Question is not clear. The detection of high energy particle is possible using suitable instruments or detectors..The precision depends on several factors..detectors, PMT, wavelength, energy, nature of particle, charges..etc..You are not mentioned the particle name...
If you are talking about a high energy particle, I assume you mean one that has a high mass. If that is the case, then what one would detect is not the particle itself. Basically there are two ways how you can "see" a new particle. Either you detect it directly, or you see missing Energy in an event.
If you detect it, what you actually see is not the particle itself but the daughters it decays into or it's sisters particles. Having measured those daughters/sisters one is then able to reconstruct the particle and learn things about it.
If you did not see the particle directly, you can still search for what is missing. Basically you are looking for events, in which Energy/Momentum is lost and there is no other explanation for this (a not detected Standar Model daughter for example). Again, if you measure this you can study some aspects of it, but it is getting more challenging as you can imaging.
Otherwise I am not aware how you could discover a new particle. So there are not necessarily new precision measurements needed, in the sense you mentioned in your question, but rather higher energies to produce the particle or higher statistics, if the events are very rare.
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