance explicitly you will end up with a nonrenormalizable theory, which will break down at roughly 4pi*M (M=mass of the gauge boson). This requires a bit of calculation to prove, but it's true. Therefore, with M_W = 100 GeV, we expect to either see a Higgs boson (or something like it), or we expect to see the theory break down at around a TeV. Thus Spake the LHC!!

One solution for this situation is spontaneous symmetry breaking(SSB).

one might go so far as to say the "ONLY solution!" :tongue2:
We introduce a scalar field to accomplish SSB, it is Higgs boson.
Higgs field also accounts for the masses of the gauge bosons and fermions. They would eat the Higgs particle and turn into masses. The Higgs boson is not the fundamental matter particles(quarks, leptons...) nor the gauge bosons.
So I guess it would not interact through the four fundamental interactions.

now you've lost it. The higgs is not a gauge boson, or a fermion, but it DOES have quantum numbers under SU(2)xU(1) - it has isospin = 1/2 and hypercharge = 1/2 (in a certain normalization) so it WILL interact with the W and Z boson, but since it is electrically neutral it won't interact with the photon, and since it has no color, it won't interact with the gluon. It's interactions with the fermions are given by additional interactions called "Yukawa interactions", and these will generate a Yukawa force between the fermions (see above) as well as allowing the fermions to get mass when the Higgs gets a vev.

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blechman
BTW, I have also some questions about Higgs mechanism. Is there anyone can explain what is the "hierarchy problem"?
And, what is "little Higgs theory?" Thanks!

Those are two very different questions. The "Hierarchy Problem" is the statement that when you turn QUANTUM field theory on, the quantum corrections make the Higgs mass want to be around the heaviest scale there is. If you think about it for a second, that scale is the Planck mass (where Gravity is important) around 10^{18}[/itex] GeV. But recall what I said above: we expect to see the Higgs below a TeV, or else the electroweak theory breaks down! So the Higgs cannot be that heavy!

So what's stopping it?! That's the million dollar question in particle physics right now. There are lots of ideas. I will list three of the more popular (but by NO means exaustive):

1. Supersymmetry - this is when every fermion of the standard model gets a boson buddy, much in the same philosophy that every particle gets an antiparticle. Then fermions and bosons are contributing to the quantum corrections, and it turns out that these contributions are equal and opposite in sign so they cancel. Of course, we have not seen a spin-0 electron with a mass of 0.5 MeV, nor have we seen a massless spin-1/2 gluon, so this symmetry must be broken. but if it's broken SPONTANEOUSLY (there it is again!) then it turns out that the cancellation persists. And we would expect to see a bunch of new particles at the LHC. This is probably the most popular solution right now for a variety of reasons (political as well as physical!).

2. Technicolor: this is what I was mentioning earlier, where the Higgs is replaced with new fermions that condense. This is a solution since when you get to the TeV energies, you can actually MAKE these new fermions so that's what prevents the electroweak force from going berserk, and now there's no scalar so there's no problem with light masses.

3. Little Higgs: what you want. Without trying to go too far, the basic idea is the the Higgs boson itself is a goldstone boson of yet another spontaneously broken symmetry. This saves the day, since goldstone bosons are massless, so there's no problem with the mass being too heavy (it's zero!). Of course, the mass cannot be exactly zero (1. that would not be consistent with the nature of SM; 2. we haven't seen it!) so it must get a small mass from explicit breaking of the symmetry. This is exactly how pions get mass in the chiral lagrangian - they are goldstone bosons (massless) that get a mass from the chiral-symmetry-breaking quark masses. The idea is the same here. Of course, this begs the question: what is the symmetry that the Higgs is the goldstone of? This is where the speculation starts!

Well, I see that while I've been typing this long rant, Haelfix has made the excellent suggestion of trying to look it up for yourself. But I hope this gets you started.

Hi:

I have another question, If mass of all particles may be explained by a theory called "the Higgs mechanism", Are there any theories that may explain why do particles have electric charge, color charge and flavour charge? and if there are, what do those theories say?

Thanks a lot for your help

blechman
Hi:

I have another question, If mass of all particles may be explained by a theory called "the Higgs mechanism", Are there any theories that may explain why do particles have electric charge, color charge and flavour charge? and if there are, what do those theories say?

Thanks a lot for your help

The short answer is no, there are no such theories that I am aware of. Some theories allow for the "calculation" of these charges, but they're really just shifting the problem - for example, GUT theories can explain the charges, but then why is it THAT particular GUT that Nature decided to use? A similar argument follows from string constructions, although the Landscape paradigm tries to get around this.

In the end, the key point about mass, as opposed to the charges that you mention, is that naively, mass is FORBIDDEN in the standard model (it breaks the gauge symmetry) and so it is a nontrivial question how to realize masses (which of course we have to do, since Nature has masses!). So the question of mass is on a different level than that of charges.