View Full Version : Symmetry Breaking and the Higgs Boson

2012-May-29, 08:02 AM
I was listening to a documentary on YouTube about the Higgs boson and heard some information that blew my mind, and I'd like to ask a few more questions to gain a deeper understanding of it, or to correct any misconceptions I was fed.

My current understanding is:
The laws of physics being symmetric, you would expect equal amounts of matter and antimatter to be produced. This is clearly against observations. So some symmetry breaking is needed somewhere.
W bosons and their antiparticle have recently been found to have different decay products. Implying a break in symmetry.
The presence of the Higgs field in the early Universe would have permitted this.

Now, please understand that I know next to nothing about this topic. If any of that is incorrect, please let me know.
My two questions are:
1) Was the different decay products of the W boson and its antiparticle predicted before its discovery? (If so, is there a link to that paper handy?)
2) How, in newb terms, does the Higgs field allow for symmetry breaking?

I do appreciate any responses.

2012-May-29, 05:27 PM
Afraid your understanding is a bit off.

The matter/antimatter breaking symmetry is CP violation, the breaking of the product of the C and P symmetries. Essentially swapping antimetter for matter. This is explained in the Standard model by the CKM matrix (http://en.wikipedia.org/wiki/Cabibbo%E2%80%93Kobayashi%E2%80%93Maskawa_matrix). In this the quark mixing parameters (which drive how quarks mix via the weak interaction) tun out to be complex, and this complex part gives the parameters a phase which leads to CP violation. Back in the sixties (when the first versions of this matrix were proposed) was when the first indirect CP violation was seen in neutral kaons. So I am guessing that the development of the matric came along at around the same time as evidence for CP violation - the matrix was originally introduced for a slightly different reason that CP violation.

The decay products of the W bosons preserve CP AIUI. Indirect CP violation always involves a weak current interaction, a quark to quark one.

The Higgs field not about CP violation, it is about mass. There is no simple way to explain the Higgs mechanism - I tend to glaze over at the full explanation. Essentially the only Higgs mechanism that is close to fully worked through is only applicable to W and Z bosons. Back at very high energies early in the universe the electromagnetic and weak forces were one, the electroweak force. Essentially this field was highly symmetric but unstable and at some point the symmetry broke. This led to the EM force (with massless photons as the carrier) and the weak force (with massive bosons) separating. Via one of several mechanisms (the precise one is not known) the W/Z couple to a Nambu-Goldstone boson related to this symmetry breaking and an underlying field (the Higgs field). This gives them mass. The origin of the mass of fermions and other stuff is thought to be related to this but the details are far from worked out. Mainly because the symmetry breaking has some free parameters that need to be observed - and even getting through the maths to the point where we can work them out is really hard work. To clear the jam we need to know more about the Higgs boson itself.

2012-May-30, 04:53 PM
The word I fixated on was "jam"

(must be time for my tea)


2012-Jul-05, 10:15 PM
Here's my favorite analogy:

For full symmetry, imagine a marble and a bowl with rotational symmetry. Drop the marble into the bowl. It will oscillate back and forth and settle down in the center. The bowl+marble system still has rotational symmetry. If you push the marble out of the center, it will oscillate back and forth with the same frequency no matter what direction.

For broken symmetry, imagine a bowl with a hump in the middle, but still with rotational symmetry. A bowl like a juice squeezer. Drop a marble into that bowl. It will come to rest in the trough around the hump. The bowl+marble system has lost its rotational symmetry. Furthermore, if you push the marble, it will oscillate radially, but keep going without oscillating tangentially.

The Higgs field is like that marble in a bowl with a central hump. Its lowest-energy state gives it a nonzero value.

The Higgs particle (remember wave-particle duality!) interacts with most of the Standard Model's particles, and since it has a nonzero lowest-energy field value, it's essentially omnipresent. The stronger an interaction with a particle, the more mass that particle gets as a result of that interaction.

One can predict the masses of of the W and Z from low-energy electromagnetic and weak interactions, but the elementary fermions require some fudge factors, so the Higgs explanation of their masses puts the problem back a step. But it will be possible to test the hypothesized Higgs-interaction strengths by studying Higgs-particle decays.

Ivan Viehoff
2012-Jul-06, 08:38 AM
The article Secret Symmetry and the Higgs Boson (in two parts) is excellent introduction (for the mathematically literate layman - and if you aren't at least that you have little chance) to this.