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And if so whats the motivation for the introduction of hypercharge?

Adrien
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    The EW interaction conserves electric charge and breaks weak hypercharge. Strong hypercharge is irrelevant here, but of course it is violated. What is your point? – Cosmas Zachos Nov 17 '21 at 14:24
  • i mean weak hypercharge, i was under the impression that weak hypercharge is conserved during weak interactions? – Adrien Nov 17 '21 at 14:25
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    Absolutely not! It is the U(1) of SU(2)xU(1), and it is broken just like the SU(2). Only a linear combination of it with $T_3$ of SU(2) survives as the electric charge. It is summarized in the WP article linked. – Cosmas Zachos Nov 17 '21 at 14:29
  • So if weak hypercharge isnt conserved then neither will weak isospin be, surely this would imply that the weak force can produce right handed states, which is strictly forbidden? – Adrien Nov 17 '21 at 14:37
  • Weak isospin is spontaneously broken, indeed. I don't understand your "surely" non-sequitur, but you must detail your thinking in your answer. The higgs couplings and quark masses do reflect coupling to right-chiral fermions. Why don't you just read up on the SM? – Cosmas Zachos Nov 17 '21 at 14:42
  • I was under the impression that all right handed fermions had T=T_3=0, whilst left handed fermions had T=1/2, T_3=1/2 or -1/2, and that T_3 had to be conserved at weak interaction vertices. Clearly I'm out of my depth trying to understand this (for now), but thanks for your help anyway. – Adrien Nov 17 '21 at 15:08
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    Depends on what you mean by "weak". The Yukawa couplings to the Higgs doublet, the second heart of the SM!, involve left and right chiral fermions, but, upon SSB, the resulting fermion mass terms most definitely break weak hypercharge and T_3! – Cosmas Zachos Nov 17 '21 at 15:31
  • You have a point (subtle), addressed in this question. But you have to be very careful with your vertices and propagators. Any "contamination" by Higgs couplings and fermion masses in propagators will upend your conservation accounting. – Cosmas Zachos Nov 17 '21 at 15:55
  • Ah thanks i really appreciate it, i think i just got confused by the wikipedia page where they said all weak isospin is conserved – Adrien Nov 17 '21 at 17:56
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    Ah.. daft and irresponsible statement. They mean weak current couplings, not Higgs couplings. In the limit of vanishing Yukawa couplings, one could make that (pointless) statement, but that would definitely not be the weak interactions as we know them... – Cosmas Zachos Nov 17 '21 at 20:45
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    Thanks for clearing that up i really appreciate it! – Adrien Nov 17 '21 at 22:53

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