I've been Wikipedia-ing the weak interaction and GUTs and I came across 2 seemingly conflicting pieces of information. In the page for Weak Hypercharge it says this:

one of the interactions is with the Higgs field. Since the Higgs field vacuum expectation value is nonzero, particles interact with this field all the time even in vacuum. This changes their weak hypercharge (and weak isospin $T_3$). Only a specific combination of them, $Q = T_3 + (1/2) Y_W$ (electric charge), is conserved.

So this means that YW isn't conserved in interactions with the Higgs field, because of symmetry breaking. But on the other hand, when you go to the page for X-charge, it says this:

In particle physics, the $X$-charge (or simply $X$) is a conserved quantum number associated with the SO(10) grand unification theory. It is thought to be conserved in strong, weak, electromagnetic and gravitational and Higgs interactions.

But X = 5 (B-L) - 2 YW, and interactions with the Higgs don't change B-L, and they also don't change X.... but they do change YW? I'm really confused by this.

There's clearly something I'm not understanding about this.

  • $\begingroup$ Note $Y_W$, X, & X' are conserved at the diagram level. $\endgroup$ Commented Aug 20, 2021 at 3:30

1 Answer 1


At the energy where the process in which we observe this violation of $Y_W$ hypercharge lives, the $\mathrm{SO}(10)$ GUT is broken. As there is no well-defined Noether charge for spontaneously broken symmetries (cf. e.g. Cosmas Zachos' answer to a different question), you cannot straightforwardly try to apply the conservation of the $X$-charge in the unbroken description to a process that you describe with the broken description.


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