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 $(α<em>Y,λ)$ parameter space, finding optimal performance at scales comparable to the experimental geometry, reaching $|α_Y| = 2.4\times10<sup>{-5}$ at $λ= 8\mathrm{m}$. The sensitivity is limited by residual Newtonian torque from imperfect cancellation rather than statistical noise, with a systematic floor reached at $$T</em>{\rm eq} \simeq 9.25\times10<sup>{4}\mathrm{s}$$ ($\sim 26$ 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.