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.
I believe "flavor-diagonal" means not changing flavor? What flavor are we refering to in this electrowerak contex?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.
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.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..?
I always thought the quark condensate [tex]<\bar{q}q>[/tex] order parameter for the dynamical breaking of chiral symmetry constitues another motivation, but maybe I am oversimplifying.The reason why I said that "technicolor" is the most "obvious" choice is because it happens elsewhere: that's how superconductors work!
I've just learned Higgs mechanism in my particle physics course.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?
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...I always thought the quark condensate [tex]<\bar{q}q>[/tex] 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?
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...It is not a force since it is scalar, forces have direction.
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!!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 [tex]U(1)\times SU(2)[/tex] 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 might go so far as to say the "ONLY solution!" :tongue2:One solution for this situation is spontaneous symmetry breaking(SSB).
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.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.
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!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!