# Running couplings from adiabatic regularization

## TL;DR

This paper introduces an extended adiabatic regularization method with an arbitrary mass scale to derive the running of coupling constants, including electric charge, cosmological constant, and gravitational constant, revealing new non-logarithmic effects.

## Contribution

The authors develop a robust extension of adiabatic regularization incorporating a mass scale, enabling the derivation of running coupling constants with novel non-logarithmic contributions.

## Key findings

- Derived the running of electric charge in QED.
- Renormalized the cosmological and gravitational constants.
- Identified new non-logarithmic contributions to running.

## Abstract

We extend the adiabatic regularization method by introducing an arbitrary mass scale $\mu$ in the construction of the subtraction terms. This allows us to obtain, in a very robust way, the running of the coupling constants by demanding $\mu$-invariance of the effective semiclassical (Maxwell-Einstein) equations. In particular, we get the running of the electric charge of perturbative quantum electrodynamics. Furthermore, the method brings about a renormalization of the cosmological constant and the Newtonian gravitational constant. The running obtained for these dimensionful coupling constants has new relevant (non-logarithmic) contributions, not predicted by dimensional regularization.