Pair production form high energy cosmic microwave background photons and related calculations

Question

If assume that fluctuating fermion-antifermions pairs in space are products of photon-photon fusion reactions. Thus their total electric charge and total color are null. And the pairs spins are antiparallel and they are on their mass shell. The only quantity which is not conserved is therefore the energy and this is the reason for their limited lifetimes. And suppose that first order properties can be deduced assuming that pairs are created with an average energy, not taking into account full probability density of the pair’s kinetic energy.

Then the energy of an ephemeral fermion/antifermion $ E $ is,

$ E=φm_0 c^2 $

Whereas $ φ $ is the constant of proportionality. And it’s value can be deduced if we know the energy spectrum of the photons with their probabilities to create fermion pairs.

Now, can the high energy-cosmic microwave background photons create fermions as explained above? And if they can how can i calculate the value of $ φ $?

I forgot how to calculate the value of $ φ $ and i'm curious to know whether high energy-cosmic microwave backgound photons can produce fermion-antifermion pairs.