An effective field theory treatment of the production and annihilation of magnetic monopoles and their relic abundance

We revisit the thermal production and annihilation of magnetic monopoles and their relic abundance in order to gain a deeper physical interpretation on the monopole phenomenology predicted from the Baines et al.’s effective field theory, recently proposed in the description of monopole pair production via Drell–Yan and photon fusion processes. In this sense, we use of the vacuum cross sections for the Drell–Yan reactions derived within the mentioned framework to evaluate the cross section averaged over the thermal distribution associated to other particles that constitute the hot medium where the monopoles propagate. In the considered range of monopole mass with spin-zero and spin-half, our findings suggest that the thermally averaged cross sections for the pair production are highly suppressed, while at higher temperatures those for the annihilation of lighter pairs reach larger magnitudes. Besides, we observe that smaller temperature leads to a rate of annihilation for scalar monopoles smaller than the one for fermionic monopoles, which might be interpreted as a theoretical evidence of a more pronounced stability for spin-zero and heavier monopoles. Then we input these thermally averaged cross sections into the kinetic equation that describes the evolution of the monopole abundance via an extension of a freeze-out theory. Our results infer that heavier monopoles achieve the equilibrium at earlier stages of the expansion, and consequently at higher temperatures. In addition, larger monopole masses produce higher values of the relic abundance. Besides, the results indicate that the abundance does not behave differently for spin-zero and spin-half relic monopoles.