  We discuss the renormalization of the Newton constant due to fields of
various spin $s$. We first briefly review the cases of $s=0, \, 1/2, \, 1,\,
3/2$ already discussed in the literature and notice the appearance of the
well-known contact terms for the vector bosons. We then extend this discussion
of the contact terms to massive vector fields, $p$-forms and to the case of
spin $s=2$ particles (gravitons). We observe that, in general, the contact
terms originate from the fields which mediate the interactions (such as vector
gauge bosons and gravitons). We then discuss entanglement entropy and the
conical entropy and their relation to the renormalized Newton constant. We
address the puzzle of the non-analytic terms due to fields of spin $s=2$ and
suggest that the resolution of this puzzle comes from the non-equivalence of
the orbifold and $n$-fold cover constructions which are used in the entropy
calculations. Finally, we propose a mechanism by which the Bekenstein-Hawking
entropy is identified with entanglement entropy in any theory which includes
both matter fields and the mediators of interactions (vector gauge bosons and
gravitons).
