Conjecture on the origin of discrepancies between momentum running and μ-running in gravitational couplings

Investigate whether the discrepancy in the running of gravitational couplings reported by Buccio, Donoghue, Menezes, and Percacci and by Buccio, Parente, and Zanusso originates from the premature omission of UV-divergent integrals and the identification of the physical running with the logarithmic dependence of the scalar integral B0(p^2, m^2, m^2) without implementing the necessary ultraviolet cancellations; determine if retaining UV-finite combinations such as B0(0, m^2, m^2) − B0(p^2, m^2, m^2) resolves the discrepancy.

Background

The paper contrasts conventional μ-running (from MS counterterms) with a “physical” running extracted from momentum logarithms, showing in QED that both agree once infrared effects are separated. In quadratic gravity, the photon self-energy is ultraviolet finite at one loop, leaving only infrared-controlled logarithms that should not be interpreted as UV running.

The authors propose a specific mechanism to explain discrepancies reported in the literature: that identifying physical running solely with the momentum dependence in B0 while dropping momentum-independent UV-divergent pieces obscures essential UV cancellations, leading to misinterpretation of infrared logarithms as running.