How can we know that there are no other elementary particles at the mass-level of the SM particles? Well, if they exist, there is a very small  probability to generate them  in a nuclear reaction. But, what is an estimate for a  bound to this  probability based in accelerator experiments?
 A: The standard model has been changing over the years , as more and more data are accumulated. Something as drastic as introducing new elementary particles to its table will require  a New Standard Model, which will include the present one as a subset, because the present one describes all the data up to now.
A new model is for example the Grand Unified Theory, which has extra gauge bosons X and Y and makes various predictions. Supersymmetry doubles the number  of elementary particles.Various other models exist.
LHC experiments search for new particles and, as they have not yet found any , the papers give limits to their probable existence, according to the theories studied.  For example here is a specific search in CMS  for  supersymemtric particles.
You can go to the CERN document server and find a number of experimental papers for given new models. For example using "GUT searches"  One of the first entries is this.
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A search for a heavy Higgs boson in the mass range from 0.2 to 3.0 TeV, decaying to a pair of W bosons, is presented. The analysis is based on proton-proton collisions at √ s = 13 TeV recorded by the CMS experiment at the LHC in 2016, corresponding to an integrated luminosity of $35.9 fb^{−1}$ . The W boson pair decays are reconstructed in the $2l2ν$ and $2ν2q$ final states (with l` = e or µ). Both gluon fusion and vector boson fusion production of the signal are considered. Interference effects between the signal and background are also taken into account. The observed data are consistent with the standard model (SM) expectation. Combined upper limits at 95% confidence level on the product of the cross section and branching fraction exclude a heavy Higgs boson with SM-like couplings and decays up to 1870 GeV. Exclusion limits are also set in the context of a number of two-Higgs-doublet model formulations, further reducing the allowed parameter space for SM extensions.
