Probing Yukawa Gravity with Modulated Newtonian Cancellation in the CHRONOS Detector

TL;DR

This paper demonstrates how a torsion-bar gravitational-wave detector can be used to detect Yukawa-type deviations from Newtonian gravity at meter scales, with sensitivity limited by systematic uncertainties.

Contribution

It provides an exact residual torque expression and maps Yukawa signals into strain responses, establishing torsion-bar detectors as systematic-limited probes of non-Newtonian gravity.

Findings

Achieves sensitivity of |_Y| = 2.4^{-5} at  = 8 m

Sensitivity limited by residual Newtonian torque from imperfect cancellation

Systematic floor reached at approximately 26 hours of measurement

Abstract

We investigate the sensitivity of a torsion-bar gravitational-wave detector to Yukawa-type deviations from Newtonian gravity using a differential gravitational calibrator (GCal), where two rotating mass systems cancel the leading Newtonian torque. We derive an exact expression for the residual torque and map the Yukawa signal into a strain-equivalent response in the sub-Hz band. We evaluate the sensitivity in the $(\alpha_Y,\lambda)$ parameter space, finding optimal performance at scales comparable to the experimental geometry, reaching $|\alpha_Y| = 2.4\times10^{-5}$ at $\lambda = 8\mathrm{m}$. The sensitivity is limited by residual Newtonian torque from imperfect cancellation rather than statistical noise, with a systematic floor reached at $T_{\rm eq} \simeq 9.25\times10^{4}\mathrm{s}$ ($\sim 26$ hours). This limit is dominated by uncertainties in the source-mass geometry. The differential configuration retains sensitivity even at large interaction ranges, enabling constraints at meter-scale distances. These results establish torsion-bar detectors as a systematics-limited probe of non-Newtonian gravity in the sub-Hz band.