Why is the energy of particles in accelerators much higher than the energy of the particles they are trying to find?

Question

I have been wondering. In the LHC, or other particle accelerators for that matter, they are colliding particles with energies above TeV. The LHC is going to be 14 TeV or something like that the next time they are turning it on, right ?

So, when they were searching for the Higgs, it turned out it had a mass around 125 GeV, if I'm not mistaken. So basically my question is: Why is so high colliding energy needed to detect masses that are way below that ?

The only thing I've heard of is, that the particle might have the TeV energies, but the quarks inside does not, do to something I can't remember. But is that really it, or is there a better reason I can't seem to figure out ?

Answer 1

The proton is not fundamental. It is made up of quarks and gluons. It is these constituents that are colliding in the LHC to produce, in your example, a Higgs boson. The quarks and gluons only carry a fraction of the energy of the proton.

In addition, the colliding gluons or quarks in general do not have the same momentum. Therefore some of the energy will be "wasted" boosting the produced particles. Finally, sometimes the particle (eg Higgs) will be produced in association with other particles which will carry some of the energy of the interaction.