Renormalization of the classical-quantum (CQ) gravity model

Develop a consistent renormalization procedure for the classical-quantum (CQ) gravity model defined by the non-relativistic Lindblad master equation with dissipative kernel F2(x−y)=D2 G_C(x−y)+D0 δ^3(x−y) (where G_C has 1/(k^2+m_φ^2)^2 momentum dependence), so as to remove the dependence on the ultraviolet regulator length scale ℓ introduced in practical calculations and to yield finite, cutoff-independent predictions for observables such as the force-noise spectral density S_FF in experiments with composite masses.

Background

In the paper’s analysis of the classical-quantum (CQ) gravity framework, the authors show that the non-relativistic limit is described by a Lindblad master equation with two free parameters (D0, D2) and a dissipative kernel whose momentum-space structure involves 1/(k^2+m_φ^2)^2. To compute force-noise levels for composite test masses, a short-distance regulator length scale ℓ is introduced.

The resulting predictions, including the force-noise spectral density S_FF, depend sensitively on ℓ, indicating ultraviolet sensitivity of the model. The authors explicitly note that they currently lack an appropriate renormalization procedure to eliminate this dependence and render predictions cutoff-independent, although they cite one recent attempt toward such a renormalization. Addressing this issue is necessary for making definitive, regulator-independent comparisons with experimental noise measurements.