The 1999/2000 Eöt-Wash Rot-Wash experiment compared the accelerations of Cu and Pb test bodies in the field of a rotating 3-ton uranium attractor, reaching a differential-acceleration sensitivity of about 3×10−13 cm/s23\times10^{-13}\ \mathrm{cm/s^2} and setting the definitive laboratory limits on Yukawa-type equivalence-principle-violating interactions with ranges down to 1 cm, together with bounds on two-boson-exchange power-law potentials. The authors identified the prerequisites for a further order-of-magnitude gain: a large increase in the torsion-oscillator quality factor Q0Q_0 (the measurement was thermal-noise limited) and tighter control of systematic torques. A quarter-century later, the composition-dependent core of that challenge remains open: sub-millimeter progress has been confined to universally coupled inverse-square-law tests (down to 52 μm separations), long-range tests have reached 10−1510^{-15} in the Eötvös ratio, and the most sensitive direct composition-dependent constraint at the shortest ranges is still only at the percent level.

Background

The weak equivalence principle (WEP) — the statement that the gravitational acceleration of a body is independent of its composition — underlies the metric description of gravity in general relativity. Most frameworks for physics beyond the Standard Model (light scalar fields such as dilatons or moduli, new U(1) gauge bosons, and gravity propagating in large extra spatial dimensions) predict its violation at some level. Such violations are conventionally parameterized by adding to Newtonian gravity a Yukawa-type interaction of range λ\lambda and dimensionless strength αE\alpha_E that couples to a composition-dependent charge qq (for example baryon number per unit mass) rather than to mass itself, V(r)=−GNm1m2r−GNm1m2 αE q1q2 e−r/λr,V(r)=-\frac{G_N m_1 m_2}{r}-\frac{G_N m_1 m_2\,\alpha_E\, q_1 q_2\, e^{-r/\lambda}}{r}, so that two test bodies of different composition feel slightly different accelerations toward the same attractor. Two-boson exchange of light pseudoscalars additionally generates power-law potentials VN(r)∝1/rNV_N(r)\propto 1/r^N (NN up to about 5), which are also composition dependent. Laboratory limits on both forms are displayed as exclusion curves in the (αE,λ)(\alpha_E,\lambda) or (VN,λ)(V_N,\lambda) planes.

The most sensitive laboratory instrument for such tests is the torsion balance: a pendulum hung from a thin fiber, whose angular deflection measures the torque exerted by an external attractor. In the Rot-Wash experiment (Smith et al., Phys. Rev. D 61, 022001 (2000)) the Eöt-Wash group at the University of Washington rotated a 3-ton 238^{238}U attractor around a compact torsion pendulum carrying Cu and Pb test bodies, modulating any composition-dependent (universality-of-free-fall-violating) torque at the attractor rotation frequency while suppressing magnetic, thermal, and gravity-gradient backgrounds. They measured aCu−aPb=(1.0±2.8)×10−13 cm/s2a_{\mathrm{Cu}}-a_{\mathrm{Pb}}=(1.0\pm2.8)\times10^{-13}\ \mathrm{cm/s^2} against the common gravitational acceleration of 9.2×10−5 cm/s29.2\times10^{-5}\ \mathrm{cm/s^2}, setting the definitive laboratory limits on Yukawa-type WEP-violating interactions with ranges down to 1 cm, improving existing limits for ranges between 10 and 1000 km, and strongly constraining two-boson-exchange power-law potentials.

A torsion pendulum used this way is a torsion oscillator whose quality factor Q0Q_0 — the ratio of stored oscillation energy to the energy dissipated per radian, set mainly by internal friction in the suspension fiber — controls the Brownian torque noise through the fluctuation-dissipation theorem. With Q0≈2100Q_0\approx2100 the Rot-Wash run was already essentially thermal-noise limited. In their closing Future Prospects section the authors therefore stated that improving the differential-acceleration sensitivity of roughly 3×10−13 cm/s23\times10^{-13}\ \mathrm{cm/s^2} by a factor of 10 or more would require a large increase in Q0Q_0 together with better control of systematic errors: gravity-gradient torques (the coupling of the pendulum's mass multipole moments to the attractor's field multipoles), thermal and magnetic effects, sidepull (gravitational deflection of the pendulum toward the attractor) and tilt couplings, and reproducibility of the attractor geometry. Rather than upgrade Rot-Wash, they built a new pendulum-and-attractor system to test the gravitational 1/r21/r^2 law down to 0.1 mm — a measurement of distance-dependence that constrains universally coupled forces but not composition dependence.

That division still defines the frontier. The successor sub-millimeter instruments (Eöt-Wash: Hoyle et al. 2001 and 2004, Kapner et al. 2007, Lee et al. 2020, reaching detector-attractor separations of 52 μm; HUST: Tan et al. 2016 and 2020, holding ∣α∣≤1|\alpha|\le1 down to λ=48 μ\lambda=48\ \mum) test gravity-like, universally coupled Yukawa and power-law deviations, where the dominant obstacles are electrostatic patch potentials (spatially varying surface potentials on conducting shield surfaces), Casimir forces (the quantum-electrodynamic attraction between nearby surfaces), and shield-membrane vibration. Composition-dependent tests, by contrast, have advanced only at long range: rotating torsion balances using the Earth as source (Schlamminger et al. 2008) and the MICROSCOPE space mission (Touboul et al. 2022, Eötvös ratio η\eta — the fractional differential acceleration of the two test masses — at the 10−1510^{-15} level) reach far better precision but are insensitive to Yukawa ranges far below planetary scales. The only dedicated composition-dependent test at the shortest ranges, the Rikkyo torsion balance of Ninomiya et al. (2017), compared the effective gravitational constant between tungsten targets and copper versus aluminum attractors at millimeter separations and reached only the percent level, ηAl−Cu(r∼1 cm)≈5×10−2\eta_{\mathrm{Al-Cu}}(r\sim1\ \mathrm{cm})\approx5\times10^{-2}. Between roughly 0.1 mm and 1 cm, the sector of composition-dependent Yukawa and power-law interactions therefore remains essentially untested.

Problem Statement

Improve laboratory sensitivity to composition-dependent, equivalence-principle-violating interactions at short range by an order of magnitude or more beyond the Rot-Wash benchmark of roughly 3×10−13 cm/s23\times10^{-13}\ \mathrm{cm/s^2} differential acceleration (Cu versus Pb test bodies) at centimeter-scale source distances, tightening the corresponding laboratory bounds on Yukawa-type and two-boson-exchange power-law equivalence-principle-violating interactions.

Deliver a laboratory design, with a quantitative noise budget, whose projected differential-acceleration sensitivity to composition-dependent couplings at centimeter-scale source distances is at least an order of magnitude below the Rot-Wash benchmark, together with the projected bounds on Yukawa-type and two-boson-exchange power-law equivalence-principle-violating interactions that the design would set. The design must quantify the gain in oscillation quality it relies on — the Rot-Wash measurement was thermal-noise limited with internal-friction-dominated Q0≈2100Q_0\approx2100, and the fluctuation-dissipation relation ties the Brownian torque noise directly to that loss — and must reduce and quantitatively characterize, to below the new noise floor, the systematic torques that grow in relative importance with sensitivity: gravity-gradient (multipole) torques, thermal and magnetic effects, sidepull/tilt couplings, and attractor-geometry reproducibility. No particular apparatus is mandated, provided the design meets these requirements; a non-torsion technique must quantify the equivalent reduction of its dominant noise loss in place of the oscillator quality factor.

This problem is restricted to composition-dependent couplings; sub-millimeter tests of the gravitational 1/r21/r^2 law itself constrain only universally coupled deviations and are outside its scope.

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