When it is said that the photon is ["a mixture of W and B"] ($B$ being a gauge field associated with the $U(1)$ hypercharge)
I have one question on this:
- Why there isn't a boson directly generated by this $B$ gauge?
As Kosm suggests in his comment, there technically is a massless boson directly generated by the $B_\mu$ field. The reason we do not see it in (say) particle accelerators is because our universe is "too cold," and hence spontaneous symmetry breaking in the Higgs field generates the $A_\mu$ (photon), $Z_\mu$, and two $W^\pm_\mu$ fields.