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Flip Tanedo | USLHC | USA

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An experiment: Feynman Diagrams for Undergrads

The past couple of weeks I’ve been busy juggling research with an opportunity I couldn’t pass up: the chance to give lectures about the Standard Model to Cornell’s undergraduate summer students working on CMS.

The local group here has a fantastic program which draws motivated undergrads from the freshman honors physics sequence. The students take a one credit “research in particle physics course” and spend the summer learning programming and analysis tools to eventually do CMS projects. Since the students are all local, some subset of them stay on and continue to work with CMS during their entire undergraduate careers. Needless to say, those students end up with fantastic training in physics and are on a trajectory to be superstar graduate students.

Anyway, I spent some time adapting my Feynman diagram blog posts into a series of lectures. In case anyone is interested, I’m posting them publicly here, along with some really nice references at the appropriate level.

There are no formal prerequisites except for familiarity with particle physics at the popular science/Wikipedia level, though they’re geared towards enthusiastic students who have been doing a lot of outside [pop-sci level] reading and have some sophistication with freshman level math and physics ideas.

The whole thing is an experiment for me, but the first lecture earlier today seems to have gone well.

  • Ohman

    I think you should consider to make a separate web site with your blog posts. I think they are really great for a laymen like me.

  • Ben

    Just want to say, that as an physics undergraduate, your Feynman diagram blog posts were REALLY useful for my course, and actually helped me to understand the idea of them and why they’re used. And it’s awesome that you’re actually teaching this to people, because you’re really good at it.

  • Great notes, and the handwriting made them come alive, as if I was actually listening to you.

    Though the use of hypothetical massless neutrinos to illustrate the chirality of the SM was jarring, because we know they have mass – I would have used a neutral symbol like X.

    And particle helicity left me with a puzzle – if left versus right depends on whether I am going faster or slower than the particle, what is it when I am going at the same speed and the particle appears at rest (probably its chirality, but that seems an odd unsymmetric bias) ?

  • Hi everyone, thanks for the kind words.

    @ Ohman: I’ll try to keep the index of Feynman diagram posts (in the original post, link above) updated.

    @ maalpu: Unfortunately I didn’t spell everything out in my hand written notes. For a massive particle, helicity is “not a good quantum number”. As long as the particle has an energy much larger than its mass, then you can pretend its massless and talk about helicity. But once you’re in the rest frame, then you really shouldn’t be talking about helicity: that’s where the particle is *most* mixed up with its left/right sibling.

    In other words, in the muon’s rest frame, you really can’t tell if it’s a left-chiral mu (which can talk to W bosons) or a right-chiral mu (which cannot). Indeed, it’s really a 50/50 mixture of both. So it will talk to W bosons, but only “half” as loudly as it would if it were a pure left-chiral mu.

    Kind of weird, huh!


  • But if a given mu is really a 50/50 mixture of left-chiral and right-chiral in its rest frame, and chirality (unlike helicity) is a good quantum number, then that mu must be a 50/50 mixture in all reference frames ?

    And how then does a pure left-chiral mu behave – it must be left chiral in all reference frames, despite having different helicity in some where it has energy much larger than its mass ?

  • Hi maalpu, great questions. The mixing between the right-chiral and left-chiral is frame-dependent.. There’s a mistake if I wrote that chirality is a good quantum number for massive particles, my apologies! This frame-dependence is nothing weird: we know that in the limit of small mass, the fermion behaves as if it were chiral. It doesn’t make sense to talk about mass being small unless we have something to compare to, and the natural comparison is the particle’s total energy—thus when the mass is much smaller than the kinetic energy (i.e. in a frame where the particle is boosted), then chirality becomes a more reasonable quantum number.

    For a given particle in a fixed frame: helicity is a good quantum number since it reflects conservation of angular momentum. Suppose I measure an electron which is spinning in the +z direction. This physical electron is a mixture of a left-chiral electron and the anti-partner of right-chiral electron. (In my previous blog post on chirality I called this an anti-positron, but this seemed to confuse people.)