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Thanks to the LHC one can make particles collide and annihilate into other particles.

  1. Therefore, currently, what is the mass of the most massive particle one could create theoretically given the capacities of the LHC.

  2. Can we create dark-matter particles via the LHC?

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  • $\begingroup$ Can the answer be : a black hole of a mass corresponding the total energy:) ? $\endgroup$
    – jaromrax
    May 15, 2017 at 11:10
  • $\begingroup$ Take a look at papers about Dark Matter searches and other exotics. You'll see not discoveries (unfortunately), but exclusions: these tell you that, although e.g. a 2 TeV gluino could be theoretically produced and observable in some decay channel, it wasn't. In general, I don't think any exclusion goes much higher than 2 TeV (for the more "sensible" models at least). $\endgroup$
    – Demosthene
    May 15, 2017 at 14:04

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The absolute maximum is the centre of mass energy, 14 TeV. But that's the energy of the colliding protons. In fact, outgoing particles are created through the collision of a constituent of one proton, and the constituent of the other proton. Constituent here means a quark or a gluon. The problem then becomes rather complex, involving what particle physicists call Parton Density Function, i.e. what is the probability to find a given type of parton carrying a given fraction of the proton momentum. But I think you will allow me to give a layman answer and say that introducing a factor 3 (for the 3 quarks the proton is mostly made of) is good enough! So that's a reduction of a factor 10 basically (I mean 9 = 10 at that level of handwaving!).

There is a lot of work on searching for Dark Matter particles at LHC, definitively! A very recent review can be found at https://arxiv.org/abs/1702.02430. This is a "pro" article, but I think you could get some useful info from the conclusion.

A more thorough answer requires to pay attention to those Parton Density Functions (PDF) I mentioned. Let's take an example: it is possible to find a quark up carrying 99% of the proton momentum but this is much less probable than finding one carrying close to 1/3 let's say. So in the absolute, 14 TeV is the maximum but collisions even approaching this would be extremely unlikely. Eventually, it becomes a probabilistic argument because for each maximum mass between 0 and 14 TeV, you have a probability assigned to it. When I wrote 1.4 TeV above, I therefore meant an approximation of the most likely maximum mass, across a vast number of collisions.

From there, if you wanted to see the distribution of probability, it becomes really involved as you have to consider all possible quark-quark, quark-gluon and gluon-gluon collisions. I ought to have the answer as I did my PhD on a very related subject but this was 20 years ago!

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  • $\begingroup$ So do you mean that one can create particles of mass up about 1.4 TeV ? $\endgroup$
    – ketherok
    May 15, 2017 at 11:37
  • $\begingroup$ This is only an order of magnitude. If you want to dig deeper, there is no way around discussing the Parton Density Functions (PDF). I expanded my answer. $\endgroup$
    – user154997
    May 15, 2017 at 12:09
  • $\begingroup$ Just to be clear that 14 TeV is the energy maximum, but that includes kinetic energy, and in principle any group of particles can be generated with with that level of kinetic energy. I think the OP may want to know what the highest "rest mass" would be. $\endgroup$
    – StephenG - Help Ukraine
    May 15, 2017 at 12:29
  • $\begingroup$ @StephenG The 14 TeV can be the rest mass. In that case the particle would be created at rest with respect to the collision center of mass. $\endgroup$
    – mpv
    May 15, 2017 at 14:59
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Short answer, the Top quark.

In Hadron collisions top quarks are produced in pairs through the processes $q \overline{q} \rightarrow t\overline{t}$ and $g \overline{g} \rightarrow t \overline{t}$ at leading order in QCD.

Cortiana's paper Top-quark mass measurements: review and perspectives should give you a little more information on the detection and measurements.

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    $\begingroup$ You've answered the question what is the heaviest currently known particle rather than the question that was actually asked. If we were sure we'd never create new unknown particles (heavier than top quarks) we'd shut down the LHC and go home. $\endgroup$
    – John Rennie
    May 15, 2017 at 11:41

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