The paper discusses the physical running of couplings in quadratic gravity, a theory that extends Einstein's general relativity by including terms quadratic in curvature. The authors argue that the standard beta functions for this theory do not correctly describe the physical dependence of scattering amplitudes on external momenta. They derive the correct physical beta functions, showing that asymptotic freedom can be achieved without the presence of tachyons. The key steps involve recomputing the beta functions using the background field method and considering the contributions from tadpoles and infrared divergences. The physical beta functions are found to be different from the standard ones, and the authors provide a detailed derivation of these functions, including the necessary Feynman diagrams and integrals. The results show that the theory can achieve asymptotic freedom in a region free of tachyons, making it a more plausible candidate for a complete renormalizable theory of quantum gravity.The paper discusses the physical running of couplings in quadratic gravity, a theory that extends Einstein's general relativity by including terms quadratic in curvature. The authors argue that the standard beta functions for this theory do not correctly describe the physical dependence of scattering amplitudes on external momenta. They derive the correct physical beta functions, showing that asymptotic freedom can be achieved without the presence of tachyons. The key steps involve recomputing the beta functions using the background field method and considering the contributions from tadpoles and infrared divergences. The physical beta functions are found to be different from the standard ones, and the authors provide a detailed derivation of these functions, including the necessary Feynman diagrams and integrals. The results show that the theory can achieve asymptotic freedom in a region free of tachyons, making it a more plausible candidate for a complete renormalizable theory of quantum gravity.