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Thanks in advance to anyone who takes the time to answer this, and apologies in advance for what is probably (yet another) question here due to unfamiliarity with The Math.

I had a chance recently to visit the CMS detector at CERN (sheer luck) and it's made me curious to better understand how the Higgs field interacts with the weak gauge particle field vs. the fermion field. I've read several descriptions that connect the former with electroweak symmetry breaking and the latter with "a different mechanism" which seems to be a Yukawa coupling (which I understand to be an interaction between a scalar field --the Higgs field --and the fermion field.) Damned if I really understand the difference though --do both involve virtual Higgs bosons?

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First things first: lucky you!

Anyway, regarding your question:

As always I highly recommend Matt Strassler's series of articles on particle physics and the Higgs over at his blog. If you want more math the wikipedia page is not a bad start. (Also just noticed that Matt Strassler's latest post has a nice "if you have this background and want to know more about X start here" list.)

The Higgs field gives mass to the weak gauge bosons and the fermions through interactions it has with them and the form of the interactions is dictated by basic principles (relativity and quantum mechanics). That much is the same. The main difference is that the relative strength of the Higgs coupling to the different gauge bosons is fixed by the gauge group and charge of the Higgs field, but the relative strength of the interactions with the different fermions is not fixed by any basic principle that we know of. So we understand why the $Z^0$ boson is slightly heavier than the $W^\pm$ (and precisely so), but we have no real idea why the top quark is so much heavier than the electron.

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  • $\begingroup$ Thank you --that was extremely helpful. I hadn't seen Matt Strassler's blog before but it looks like a fantastic resource. I have become acutely aware over the years since getting out of college how essential a grasp of the math is and there are aspects of it that I feel I understand in broad outline (group theory seems fundamentally not horribly intractable, although it also seems to get complicated pretty fast) but I feel immensely frustrated with the slow pace of acquisition of new knowledge. The CMS detector is wild, btw :) Large Hadron Collider is Large. $\endgroup$
    – JForster
    Commented Jul 29, 2013 at 23:12
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    $\begingroup$ @JForster If you are interested in diving in a bit more the Nobel winner Gerard 't Hooft has a nice resource list. Also Susskind's theoretical minimum. A university library is also a very nice thing to have on hand. I'm largely self-taught and I can tell you it's not easy, but if you are passionate about a subject it gets to be rewarding (emotionally and intellectually if not fiscally). Best thing to do is follow your interests. $\endgroup$
    – Michael
    Commented Jul 30, 2013 at 1:51
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    $\begingroup$ @JForster I toured Fermilab as a kid not long after they discovered the top quark. It was a wonderful experience, both for the physics and the wildlife. :) $\endgroup$
    – Michael
    Commented Jul 30, 2013 at 1:52
  • $\begingroup$ thanks again --by coincidence I started Theoretical Minimum last week. It's a shame about work ;). $\endgroup$
    – JForster
    Commented Jul 30, 2013 at 15:41

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