In a two-scalar model, one-loop diagrams with mixed light and heavy internal lines collapse to local tadpole contributions in the infrared, matching the effective low-energy quartic theory in flat and weakly curved spacetime.
Form factors and decoupling of matter fields in four-dimensional gravity
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abstract
We extend previous calculations of the non-local form factors of semiclassical gravity in $4D$ to include the Einstein-Hilbert term. The quantized fields are massive scalar, fermion and vector fields. The non-local form factor in this case can be seen as the sum of a power series of total derivatives, but it enables us to derive the beta function of Newton's constant and formally evaluate the decoupling law in the new sector, which turns out to be the standard quadratic one.
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Scalar model of effective field theory in curved space
In a two-scalar model, one-loop diagrams with mixed light and heavy internal lines collapse to local tadpole contributions in the infrared, matching the effective low-energy quartic theory in flat and weakly curved spacetime.