I am doing a piece of A-2 coursework concerning the LHC and its restart and cannot understand why the increase in energy of run 2 would allow us to detect heavier particles such as those proposed by SUSY.
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The center-of-mass energy of a particle collision puts an upper bound on the masses of the particles which can be produced through the mass-energy equivalence (which is essentially saying that mass is a form of energy). In order to create a particle of mass ##m##, you need to have an energy ##mc^2## available. Therefore, higher energies means you can create heavier particles. Then there is of course the question whether it is reasonable or not to expect SUSY particles to be at the mass scale between the previous run and this one ...
Using centre-of-mass energy 16TeV (a proton-proton collision when the LHC had the its greatest energy input of run 1, 8Tev) I get a value greater than 100,000 GeV/c squared. This seems much too large when compared to mass of particles discovered. I used the the Lorentz variant quantity expression to get the centre-of-mass energy.
The energy quoted by the LHC generally is the CoM energy of the protons ... If you have a CoM energy of 14 TeV, you will at most be able to create particles with a total of 14 TeV/c^2 of mass. Generally, the actual partons carry less than everything of the momentum and the actual parton-parton processes occur at lower CoM.
The current center of mass energy is 13 TeV, by the way.
As protons are not elementary particles, the collisions are better described by collisions of "parts" of the protons, those "parts" are called partons. They have some fraction of the total energy of the protons, and more than half of the proton energy is extremely rare. Therefore, we can search for more high-energetic particles, but not up to 13 TeV. The actual sensitivity depends on the specific model considered ("how likely is the production of particle X in model Y?"), but for every model increasing the energy helps to search for heavier particles.