With increasing energy the collision decreases in the plot for signal in LHC. why is that? and at an energy 125GeV the no of events suddenly increases. How this proves that higgs has a mass of 125GeV?
This is the CMS Higgs going to gamma gamma result :
It is a plot of the invariant mass of two photons against a weighted number of events. The curve of this invariant mass falls for high masses, because the probability of two gammas to give a large invariant mass falls with the mass, there are many more gamma pairs with small angles between them , then with the large angle necessary for a heavy particle as the Higgs. The straight line below the enhancement is what one expects as the continuity of the falling invariant mass of two photons, if they are random from various jets of particles, mainly pi0 decays. The enhancement shows that something else is happening, that it is the decay of a particle into two photons.
Here is an event display of one of such events:
The green lines are the ones falling in the range of the higgs, shown in the picture above.
The pio was discovered in a similar way, as it also goes into two photons
In this bubble chamber it is clearer that it is the decay of a new particle from a vertex:
On the right, the two photons are disentangled for convenience, they have each generated an e+e- pair , and so the energy of the two photons is known and the four vector gives the mass of the pi0. An accumulation would show an invariant mass with a width due to experimental measurement errors.
The higgs signal is in a much more complicated environment, because it decays at the vertex of the interaction and there is a large background of unconnected gammas, but it follows the same logic. The width is a measurement error width, not the real width of the resonance in the interaction.