So I'm doing some research for a physics essay on particle accelerators and I don't want to go into too much mathematical detail (as I haven't studied statistics or higher level Physics at school yet), but I have googled a lot of things and nothing seems to come up for methods scientists are currently using to improve energy resolution. Other things that I haven't managed to clarify are: -How higher particle energy upon collision results in a need for higher energy resolution. I understand that energy resolution is equivalent to the FWHM divided by the mean particle energy. Is it the case that the FWHM can remain the same (same curve width) but under higher energies, you are dividing by a larger number so obtain a smaller % resolution? -If it is so hard to measure small resolutions, why are we even trying to accelerate particles faster and faster; is it because at a higher resolution more detail can be seen about the particle or some other reason that I didn't catch?