For the W & Z bosons, their masses are derived from 3 other 'free parameters' of the SM.
The Higgs mass is indeed a free parameter, but the SM wouldn't work of it's mass was greater than 200 GeV or so. The Higgs interacts with other particles of mass, and the strength of interaction is proportional to the Higgs mass, it influences certain processes (like W boson scattering), the rate at which these happen would deviate from experimental observation if Mhiggs was over 200 GeV.
That's why the LHC was such a big deal, it reached the energies required for direct observation of sub-200 GeV Higgs, so it would either find the SM Higgs, or rule it out and invalidate the SM. Unfortunately the former seems to have happened.
Indirect constraints on Higgs mass in SM (a bit technical, slide 6 chart is the key one, strongly influenced specs & mission of the LHC)
https://indico.lal.in2p3.fr
The Higgs mass is indeed a free parameter, but the SM wouldn't work of it's mass was greater than 200 GeV or so. The Higgs interacts with other particles of mass, and the strength of interaction is proportional to the Higgs mass, it influences certain processes (like W boson scattering), the rate at which these happen would deviate from experimental observation if Mhiggs was over 200 GeV.
That's why the LHC was such a big deal, it reached the energies required for direct observation of sub-200 GeV Higgs, so it would either find the SM Higgs, or rule it out and invalidate the SM. Unfortunately the former seems to have happened.
SM free parameters: https://en.m.wikipedia.org/wiki/Standard_Model#Construction_...
Indirect constraints on Higgs mass in SM (a bit technical, slide 6 chart is the key one, strongly influenced specs & mission of the LHC) https://indico.lal.in2p3.fr