# Runaway Monopole Catalyzed Baryon Decay

I am a layman in the subject, but I have recently learned that magnetic monopoles could be used to induce baryon decay (Callan-Rubakov mechanism), according to some GUTs. I have also learned that there have been experiments which have purported to have detected magnetic monopoles, or some trace thereof. Wouldn't this have led to the destruction of the equipment? Are there different forms of magnetic monopoles? And if so, wouldn't we be able to see the effects of the baryon-decay-catalyzing ones?

There has only been one experiment that has detected even a possible sign of a magnetic monopole so far, and that's Cabrera's "Valentine's Day Monopole." This experiment, being an early search experiment, was not sensitive to basically any properties of the magnetic monopole except for its magnetic charge (the essential principle was that the passage of a magnetic monopole through a superconducting ring would induce a constant current in the ring). In addition, it detected precisely one event that would be consistent with a magnetic monopole signal, and no events have been detected since, so this result remains controversial at best.

In addition, the Callan-Rubakov mechanism only applies to a particular theorized type of magnetic monopole (the Particle Data Group calls these "GUT monopoles" in their review on the subject, due to their mass being at the GUT scale and arising from GUT theories like $$SU(5)$$). Other monopoles arising from other theories do not have this property (the PDG lists the lighter doubly-charged monopole arising from $$SO(10)$$ theory as a particular example that doesn't cause baryon decay). So it is not in general true that magnetic monopoles all cause baryon decay in the first place.

In any case, even if the Cabrera experiment actually did detect a magnetic monopole, and even if that monopole happened to be a GUT monopole, the reaction cross-section for this is still quite small, around $$10^{-27}$$ cm^2 (source: PDG review). Given that the number density of air is around $$10^{19}$$ nuclei/cm$$^3$$, the mean free path for a magnetic monopole traversing the atmosphere would be around 100 km between baryon decays! Even in solid materials, where the number density is $$10^{22}$$ nuclei/cm^3, the magnetic monopole would still have to travel through 11 meters of solid copper to have a good chance of inducing a single baryon decay. In other words, it wouldn't destroy the equipment, even if it was the right kind of monopole.

Note that the baryon decay catalysis process is not "runaway," as the decay process does not create more magnetic monopoles. The reaction referred to by the Callan-Rubakov mechanism is $$p+M\to e^+ + \pi^0 + M$$, where $$M$$ is the monopole. The monopole survives the reaction and converts the proton into a positron and a pion, neither of which can cause further baryon decay. So there doesn't seem to be any particular reason why the baryon decay rate would increase afterwards (which is what the word "runaway" usually implies).

Whether or not we can see baryon decay catalyzed by magnetic monopoles depends on many things:

• How many of them there are; if there's only one in the universe, we'll never see its effects (and, since there are arguments like the one put forth by Dirac for the quantization of charge that only require the existence of a single monopole somewhere in the universe to work, this may actually be a possiblity).
• What the reaction cross-section is; current proton-decay experiments only have a limited sensitivity based on their size and the magnitude of the background, as well as the efficacy of the background reduction. Even if the monopoles existed in significant number, if the coupling to baryon decay was very weak, then we also wouldn't see them.
• Whether there are other baryon-number-violating processes at a similar scale, and what their reaction cross-section is. If it is impossible to disentangle baryon decay caused by monopoles from baryon decay caused by other mechanisms, then this would also make detection far more difficult.

Let me emphasize that there is currently no solid evidence that fundamental magnetic monopoles exist, and the simplest current explanation for the fact that we haven't seen their effects is that they simply don't exist. Theories that predict the existence of magnetic monopoles also don't have any solid evidence confirming any of their other predictions, either.