Thomson, in Modern Particle Physics, chapter 17, says
The SM Higgs boson H is a neutral scalar particle. Its mass is a free parameter of the SM that is given by $m_H=2\lambda v^2.$
In the next section he adds
Prior to the turn-on of the LHC at CERN, the window for the SM Higgs was relatively narrow.The absence of a signal from direct searches at LEP implied that $m_H>114GeV$. At the same time, the limits on the size of the quantum loop corrections from the precision electroweak measurements at LEP and Tevatron suggested that $m_H <\approx 150 GeV $ and that $m_H$ was unlikely to be greater than 200GeV.
I would like some help with
- Why do people sometimes refer to the mass of the Higgs boson and sometimes to the mass parameter of the Higgs boson?
- Why is it a free parameter?
- If I get it write the mass of the Higgs boson can be calculated by the equation above, right? Then why did the experimentalists had to narrow the possibilities of where (in the "mass spectrum") they would find it instead of going straight to 125GeV?