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From Wikipedia, Higgs boson has hypercharge of +1 and isospin of -1/2.

W bosons have hypercharge 0 and isospin +-1.

Now Higgs boson can decay into 2 W bosons of opposite electric charge. No matter how hard I try, the quantum numbers don't add up.

Is hypercharge and isospin not conserved in Higgs decays?

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Is hypercharge and isospin not conserved in Higgs decays?

Indeed, they are not. Both weak hypercharge and isospin are spontaneously broken in the SM, so they are not good symmetries: the SM vacuum "ate" some of them.

A detailed technical way to "see" this is by writing down the original term in the SM Lagrangian that gave rise to the trilinear vertex describing your decay, g²vHWW. It, along with the mass term for the Ws, g²v²WW, came out of the original, symmetric quadrilinear term in the covariant completion of the $\phi$ kinetic terms, $$ g^2\phi^\dagger \tau^-\tau^+ \phi W^{+~\mu}W^{-}_\mu. $$

Upon symmetry breaking, in unitary gauge, $$ \phi \propto \begin{pmatrix} 0\\ v+H \end{pmatrix}, $$ so the term $O(v^2)$ represents the W mass term, while the $O(v)$ one represents the isospin and hypercharge-violation of the Higgs decay.

But note the electric charge is unbroken, and the iso-breaking matches/cancels the hyper charge braking, so charge is still a good symmetry, and thus conserved. Phew...

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