Logarithmically Divergent Vacuum Energy in Effective Field Theory

The vacuum energy density due to a single quantum field diverges quarticly with the ultraviolet cutoff $\mathrm{\Lambda }$, in wild disagreement with the value implied by cosmological observations. We show that in effective field theories containing bosons and fermions the requirement of a Lorentz invariant vacuum makes any divergence faster than logarithmic exponentially unlikely. We show this by generating an ensemble of mass spectra by Monte Carlo, and find that the probability distribution function for the vacuum energy is a gaussian centered on zero with a width that grows only logarithmically with the ultraviolet cutoff.