# On the mass of the Higgs Boson

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

1. Why do people sometimes refer to the mass of the Higgs boson and sometimes to the mass parameter of the Higgs boson?
2. Why is it a free parameter?
3. 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?

## 1 Answer

The masses and couplings in the Standard are free parameters. This is because they are not fixed by any experimentally verified theory till now. Standard model in itself is not a framework from which the values of masses and couplings can be exactly calculated at a given energy scale. Therefore we need to put the masses by hand. There are proposals like grand unification etc. which reduce the number of free parameters in the theory and semi-explain the observed masses, but they have not been experimentally verified, i.e., the extra particles predicted by them have not been observed/their effects on low energy physics are very small.

Same is the case for the mass parameter of the Higgs boson, which enters in the Standard Model Lagrangian as an undetermined parameter. The physical mass is the experimentally observed one.

As a naive answer to the third part, with the previous technology prior to LHC, it was not possible to go to 125 GeV and people had to put mass bounds like that on the Higgs. Please note that the different mass bounds were given by analysing different processes and a single process couldn't be used to carry out the observation.

• Isn't it true that the change of the Higgs mass would affect the outcome of numerous scattering experiments? If so, why couldn't we determine it by studying those cross-sections? – mavzolej Dec 20 '16 at 22:30
• @mavzolej that's exactly how it is determined.the mass bounds are obtained by studying scattering cross sections of different processes.. – Bruce Lee Jan 8 '17 at 12:23
• But there were numerous experiments prior to 'discovery of Higgs boson' - why couldn't we determine its mass from them, by studying all the outcomes thoroughly? And what was the specific experiment which gave the explicit confirmation? – mavzolej Jan 9 '17 at 14:16