Hot answers tagged higgs-mechanism
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Explaining the Higgs mechanism properly is a fair bit beyond the level of the Feynman lectures, but here's an attempt.
Spontaneous symmetry breaking
In order to understand the Higgs mechanism in detail, you need to know about two concepts that are involved in quantum field theory. The first is spontaneous symmetry breaking. This is actually a pretty simple ...
9
Top's Yukawa coupling of order one is technically natural, the much smaller couplings are not natural. One may find this problem discussed under the term "hierarchy of Yukawa couplings".
The previous paragraph really says that the Standard Model doesn't have any mechanism to explain the smallness of any non-top Yukawa couplings. First, let me discuss ...
9
The anomalies in four dimensions are calculated from a triangular Feynman diagram with a chiral (left-right-asymmetric, when it comes to the couplings with the gauge bosons or gravitons) fermion running in the loop and three gauge bosons (and/or graviton[s]) attached at the vertices. For the Standard Model, all the gauge anomalies cancel (both leptons and ...
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Dbrane, aside from "beauty", the electroweak unification is actually needed for a finite theory of weak interactions. The need for all the fields found in the electroweak theory may be explained step by step, requiring the "tree unitarity".
This is explained e.g. in this book by Jiří Hořejší:
http://www.amazon.com/dp/9810218575/
Google books: ...
7
Actually, mass and charge are only superficially similar. Yes, they both appear in inverse square force laws, namely Newton's law of gravitation and Coulomb's law of electrostatic force, but both of those are approximations. Coulomb's law ignores quantum effects, which is a very slight approximation, but Newton's law ignores all of relativity, which makes a ...
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This is not as easy as it may sound: in every analogy one has to make a choice between rigor and 'poetic license'.
Personally, the one i like better is Higgs for Waldegrave: where a crowd-analogy is given. But, as they say, your milage may very.
If you'd like, you can think in terms of a 'caramel pool', Milky Way Simply Caramel: Pool : when we say that a ...
7
First, it's not really true that nothing breaks for any mass in the Standard Model. Because of the "renormalization group flows", i.e. the dependence of the couplings on the characteristic energy scales, most of the values of the Higgs mass are inconsistent and imply that the theory breaks down almost immediately at higher energies.
In particular, even the ...
6
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 ...
6
A quick answer: "screening" currents in the superconductor are proportional to the vector potential. With an appropriate choice of gauge, the screening current appears as a mass term in the wave equation for the vector potential. From "An Informal Introduction to Gauge Field Theories":
(This excerpt from Google books)
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The Higgs mechanism is no different from superconductivity, except the condensate responsible for superconductivity is a relativistically invariant scalar field.
If you have a bosonic field, its particles can be in a Bose-Einstein condensate. When this condensate is charged, you call it a superconductor. A photon in a superconductor gets a mass, and this is ...
5
In the actual local quantum field theories, theories of point-like particles, the mass correction due to the renormalization effects from (2) is divergent. It has a short-distance divergence so it is infinite. One needs to cancel the "infinite part" so that there's a finite leftover. What is the separation of the physical observed mass to (1) and (2) depends ...
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The spin-statistics thing isn't a problem, it is a theorem (a demonstrably valid proposition), and it shouldn't be addressed, it should be understood and celebrated.
The Higgs field gives us interactions between chiral fermions and the Higgs, $yh\cdot \chi_\alpha\eta^\alpha$ which produces mass terms $m \chi_\alpha\eta^\alpha$ if the Higgs field has a ...
4
Once again, I am way out of my league in answering this. I may be wrong about many things here, comments appreciated
That was just a definition of mass. The Higgs explains where rest mass (but not gravity) comes from in a mathematically rigorous manner.
One of the attempts to explain how our universe works in a mathematically rigorous manner is the ...
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The mass of a particle is the energy that it has when it is at rest. The Higgs only makes it that particles oscillate between different helicities, so that you can make them be at rest, and their energy at rest is equal to the rate of oscillation between the two helicities. This energy gravitates like any other energy.
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I think that I am confused by the question and even more confused by the last remark. When you use PV regulator, you necessarily encounter for the ghosts. When you add to a propagator of a physical field another part, which looks like a propagator with a minus sign and a mass $\Lambda_{UV}$, you pretend that there is a heavy ghost "particle" in the theory ...
4
This is my favourite simplified picture explaining the higgs mechanism:
http://krbowie.files.wordpress.com/2010/03/higgs-boson-cartoon22.jpg
In the first tree panels You can see how Einstein (a massless particle) enters a room with physicists (the higgs field) and gets slowed down by his colleagues wanting to talk to him (he couples to the higgs field and ...
4
The full answer is unknown, i.e. nobody can tell you why the electron is only 0.00484... times as heavy as the muon. In fact, all interactions of massive particles (leptons) with the Higgs are of the same form (called a 'Yukawa interaction'), but for every particle, there is a different constant of proportionality ('Yukawa coupling constant'). For ...
3
The Higgs field is a scalar field and it happens that the vacuum expectation value of that field is non-zero in our universe. It is this non-zero Higgs vacuum expectation value that gives the elementary fermions of the standard model of particle physics their rest mass. Now this Higgs field is a scalar so it is as if there is a single numerical value that ...
3
I will try to address your question, though, as David says in the comments, it is evident that you have very little background in elementary particle physics. I will bring over an event much simpler than a display of an event that could show a Higgs particle decay.
Here is a simple antiproton annihilation event whose end particles are recorded by their ...
3
Gravitational mass is a bit of a misnomer, because in General Relativity the spacetime curvature is determined (mostly) by the energy density. Mass is simply treated as equivalent to the amount of energy given by $E = mc^2$, or conversely energy is just treated as the equivalent amount of mass.
So the fact the particles are massless above the electroweak ...
3
The Higgs mechanism is itself an extension to nonabelian gauge theory of an everyday tabletop phenomenon (at least in laboratories), called superconductivity. The origin of superconductivity is the formation of a charged Bose-Einstein condensate of electron pairs, which means that magnetic fields in the material are excluded. The exponential decay of ...
3
Not quite. The Higgs mechanism actually applies at low energies. Don't think of it as an event that happens once and bestows mass upon all particles for the rest of time; instead, the Higgs mechanism is a continuous effect that explains how particles are able to have mass at low energies.
For a full(er) explanation, I'll point you to another answer of mine, ...
3
The Higgs ghosts are not Faddeev-Popov ghosts. (For starters, the Faddeev-Popov ghosts in the standard model are Grassmann-odd, while the Higgs ghosts are Grassmann-even.)
The Higgs ghosts are Goldstone bosons for the spontaneously broken part of the electroweak symmetry $SU(2) \times U(1)$, which, popularly speaking, get eaten by the massive gauge bosons ...
3
The MSSM has 2 complex doublets i.e. 8 real components in the Higgs fields. Four of them are electrically neutral (real bosons, antiparticles to themselves), four of them (i.e. two particle-antiparticle pairs) are electrically charged.
One neutral real boson and two charged ones (one charged pair) get eaten by the gauge bosons because 3 generators are ...
3
The simplest $SU(5)$ GUT Higgs transforms as ${\bf 10}$ under the gauge group, an antisymmetric tensor $5\times 4/2\times 1$ with two indices of the same kind (without complex conjugation). The 2-dimensional representation of $SU(2)$ has an antisymmetric invariant $\epsilon_{ab}$ and if you extend this antisymmetric tensor to 5-valued indices of $SU(5)$ and ...
2
Think of the Higgs mechanism as affecting rest-mass. This is the mass that a particle has when it is sitting still (you can weigh it to figure it out).
Think of gravity as affecting energy. More energy = more gravitational force. So an electron that is moving very quickly has a total energy of its rest mass (E = mc^2) + its kinetic energy.
Consider an ...
2
General relativity doesn't care about the difference between mass and energy. In the stress-energy tensor T$_{00}$ is the energy density and mass is just treated as energy divided by $c^2$. GR doesn't care what the Higgs' mechanism does, and will work just as well above the electroweak transition where the particles (well, the vector bosons at least) are all ...
2
The best non-technical explanation I've seen of this is Matt Strassler's blog article, though even this is still fairly technical, so let me see if I can interpret it a bit.
The key point is that an electron is not a particle. In Quantum Field Theory it's described as an excitation in the electron quantum field. This excitation will propagate in spacetime, ...
2
Though charge and mass are fundamentally different concepts, one can cook up an interaction like
$L = |d\phi - |\alpha|^2 A \phi|^2+\lambda(|\alpha|^2-c^2)^2 + |d_B \alpha|^2 + dA^2 + dB^2$.
Here $\alpha$ and $\phi$ are complex scalars and $A$ and $B$ are $U(1)$ gauge fields. $|-|$ denotes complex magnitude and $d_B$ is the covariant derivative for ...
2
This is a simple way to understand the screening currents in Alfred Centauri's answer. Consider the simplest model of a Superconductor--- the Landau Ginsburg model. Here you have a nonrelativistic scalar field which is both charged and has an expectation value. The situation is described by a Schrodinger field Hamiltonian:
$$ H = \int_{x} ...
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