How do particles interact with Higgs field?

[robheus]

Is there someone capable enough of telling in laymen's terms how particles interact with the Higgs field which causes them to acquire the property we call mass?

 

As we know how inertia works and from relativity, we know that no forces act on a mass when not in a gravity field and uniform, linear motion. Only the change of motion requires a force.

 

Does the existence of the Higgs field somehow means that there is some absolute frame of reference? (could we in theory measure our speed relative to the higgsfield?).

 

In what way is the Higgs field not an ether theorie, since that was ruled out by the Michelson-Morely experiment.

 

EDIT: in some communications the Higgs mechanism was popularly described as going through a sirope, but this anology is of course inadeqate, because it would slow down particles. But particles in a vacuum having uniform, linear speed, are not slowed down. So I guess you could not detect the absolute speed relative to the Higgs field.

 

EDIT(2): Is the Higgs field in any way related to dark energy, or are that comletely different concepts? Can a Higgs field be a candidate for the inflaton, the inlfation field?

Edited July 4, 2012 by robheus

[Aethelwulf]

There is an interaction term on your equations. If I have any time tomorrow, I will start to write up something on the Higgs Boson to try and explain how it gives a mass to systems.

[robheus]

There is an interaction term on your equations. If I have any time tomorrow, I will start to write up something on the Higgs Boson to try and explain how it gives a mass to systems.

 

great. thanks.

[alpha2cen]

Is it a concept based on the microscopic physical model?

[Aethelwulf]

Is it a concept based on the microscopic physical model?

 

The reason why I wll write it up tomorrow is because it will involve some latex and a bit of patience.

[MigL]

I know a little of the interaction as it pertains to electroweak symmetry breaking, AJB seems to be the resident expert, but maybe Aethelwulf will write up something for us.

In the above mentioned gauge theory, the spontaneous symmetry breaking creates, from the Higgs field, Goldstone bosons which interact with the formerly massless +/-W and Z gauge bosons to give mass. The Higgs field has been compared to an 'inertial drag', but it is not that simple, there is an interaction involved. And no, I don't do laTEX, so we'll have to wait for Aethelwulf.

[Severian]

The mass is defined by the two-point correlation function. Basically, every theory is described by an equation called a Lagranian. This contains all the information about the theory, including input masses and interactions. It is written in terms of the particle fields and their space-time derivatives. For example, a universe consisting of just one free real scalar particle [math]\phi[/math] with mass [math]m[/math] would be:

 

[math] L = \frac{1}{2} (\partial_\mu \phi \partial^\mu \phi - m^2 \phi^2 ) [/math]

 

Notice that the second term contains the mass. A "mass term" is a term which contains exactly two powers of the field. Basically, when you quantise the fields, each [math]\phi[/math] will be linear in both creation and annihilation operators, so each [math]\phi[/math] can create or destroy exactly one particle. Therefore a [math]\phi^2[/math] can create a particle at one point and destroy it at another, so tells you how the particle freely moves through space. The coefficient of this term is either the mass squared, for a boson, or the mass itself, for a fermion.

 

The corresponding term for a fermion would be [math] m \bar \psi \psi[/math] (in this case the fermion field is [math]\psi[/math]). Part of the problem is that terms like this would violate the electroweak symmetry. This is because the mass term mixes the left and right handed fields, while the weak force only wants to play with left handed particles. (You can see this quite physically - a left handed particle is one which has spin in the opposite direction from the direction it is travelling. But a massive particle travels slower than light, so I can switch it from left to right handed by overtaking it. Left and right handedness become frame dependent, but how can a force act on the particle in one frame but not in another?)

 

So instead (and I am simplifying a bit here) you could write a term [math]\lambda \phi \bar \psi \psi[/math] which is an interaction of a boson with a fermion (now since each field creates or annihilates one particle, this term includes things like a fermion emitting a boson, or a boson turning into two fermions. The [math]\phi[/math] is (the analogue of) the Higgs field (in this toy example). [math]\lambda[/math] is just a coefficient (called the Yukawa coupling) which is a property of the fermion.

 

Now, if the lowest energy state of the system is for when the Higgs field has a non-zero value, the universe will oscillate about this value, and we should re-express the Higgs field to remove the constant piece. So write [math] \phi = \langle \phi \rangle + h[/math] where [math]\langle \phi \rangle[/math] is a constant which is the value of the Higgs field in the lowest energy configuration. In other words, we expand around this point rather than around zero. Then the interaction I wrote above becomes:

 

[math]\lambda \phi \bar \psi \psi = \lambda \langle \phi \rangle \bar \psi \psi + \lambda h \bar \psi \psi[/math]

 

The first term is now a mass for the fermion, because it contains only two fields ([math]\langle \phi \rangle[/math] is just a constant) and the mass is [math]m=\lambda \langle \phi \rangle[/math]. The second term is an interaction between the Higgs boson and the fermion, and notice that, since [math]\langle \phi \rangle[/math] is the same for all fermions, the mass and the interaction coupling are proportional to one another.

 

Did this answer the initial question?

 

To answer the last question in the OP, the SM Higgs can't be used as the inflaton, since it has the wrong properties, but you can insert another scalar into the theory, which is also a Higgs boson (sort of) which can be used as the inflaton.

Edited July 6, 2012 by Severian

[robheus]

Thanks for this post. But I think I miss a lot of knowledge to make much sense of this, and perhaps I should investigate the basic concepts of quantum field theory and the mathematics involved more thoroughly to understand this a bit better. Any hints for some online resources (documents or lectures) that gives me more clues to quantum field theory? I have been following some video lectures from Stanford university on these kind of subjects and also some lectures of Feynmann, which helped me a lot in understanding quantum electro dynamics.

 

Unrelated to my OP I have a more philosophical question. What is the ontological status of a field, and what I mean is, in what sense does a field exist apart from particles. Isn't it the case that the field always implies particles must exist and vice versa? What would it mean if the universe consisted wholely of fields only (as was supposedly the case before baryogenenesis), since without particles interacting with the field, in what way does the field itself exist?

 

As I understand it in physics matter is described in terms of spacetime and vice versa, so matter does not exist apart from spacetime, nor does spacetime exist apart from matter. Wouldn't this also imply that fields presuppose particles exist and vice versa?

[Severian]

In particle physics the word "particle" really just means a quantized field, so particles never exist in a form that is separate from fields. So I would say that the universe is indeed composed entirely of (quantum) fields. I think the notion of wave particle duality is just confusing to students, and in my opinion shouldn't be taught.

[StringJunky]

In particle physics the word "particle" really just means a quantized field, so particles never exist in a form that is separate from fields. So I would say that the universe is indeed composed entirely of (quantum) fields. I think the notion of wave particle duality is just confusing to students, and in my opinion shouldn't be taught.

 

Can all quantum physics phenomena where it applied be described now without it?

[robheus]

In particle physics the word "particle" really just means a quantized field, so particles never exist in a form that is separate from fields. So I would say that the universe is indeed composed entirely of (quantum) fields. I think the notion of wave particle duality is just confusing to students, and in my opinion shouldn't be taught.

 

So, this means, where there is a particle there is a field, and where there is a field, there must be a particle. And it also means, before baryogenesis, during inflation, there were particles too.

 

Is that correct?

[ajb]

So, this means, where there is a particle there is a field, and where there is a field, there must be a particle. And it also means, before baryogenesis, during inflation, there were particles too.

 

Is that correct?

 

I would say that us correct; within a Poincare invariant theory we have a direct correpondence between particles and fields. However, this is muddied when we have curved space-times in general. Quite generally we should think of quantum field theory as just that, a theory of quantised fields. The particle concept is a derived notion and a special one at that.

 

It is not usually explained very well in introductory book in quantum field theory, but Poincare invariance plays a very important role in the particle concept within quantum field theory. It allows us to pick out a single vaccum which we all agree on as being empty. This is important when defining particle states. Particles are classified in terms of the representation theory of the Poincare group.

[alpha2cen]

In the Higgs' field system

Is Higgs wave generated during LHC collision?

 

Proton(Higgs acting 1, velocity near C) + Proton (Higgs acting 1, velocity near C) --->(Higgs acting disappear ---Higgs wave ?) + Energy

 

lead(Higgs acting 82) + lead (Higgs acting 82)----->(more high Higgs acting disappear ---Higgs wave ?) + Energy

 

Other examples

 

gravity disappear ===> gravity wave

 

Supernova explosion ===> gravity wave + Higgs wave???

Edited July 17, 2012 by alpha2cen

[Severian]

Actually, I take back that statement a little bit, or at least qualify it. A particle is really a quantised excitation of a field - not so much the field itself. So the Higgs boson, for example, is an excitation of the Higgs field.

 

I am not sure what alpha2cen is asking, but a (real) Higgs has a non-zero probability of being created in any collision that is energetic enough to provide its mass (125 GeV or so). You can make a virtual Higgs with any energy though - it will just decay even quicker than usual.

[alpha2cen]

How about thinking this case? A rubber balloon is in the water bath.

When we puncture the rubber balloon with a needle, does the water make a water wave?

Edited July 18, 2012 by alpha2cen

[Severian]

The wave is made up of water but the water itself did not cause the wave. But I confess, I don't see how this is relevant...

[Bobitron]

I am currently reading "The Theory of Almost Everything. The Standard Model, the Unsung Triumph of Modern Physics" by Robert Oerter. I have found it explains some of the concepts discussed very well.