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Semiclassical contributions to the gravitational action include various termswith zero, two, and four derivatives of the metric as well as nonlocal formfactors for these terms. Contributions to some of these terms could be confusedwith others on a specific metric background or for a particular gauge fixing.We present a critical analysis of the recent works where the tensor structureand the number of derivatives in the action of gravity were not properly takeninto account. Taking these relevant aspects into account, we show that althoughsome contributions owing to the quantum fluctuations of massive or masslessscalar as well as fermion and vector fields may be attributed to the "running"of the cosmological constant, in reality they correspond to the fourthderivative terms of the action.

Nonlocality of quantum matter corrections and cosmological constant running