Restricting One-Loop radiative effects in quantum gravity: Demonstrating 4D GR as an EFT and its consistent unification with the Standard Model

Abstract

In ``On restricting to one-loop order the radiative effects in quantum gravity" (Brandt, Frenkel, and McKeon, 2020) \cite{Brandt2020}, a Lagrange multiplier (LM) field is introduced into the Einstein-Hilbert action, removing all multi-loop graviton diagrams and confining quantum-gravity corrections to just one loop. The resulting one-loop effective action carries a term proportional to {$\ln(μ/Λ)$}, which they suggest could be experimentally determined, hinting at direct measurements of quantum-gravity effects. We {demonstrate}, however, that {$μ$ and $Λ$} emerge from a chosen renormalization scheme, not from physical observables, implying that {$\ln(μ/Λ)$} signals a finite UV cutoff in this ``LM renormalization scheme.'' Although Newton's constant remains fixed (no running of {$G_N$}), the resulting logarithmic dependence encodes a limited domain of validity for General Relativity (GR) in four dimensions, thereby demonstrating explicitly that 4D GR behaves as an effective field theory (EFT) for energies below the cutoff. {Using the Appelquist-Carazzone decoupling theorem, we prove mathematically that this framework has a well-defined low-energy limit.} We then illustrate how this truncated, renormalized gravity sector can be consistently unified with the Standard Model (SM), yielding a finite and renormalized EFT encompassing both gravity and particle physics up to a scale {$Λ_{\text{grav}}$}. As such, we term this unification as the USMEG-EFT (Unified Standard Model with Emergent Gravity-EFT) framework. Our work represents a breakthrough in theoretical physics with a first successful unification of gravity with the Standard Model through a fully renormalizable and EFT framework.