Higgs primer for someone without field theory

[nomadreid]

Could I get a rough explanation of the following? I know I would need a whole course in field theory to understand a proper explanation of the following, but could someone give me rough answers to what certainly are naïve questions?
First, the Higgs particles are supposed to produce the masses of the W and Z bosons. This brings up three questions:
(a) What were the particles to which the Higgs particles gave the mass? Photons? Or can you separate the particles into pre-interaction with Higgs, and post-interaction?
(b) These pre-Higgs particles, being massless, would have traveled at the speed of light. Could they also have charge? If not, do the Higgs particles also give the charged W particles their charge?
(c) These cover the masses of the W and Z particles. What about all the other massive particles, such as the electron? Do the Higgs particles also give them their masses, or is there another mechanism?

 

[QuantumClue]

Could I get a rough explanation of the following? I know I would need a whole course in field theory to understand a proper explanation of the following, but could someone give me rough answers to what certainly are naïve questions?
First, the Higgs particles are supposed to produce the masses of the W and Z bosons. This brings up three questions:
(a) What were the particles to which the Higgs particles gave the mass? Photons? Or can you separate the particles into pre-interaction with Higgs, and post-interaction?
(b) These pre-Higgs particles, being massless, would have traveled at the speed of light. Could they also have charge? If not, do the Higgs particles also give the charged W particles their charge?
(c) These cover the masses of the W and Z particles. What about all the other massive particles, such as the electron? Do the Higgs particles also give them their masses, or is there another mechanism?

a) The Higgs gave mass to the Bosons, such as W and Z bosons. And in some cases, mass is provided to a photon. Basically all massless particles are given mass through spontaneous symmetry breaking. This happens because a Higgs Boson swallow goldstone particle which give rise to an inertial mass on the system.

b) Photons don't have charge. Never have had charge. If a symmetry breaks then they really aren't photons any more. W bosons can have an electric charge. The Z boson is nuetral.

c) Sure. The Higgs gave all matter mass. It even provides a mass to its own field. That is a slight simplification, but you'll get the idea hopefully.

 

[nomadreid]

Thanks, Quantumclue. You mentioning the Higgs boson swallowing Goldstone particles has given me a new direction to look into. Also the idea of the Higgs giving a mass to its own field is something that looks interesting, how it avoids infinite regress. But I am still puzzled as to where the electric charge comes from: whether they are in the particles before they get mass, or whether the process of getting mass also gives some of them charge. Do you have a quick answer to this last question?

 

[QuantumClue]

Thanks, Quantumclue. You mentioning the Higgs boson swallowing Goldstone particles has given me a new direction to look into. Also the idea of the Higgs giving a mass to its own field is something that looks interesting, how it avoids infinite regress. But I am still puzzled as to where the electric charge comes from: whether they are in the particles before they get mass, or whether the process of getting mass also gives some of them charge. Do you have a quick answer to this last question?

So from mass, you now ask how charge arises?

I have no quick answer. To understand charge, you might want to learn about the Dirac Equation. I can give you a sufficient lesson on the Dirac Equation if you want. Out of that equation, you can find charged particles, and even negatively charged particles.

 

[vricotti]

Hello, I have a couple questions about the Higgs particle. I don't have any real background in physics I just read about it on my spare time so forgive me if I come off naive.

1. I am confused on exactly how the Higgs particle imbues a particle with mass. Does it already have a mass and transfers some or all of it to another particle?

2. If it is what gives every object its mass, then wouldn't it be present in every mass carrying particle?

Additionally, I have only learned about quantum mechanics through a few general discussions of the science. For example on io9 http://io9.com/#!5640527/the-undiscovered-particles-on-the-edge-of-known-physics . I was able to comprehend most of what the website covered but I have no real grasp on the interactions of these particles. Can you suggest a website that goes more in depth but is still accessible to a non-science major?

 

[nomadreid]

First, Quantumclue. Again, thank you for your replies. I am a little puzzled by your last reply. As far as I can see, the Dirac equation help explains where spin comes from, not where charge comes from, which was my question. If you could point this out in the promised "sufficent lesson on the Dirac equation", that would be super (you can assume a mathematical background on my part, but only very basic quantum physics, with extremely limited field theory), but if this would be too arduous, any pointers you can give as to where to look for how the Dirac equation expresses charge as an emergent property would be much appreciated..

Might as well be hung for a sheep as for a lamb, so allow me another question on this subject. All the sites that I have seen concerning mass production talk about symmetry breaking at very high temperatures, soon after the Big Bang. However, if, as you say, all mass is acquired via the Higgs, wouldn't this also include the mass acquired, albeit for a very short time, in matter-antimatter pair production?

To vricotti: I am probably not the best source for the links you asked for, as I am not a physicist, but it would probably help those who can reply to you if you would indicate your mathematical background, because the sites explaining such things vary greatly in the amount of mathematics mastered by the reader.

 

[QuantumClue]

Hello, I have a couple questions about the Higgs particle. I don't have any real background in physics I just read about it on my spare time so forgive me if I come off naive.

1. I am confused on exactly how the Higgs particle imbues a particle with mass. Does it already have a mass and transfers some or all of it to another particle?

2. If it is what gives every object its mass, then wouldn't it be present in every mass carrying particle?

Additionally, I have only learned about quantum mechanics through a few general discussions of the science. For example on io9 http://io9.com/#!5640527/the-undiscovered-particles-on-the-edge-of-known-physics . I was able to comprehend most of what the website covered but I have no real grasp on the interactions of these particles. Can you suggest a website that goes more in depth but is still accessible to a non-science major?

If you want to have a particle in physics to have no mass, the equations describing them must preserve symmetry. If you want to have a mass, you must somehow break the symmetry on the particle. I shall give you some mathematical direction to this now.


$$\partial \phi' = [\partial \phi + i \phi \frac{\partial \theta}{\partial x}]e^{i \theta}$$

$$\partial \phi'* = [\partial \phi* + i \phi* \frac{\partial \theta}{\partial x}]e^{i \theta}$$

multiplying the two we get

$$= \partial \phi \partial \phi* + i (\phi \partial \phi* - \phi* \partial \phi) \frac{\partial \theta}{\partial x}+ \phi* \phi (\frac{\partial \theta}{\partial x})^2$$

which has no symmetry whatsoever! plus it is horrid to look at. Nice to note though that if the potential term was added into the equation (well actually taken away, but you get my drift :) it would not effect its symmetry). Why do people always forget to plug in the potential $$V(\phi* \phi)$$, it has some of the most interesting dynamics!

Nevertheless, this was not good, so we had to add an extra four-field to our system, namely the four-vector potential $$A_{\mu}$$. Added with our covariant derivative, which we have seen so far has the form:

$$D_{\mu}\phi = \partial_{\mu}\phi + iA_{\mu}\phi$$

$$D_{\mu}\phi* = \partial_{\mu}\phi* - iA_{\mu}\phi*$$

simply has an addition to our field which has an appearance of $$\partial \rightarrow \partial - iA$$.

This allowed us to have a nice symmetry in the making - interesting though how we had to mould the equations a few times, a bit of nip and tuck if you will. This gives us the same reasons why a photon for instance should be massless... because there has been no breakage of symmetry on the equations.

So a Higgs gives mass to particles when there is a breakage in symmetry, the same kind of breakage when the higgs gains a mass from it's goldstone boson, which is basically a longitudinal photon. So a Higgs gets a mass from its own field by gobbling a goldstone boson, which is a photon in the lowest energy state $$\phi=0$$, and then the Higgs gives mass to other particles via its new mass. It is undoubtably quite an elegant process, but not very believable I must add.

 

[QuantumClue]

First, Quantumclue. Again, thank you for your replies. I am a little puzzled by your last reply. As far as I can see, the Dirac equation help explains where spin comes from, not where charge comes from, which was my question. If you could point this out in the promised "sufficent lesson on the Dirac equation", that would be super (you can assume a mathematical background on my part, but only very basic quantum physics, with extremely limited field theory), but if this would be too arduous, any pointers you can give as to where to look for how the Dirac equation expresses charge as an emergent property would be much appreciated..

Might as well be hung for a sheep as for a lamb, so allow me another question on this subject. All the sites that I have seen concerning mass production talk about symmetry breaking at very high temperatures, soon after the Big Bang. However, if, as you say, all mass is acquired via the Higgs, wouldn't this also include the mass acquired, albeit for a very short time, in matter-antimatter pair production?

To vricotti: I am probably not the best source for the links you asked for, as I am not a physicist, but it would probably help those who can reply to you if you would indicate your mathematical background, because the sites explaining such things vary greatly in the amount of mathematics mastered by the reader.

Well, not quite - The dirac equation also deals with negative solutions of particles. In a sense, they predict charge! It is revolutionary, atleast for me when I learned about the Dirac equation, that it predicted oppositely charged particles.

You must remember that charge is only a marker for our tool, and our tool is mathematics. No one actually believes that a charge is either negative or positive, only that certain charges repel others and other attract in the presence of another relative charge. Charge is like mass. It is an intrinsic property of matter - even neutral particles, because they still contain a magnetic dipole moment.

The idea of charge is frought with mystery. As intrinsic as it is, we only have an incomplete picture to an otherwise complete set of theories. Yang Mills theory however can and does predict massless particles which have charges, but eventually it was decided this theory was wrong. So the higgs field might have a lot more to do with charge than what we realize.

 

[nomadreid]

Thank you again, Quantumclue. I shall go back and look more carefully at the Dirac equation.
In your reply to vricotti, you expressed a bit of skepticism vis-à-vis the present use of Higgs for mass-giving, so I pose the following question with the caveat "if the present models are correct". I would like to return to that part of my last post which you did not answer, that of the role, if any, of the Higgs field in pair production. You wrote that : "The Higgs gave all matter mass." From this I would conclude that the Higgs is involved in matter-antimatter pair production. But I do not find any mention of this in articles about pair production, which all talk about particles obtaining mass shortly after the big bang at a critical energy far larger than that which is usually available for pair production. I thought that perhaps the short-term nature of this mass might have some bearing, but in something like Hawking radiation or Unruh effect, the mass becomes more permanent, so this didn't seem to be a fruitful line of reasoning. So, in short: is the same symmetry-breaking involved for pair production as for the gaining of mass of other particles?

 

[QuantumClue]

Thank you again, Quantumclue. I shall go back and look more carefully at the Dirac equation.
In your reply to vricotti, you expressed a bit of skepticism vis-à-vis the present use of Higgs for mass-giving, so I pose the following question with the caveat "if the present models are correct". I would like to return to that part of my last post which you did not answer, that of the role, if any, of the Higgs field in pair production. You wrote that : "The Higgs gave all matter mass." From this I would conclude that the Higgs is involved in matter-antimatter pair production. But I do not find any mention of this in articles about pair production, which all talk about particles obtaining mass shortly after the big bang at a critical energy far larger than that which is usually available for pair production. I thought that perhaps the short-term nature of this mass might have some bearing, but in something like Hawking radiation or Unruh effect, the mass becomes more permanent, so this didn't seem to be a fruitful line of reasoning. So, in short: is the same symmetry-breaking involved for pair production as for the gaining of mass of other particles?

That is a very good question.

The answer is yes. Photons can have enough energy to create particles, and eventually these particles will reduce back to the energy which created them. Whilst all particles can decay into many other particles because they contain energies as well, it is a growing belief among many rouge posters and even a few scientists to speculate that photons could have been the first particles to experience symmetry breaking, since when we trace the universe back to its very early ages, we find that the first epoch was a radiation era. So it has been wondered if some kind of all-permeating electromagnetic field spontaneously broke in its internal symmetries through the presence of a mediator, the Higgs Boson of course, and created the great array of particles we observe in the Standard Model.

This next part is only an educated guess:

Symmetry-breaking however must reverse in the case of your question, simply because of the issue of conservation. Charge conservation plays the major role in determining why photons are always released in particle-antiparticle annihilations. So one could take an action on the fields Langrangian and work out some kind of relationship between the principle of least energy and how it is related to the idea of a reverse symmetry-phase. I don't know any mathematical process, but in the same idea, the goldstone boson is a photon on the lowest energy scale around some mexican hat potential. Mass only appears when that photon strays off the lowest energy scale. Symmetry is broken and viola! Mass has now entered the energy system in the form of inertia.

Equally, one could say that annihilation is the back-reaction. Instead of a longitudinal photon straying off the path and gaining mass the post state of the photon can easily fall back to the same energy state, because when a particle and an antiparticle meet, the conservation of charge dictates that two photons are released, and as I have explained before, they contain absolutely no charge whatsoever.

So what you are left with again is an energy jump, and this jump is the loss of mass when symmetry is restored on the system.

 

[nomadreid]

Thanks very much, QuantumClue. Your answer was very helpful.