How good is this PBS video at explaining weak hyper-charge?

  • #1
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Specifically this one:
I've been asking several question's about the weak force to my professors, and both on here and PhysicsSE and it seems impossible to get a consistent answer as to what weak hypercharge, weak isospin actually are with any degree of physical-ity.

So I suppose this thread is more open ended asking for somewhat decent explanations about the weak force as well.

Thank you all!
 
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  • #2
Orodruin
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It is about as accurate you can get while maintaining a popular orientation. However, you will not actually learn what the theory says unless you go into the details. Before spontaneous symmetry breaking (SSB), you have weak hypercharge and weak isospin. Upon SSB the symmetries that required that fermions are massless are broken. The only remaining linear combination that is left unbroken is a linear combination of weak hypercharge and the third component of the weak isospin - this linear combination is what we typically refer to as electric charge. Before SSB the weak hypercharge works very much like regular electromagnetism (with massless fermions), whereas the weak isospin interactions behave somewhat differently. Reading the links in your other post again, I would argue that the response is not "wrong" as much as somewhat misleading in terms of what it discusses (all the discussion is in terms of weak hypercharge and weak isospin and what we typically refer to as, eg., "electrons" are not eigenstates of either due to their mass).

One factual error that has slipped into the video is the statement that right-handed particles have no weak hypercharge - they generally do. What they do not have is weak isospin. The general expression for electric charge in terms of the weak hypercharge ##Y## and third component of weak isospin ##T_3## is ##Q = Y/2 + T_3##. The right-handed electron has no weak isospin at all and therefore ##T_3 = 0##, which means that it needs to have weak hypercharge ##Y = -2##. At the same time, the left-handed electron is part of a weak isospin doublet together with the left-handed electron neutrino, this doublet has weak hypercharge ##Y = -1## and the third component of the weak isospin is ##T_3 = -1/2## for the electron part and ##T_3 = +1/2## for the neutrino part. Thus, the electric charge of the LH electron is ##Q_e = -1/2 - 1/2 = -1## while the electric charge of the neutrino is ##Q_\nu = -1/2 + 1/2 = 0##. So, yes, the right-handed electron does have weak hypercharge (in fact, its weak hypercharge is twice that of the left-handed electron) but no weak isospin.

Edit: Of course, having different weak hypercharge, the left-handed electron still needs to interact with the background Higgs field to flip its spin to become a right-handed electron.
 

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