which preserves chiral ity In the massless case we also have a frame

Which preserves chiral ity in the massless case we

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, which preserves chiral-ity). In the massless case we also have a frame independent definition of helicitywhich coincides with the notion of chirality (in the sense that particles of definitechirality have definite helicity), as we saw in part (a). Thus, in the massless case,since chirality is preserved, so is helicity.For the massive case things are a little more complicated.First note that wedon’t have a frame independent notion of helicity anymore.A particle whichlooks left handed in one frame will look right handed in another. Of course wecan still talk about the helicity in terms of some fixed frame, for example thelab frame.However, we no longer have the nice connection between chiralityand helicity that we had in the massless case. This is obvious from the fact thathelicity is frame dependent whlie chirality is not. Thus, though interactions stillpreserve chirality in the massless case, nothing tells us that they preserve helicity.There’s another interesting point we can make about the massive case: The masstermmψψ=m(ψRψL+ψLψR) couples particles of different chiralities together.Imagine we take the mass to be small, and let’s consider treating this termperturbatively.This amounts to using a massless propagator and introducingan interaction vertex which allows for a left handed particle to turn into a righthanded one, or vice versa, with couplingim. Thus, although interactions preservechirality, the mass term does not, so not even chirality is preserved for massivefermions.(e) To measure the spin of a slow moving electron, we can use a Stern-Gerlachapparatus.(f) If we have a source of polarized light, we can use the fact that there is onlyat-channel pole in the Compoton scattering amplitude when the electron andphoton have matching handedness. In particular, if there are substantially morebackscattered photons when using either left or right circularly polarized light,it means that our electron beam is polarized.Though we haven’t discussed it in class, the weak force, which is responsible forthe given decay, only couples to left handed fermions, so it turns out only lefthanded electrons will be produced. Of course this is a little suprising, as we are
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Phys 253a 6
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