Quantum corrections to 3-body recombination in a dilute Bose-Einstein condensate

The rate at which the number density $n$ of a dilute Bose-Einstein condensate decreases from 3-body recombination scales like $n^3 a^4$, where $a$ is the scattering length. We calculate the corrections to the rate from quantum fluctuations in the condensate to second order in the diluteness variable $\sqrt{n a^3}$. The second order term depends on Efimov's 3-body parameter.