| Περίληψη: |
In "On restricting to one-loop order the radiative effects in quantum gravity", 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 GN), 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 Λgrav. As such, we term this unification as the 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 SM through a fully renormalizable and EFT framework. [ABSTRACT FROM AUTHOR] |