For a longtime magnetic-monopole aficionado like me, it was thrilling to learn from Arttu Rajantie’s article (Physics Today, October 2016, page 40) that we soon shall have data from the highest available energies at the Large Hadron Collider on whether magnetic monopoles with mass up to a few TeV have been detected.
Such an observation would be an even bigger shock to the standard model than would have been non-observation of the Higgs boson at mass 125 GeV. As Charles Goebel concluded in 1970, a consistent description of photon–monopole scattering requires the monopole to have a radius much larger than its Compton wavelength.1
Sometime later I developed another argument for the same conclusion.2 The reasoning used simple energy considerations. In principle, a monopole could be confined in a region not much larger than its Compton wavelength, with only a modest addition to its energy. However, the magnetic Coulomb field outside that region would carry an energy much greater than the rest energy. To avoid that contradiction, the monopole radius should be at least an order of magnitude bigger than the Compton wavelength.
Dirac’s quantization condition on the product of electric and magnetic charge holds in quantum electrodynamics and in the standard model. Thus in either of those theories the monopole charge cannot be spread out because little bits of magnetic charge would violate the quantization condition. As Rajantie notes, there are models, such as the ’t Hooft–Polyakov model,3 which give a very good classical-field approximation, in terms of SU(2) gauge fields, for the interior structure of a monopole.
Another possible dynamic would be a confinement mechanism for fractional monopoles, analogous to quark confinement in quantum chromodynamics. Therefore, finding a monopole with mass of a few TeV would imply the existence of new objects on scales of several hundred GeV or less to account for the fact that the magnetic charge is spread out. At the moment, we have no evidence for such objects. Thus discovery of a monopole would motivate searches for new phenomena at lower energies, which in turn would require dramatic supplementation of the standard model.
