# What would happen if the Higgs boson and the $Z$ boson collided?

I am thinking the $$z$$ boson would remain with the combined mass of both the $$Z$$ boson and the Higgs boson. This is because the Higgs boson is a spin-0 boson and the $$Z$$ boson is a spin-1 boson.

The Standard Model allows two possibilities: The $$Z$$ can absorb the Higgs, or they can scatter off each other. The first corresponds to a three-particle $$HZZ$$ vertex in a Feynman diagram and the second to a four-particle $$HHZZ$$ vertex. You can see these two possible vertices in the answer to this question.
For a real Z absorbing a real h to end up with a real Z, you'd need both energy and momentum to balance across the reaction. In the center-of momentum frame of the input particles Z and H you'd then have a total energy $$E=\sqrt{m_Z^2 + p^2} + \sqrt{m_h^2 + p^2},$$ and zero total momentum, by frame choice. The output Z would then be at rest, with total energy $$E=m_Z$$.
However, for absolutely any p, including 0, $$m_Z\neq \sqrt{m_Z^2 + p^2} + \sqrt{m_h^2 + p^2},$$ so your reaction will not go.