Probing Yukawa Gravity with Modulated Newtonian Cancellation in the CHRONOS Detector

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 $(\hat{I}{\pm }_Y,\hat{I}»)$ parameter space, finding optimal performance at scales comparable to the experimental geometry, reaching $|\hat{I}{\pm }_Y|=2.4\times 10^{-5}$ at $\hat{I}»=8\mathrm{m}$. The sensitivity is limited by residual Newtonian torque from imperfect cancellation rather than statistical noise, with a systematic floor reached at $T_{\mathrm{eq}}\simeq 9.25\times 10^4\mathrm{s}$ ($\sim 26$ 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.

17 pages, 4 figures