Ultraviolet sensitivity of the one-loop matter power spectrum

For internal momentum $q\gg k$, the P22 contribution to the one-loop matter power spectrum starts at $k^4$, while twice the P13 contribution to the one-loop matter power spectrum starts at $k^{2}P(k)$. The latter has the same momentum dependence as the effective sound-speed counterterm in large-scale structure. Short-scale stochastic contributions start at $k^4$ by mass and momentum conservation.