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Alexey Petrov | WSU | USA

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Higgs mechanism for electrical engineers

Since the Higgs boson’s discovery a little over a year ago at CERN I have been getting a lot of questions from my friends to explain to them “what this Higgs thing does.” So I often tried to use the crowd analogy that is ascribed to Prof. David Miller, to describe the Higgs (or Englert-Brout-Higgs-Guralnik-Hagen-Kibble) mechanism. Interestingly enough, it did not work well for most of my old school friends, majority of whom happen to pursue careers in engineering. So I thought that perhaps another analogy would be more appropriate. Here it is, please let me know what you think!

Imagine Higgs field as represented by some quantity of slightly magnetized iron filings, i.e. small pieces of iron that look like powder, spread over a table or other surface to represent Higgs field that permeates the Universe. Iron filings are common not only as dirt in metal shops, they are often used in school experiments and other science demonstrations to visualize the magnetic field.  It is important for them to be slightly magnetized, as this represents self-interaction of the Higgs field. Here they are pictured in a somewhat cartoonish way:

Image

How can Higgs field generate mass? Moreover, how can one field generate different masses for different types of particles? Let us first make an analogue of fermion mass generation. If we take a small magnet and put it in the filings, the magnet would pick up a bunch of filings, right? How much would it pick up? It depends on the “strength” of that magnet. It could be a little:

Image

…or it could be a lot, depending on what kind of magnet we use — or how strong it is:

Image

If we neglect the masses of our magnets, as we assumed they are small, the mass of the picked up mess with the magnets inside is totally determined by the mass of the picked filings, which in turn is determined by the interaction strength between the magnets and the filings. This is precisely how fermion mass generation works in the Standard Model!

In the Standard Model the massless fermions are coupled to the Higgs field via so-called Yukawa interactions, whose strength is parametrized by a number, the Yukawa coupling constant. For different fermion types (or flavors) the couplings would be numerically different, ranging from one to one part in a million. As a result of interaction with the Higgs field (NOT the boson!) in the form of its vacuum expectation value, all fermions acquire masses (ok, maybe not all — neutrinos could be different). And those masses would depend on the strength of the interaction of fermions with Higgs field, just like in our example with magnets and iron filings!

Now imagine that we simply kicked the table! No magnets. The filings would clamp together to form lumps of filings. Each lump would have a mass, which would only depend on how strong the filings attract to each other (remember that they are slightly magnetized?). If we don’t know how strong they are magnetized, we cannot tell how massive each lamp will be, so we would have to measure their masses.

Image

This gives a good analogy of the fact that Higgs boson is an excitation of the Higgs field (the fact that was pointed out by Higgs), and why we cannot predict its mass from the first principles, but need a direct observation at the LHC!

Notice that this picture (so far) does not provide direct analogy to how gauge bosons (W’s and Z bosons) receive their masses. W’s and Z are also initially massless because of the gauge (internal) symmetries required by the construction of the Standard Model. We did know their mass from earlier CERN and SLAC experiments — and even prior to those, we knew that W’s were massive from the fact that weak interactions are of the finite range.

To extend our analogy, let’s clean up the mess — literally! Let’s throw a bucket of water over the table covered with those iron filings and see what happens. Streams of water would pick up iron filings and flow from the table. Assuming that that water’s mass is negligible, the total mass of those water streams (aka dirty water) would be completely determined by the mass of picked iron filings, just like masses of W’s and Z are determined by the Higgs field.

This explanation seemed to work better for my engineering friends! What do you think?

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