Electroweak Symmetry Restoration and Radiation Amplitude Zeros

In high-energy collisions far above the electroweak scale, the effects of electroweak symmetry breaking are expected to become parametrically small $\delta \sim M_W/E$. This defines the extent to which the electroweak gauge symmetry is restored: $(i)$ the physics of the transverse gauge bosons and fermions is described by a massless theory in the unbroken phase; $(ii)$ the longitudinal gauge bosons behave like the Goldstone bosons and join the Higgs boson to restore the unbroken $O(4)$ symmetry in the original Higgs sector. Using the unique feature of the radiation amplitude zeros in gauge theory, we propose to study the electroweak symmetry restoration quantitatively by examining the processes for the gauge boson pair production $W^\pm \gamma,\ W^\pm Z$ and $W^\pm H$ at the LHC and muon colliders.