In the Standard Model, the W and Z bosons and fermions get their masses via the Brout-Englert-Higgs mechanism. To this end, the Lagrangian contains a scalar field H with a negative mass squared V = - m^2 |H|^2. We know that the value of the parameter m is around 90 GeV - the Higgs boson mass divided by the square root of 2. In quantum field theory, the mass of a scalar particle is expected to be near the cut-off scale M of the theory, unless there's a symmetry protecting it from quantum corrections. On the other hand, m much smaller than M,
Relaxation is a genuinely new solution, even if somewhat contrived. It is based on the following ingredients:
- The Higgs mass term in the potential is V = M^2 |H|^2. That is to say, the magnitude of the mass term is close to the cut-off of the theory, as suggested by the naturalness arguments.
- The Higgs field is coupled to a new scalar field - the relaxion - whose vacuum expectation value is time-dependent in the early universe, effectively changing the Higgs mass squared during its evolution.
- When the mass squared turns negative and electroweak symmetry is broken, a back-reaction mechanism should prevent further time evolution of the relaxion, so that the Higgs mass terms is frozen at a seemingly unnatural value.
Thanks to Brian for a great tutorial.