Non-local partner to the cosmological constant

I show that quantum corrections due to a massive particle generates a non-local term in the gravitational effective action which is of zeroth order in the derivative expansion, much like the cosmological constant. It carries a fixed coefficient which is very much larger than the cosmological constant, and which cannot be fine-tuned. The interaction is active at scales above the particle's mass. This is of the form $m^4 (\frac1{\Box}R)_x "<x|\log (\Box +m^2 )|y >" (\frac1{\Box}R)_y$, and I discuss the meaning of $"<x|\log (\Box +m^2) |y >"$ and other aspects of its interpretation.