A magnetic monopole is a hypothetical particle with only one magnetic pole. Their magnetic fields would not be divergence-less. Predicted by certain modern theories, including string theory, supergravity, and various popular grand unified theories.

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With estimates of mass constraints on magnetic monopoles, how likely is one to be found by the LHC(MoEDAL)?

Fermilab seems to have ruled out monopoles with mass less than 850 GeV, but I have seen some estimates of the mass thought to be in the order of up to $10^{18}$ GeV, which, of course, would make them ...