Torsion Balance Experiments Research Articles

Blowing in the dark matter wind

Interactions between dark matter and ordinary matter will transfer momentum, and therefore give rise to a force on ordinary matter due to the dark matter ‘wind.’ We show that this force can be maximal in a realistic model of dark matter, meaning that an order-1 fraction of the dark matter momentum incident on a target of ordinary matter is reflected. The model consists of light (mϕ ≲ eV) scalar dark matter with an effective interaction ϕ2ψ¯ψ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\phi}^2\\overline{\\psi}\\psi $$\\end{document}, where ψ is an electron or nucleon field. If the coupling is repulsive and sufficiently strong, the field ϕ is excluded from ordinary matter, analogous to the Meissner effect for photons in a superconductor. We show that there is a large region of parameter space that is compatible with existing constraints, where the force is large enough to be detected by existing force probes, such as satellite tests of the equivalence principle and torsion balance experiments. However, shielding of the dark matter by ordinary matter prevents existing experiments from being sensitive to the dark matter force. We show that precise measurements of spacecraft trajectories proposed to test long distance modifications of gravity are sensitive to this force for a wide range of parameters.

Constraining light scalar field with torsion-balance gravity experiments

The light scalar field with a coupling to standard model particles provide a possible source of the long-range Yukawa forces or violation of the weak equivalence principle, which can be potentially explored by precision gravity experiments. We describe the searches for such light scalar fields with the three types of gravity experiments, including the G-measurement experiments, Inverse-Square Law (ISL) experiments, and equivalence principle experiments. We investigate the potential influences of the scalar field as a function of its mass, and focus on the experimental constraints from torsion-balance gravity experiments. HUST-18 G-measurement torsion-balance experiments place bounds on the photon coupling and electron coupling at up to Λγ=7×1017 GeV and Λe=1×1017 GeV in the mass ranges 10−9–10−4eV. Results from the ISL experiments by the Universities of Washington, Stanford, IUPUI, HUST, Colorado, Irvine, Yale and others allow us to set limits on the photon coupling and electron coupling at up to Λγ=5×1017 GeV and Λe=3×1016 GeV for scalar field mass ranges between 10−5 and 10−1eV. Additionally, we also discuss the limits from equivalence principle experiments, and MICROSCOPE final result updates the constrains on the coupling parameters at up to Λγ=7×1022 GeV and Λe=4×1021 GeV for mass ranges ≲10−13eV. These results contribute experimental constraints to relatively unexplored mass regions of light scalar field parameter space and improve upon previous limits in some mass ranges. This work paves the way for long-range Yukawa forces mediated by light scalar fields in future high-precision gravity experiments.

The dark Stodolsky effect: constraining effective dark matter operators with spin-dependent interactions

We present a comprehensive discussion of the Stodolsky effect for dark matter (DM), and discuss two techniques to measure the effect and constrain the DM parameter space. The Stodolsky effect is the spin-dependent shift in the energy of a Standard Model (SM) fermion sitting in a bath of neutrinos. This effect, which scales linearly in the effective coupling, manifests as a small torque on the SM fermion spin and has historically been proposed as a method of detecting the cosmic neutrino background. We generalise this effect to DM, and give expressions for the induced energy shifts for DM candidates from spin-0 to spin-3/2, considering all effective operators up to mass dimension-6. In all cases, the effect scales inversely with the DM mass, but requires an asymmetric background. We show that a torsion balance experiment is sensitive to energy shifts of ΔE ≳ 10-28 eV, whilst a more intricate setup using a SQUID magnetometer is sensitive to shifts of ΔE ≳ 10-32 eV. Finally, we compute the energy shifts for a model of scalar DM, and demonstrate that the Stodolsky effect can be used to constrain regions of parameter space that are not presently excluded.

Electrostatic effect due to patch potentials between closely spaced surfaces

The spatial variation and temporal variation in surface potential are important error sources in various precision experiments and deserved to be considered carefully. In the former case, the theoretical analysis shows that this effect depends on the surface potentials through their spatial autocorrelation functions. By making some modification to the quasilocal correlation model, we obtain a rigorous formula for the patch force, where the magnitude is proportional to $\frac{1}{{a}^{2}}{(\frac{a}{w})}^{\ensuremath{\beta}(a/w)+2}$ with $a$ the distance between two parallel plates, $w$ the mean patch size, and $\ensuremath{\beta}$ the scaling coefficient from $\ensuremath{-}2$ to $\ensuremath{-}4$. A torsion balance experiment is then conducted, and we obtain a 0.4 mm effective patch size and 20 mV potential variance. In the latter case, we apply an adatom diffusion model to describe this mechanism and predicts a ${f}^{\ensuremath{-}3/4}$ frequency dependence above 0.01 mHz. This prediction meets well with a typical experimental results. Finally, we apply these models to analyze the patch effect for two typical experiments. Our analysis will help to investigate the properties of surface potentials.

A cryogenic torsion balance using a liquid-cryogen free, ultra-low vibration cryostat.

We describe a liquid-cryogen free cryostat with ultra-low vibration levels, which allows for continuous operation of a torsion balance at cryogenic temperatures. The apparatus uses a commercially available two-stage pulse-tube cooler and passive vibration isolation. The torsion balance exhibits torque noise levels lower than room temperature thermal noise by a factor of about four in the frequency range of 3-10 mHz, limited by residual seismic motion and by radiative heating of the pendulum body. In addition to lowering thermal noise below room-temperature limits, the low-temperature environment enables novel torsion balance experiments. Currently, the maximum duration of a continuous measurement run is limited by accumulation of cryogenic surface contamination on the optical elements inside the cryostat.

Detection of QCD axion dark matter by coherent scattering

The QCD axion is a promising candidate of the dark matter. In this paper, we discuss elastic scattering processes between nucleons and the QCD axion dark matter. We point out that the cross section can be enhanced by more than $\mathcal{O}({10}^{25})$ by the coherent effect, compared to classical processes. As a result, for example, we show that QCD axions may scatter at the sun with $\mathcal{O}(1)$ probability for ${f}_{a}\ensuremath{\lesssim}{10}^{11}\text{ }\text{ }\mathrm{GeV}$. In addition, one may expect stimulated emission effects can also enhance the cross section because the number density of the axion DM is very large. The enhancement factor can be as large as another $\mathcal{O}({10}^{25})$ and, if the factor exists, the force from the dark matter wind may be detected via, e.g., torsion balance experiments. However, it is also found that there is a cancellation of the stimulated emission factor and the force is too small to be detected.

Elimination of the Blue Loops in the Evolution of Intermediate-mass Stars by the Neutrino Magnetic Moment and Large Extra Dimensions

Abstract For searching beyond Standard Model physics, stars are laboratories that complement terrestrial experiments. Massless neutrinos in the Standard Model of particle physics cannot have a magnetic moment, but massive neutrinos have a finite magnetic moment in the minimal extension of the Standard Model. Large extra dimensions (LEDs) are a possible solution of the hierarchy problem. Both of these provide additional energy-loss channels in stellar interiors via the electromagnetic interaction and radiation into extra dimensions, respectively, and thus affect stellar evolution. We perform simulations of stellar evolution with such additional energy losses and find that they eliminate the blue loops in the evolution of intermediate-mass stars. The existence of Cepheid stars can be used to constrain the neutrino magnetic moment (NMM) and LEDs. In order for Cepheids to exist, the NMM should be smaller than the range ∼2 × 10−10 μ B–4 × 10−11 μ B, where μ B is the Bohr magneton, and the fundamental scale in the (4+2)-spacetime should be larger than ∼2–5 TeV, depending on the rate of the 12C reaction. The fundamental scale also has strong dependence on the metallicity. This value of the magnetic moment is in the range explored in the reactor experiments, but higher than the limit inferred from globular clusters. Similarly the fundamental scale value we constrain corresponds to a size of the compactified dimensions comparable to those explored in the torsion balance experiments, but it is smaller than the limits inferred from collider experiments and low-mass stars.

Automation of the Cavendish torsion-balance experiment to measure G

We describe a simple and inexpensive method for automating data collection in the well-known Cavendish torsion-balance experiment to determine the gravitational constant G. The method uses a linear array of phototransistors and requires no moving parts. Multiplexers and a data-acquisition device are used to sample the state of each phototransistor sequentially. If the sampled phototransistor is illuminated by the laser spot, the position and time are recorded to a data file. The recorded data does an excellent job of capturing the damped harmonic oscillations. The resulting data were analysed to extract an experimental value of G that was within 5% of the accepted value.

On the gravitational seesaw in higher-derivative gravity

Local gravitational theories with more than four derivatives are superrenormalizable. They also may be unitary in the Lee–Wick sense. Thus it is relevant to study the low-energy properties of these theories, especially to identify observables which might be useful for experimental detection of higher derivatives. Using an analogy with the neutrino physics, we explore the possibility of a gravitational seesaw mechanism in which several dimensional parameters of the same order of magnitude produce a hierarchy in the masses of propagating particles. Such a mechanism could make a relatively light degree of freedom detectable in low-energy laboratory and astrophysical observations, such as torsion-balance experiments and the bending of light. We demonstrate that such a seesaw mechanism in the six- and more-derivative theories is unable to reduce the lightest mass more than in the simplest four-derivative model. Adding more derivatives to the four-derivative action of gravity makes heavier masses even greater, while the lightest massive ghost is not strongly affected. This fact is favorable for protecting the theory from instabilities but makes the experimental detection of higher derivatives more difficult.

Submillimeter spatial oscillations of Newton’s constant: Theoretical models and laboratory tests

We investigate the viability of sub-millimeter wavelength oscillating deviations from the Newtonian potential at both the theoretical and the experimental/observational level. At the theoretical level such deviations are generic predictions in a wide range of extensions of General Relativity (GR) including $f(R)$ theories, massive Brans-Dicke theories, compactified extra dimension models and nonlocal extensions of GR. However, the range of parameters associated with such oscillating deviations is usually connected with instabilities. An exception emerges in nonlocal gravity theories where oscillating deviations from Newtonian potential occur naturally on sub-millimeter scales without instabilities. As an example of a model with unstable Newtonian oscillations we review an $f(R)$ expansion around General Relativity of the form $f(R)=R+\frac{1}{6 m^2} R^2$ with $m^2<0$ pointing out possible stabilization mechanisms. As an example of a model with stable Newtonian oscillations we discuss nonlocal gravity theories. If such oscillations are realized in Nature on sub-millimeter scales, a signature is expected in torsion balance experiments testing Newton's law. We search for such a signature in the torsion balance data of the Washington experiment (combined torque residuals) testing Newton's law at sub-millimeter scales. We show that an oscillating residual ansatz with spatial wavelength $\lambda \simeq 0.1mm$ provides a better fit to the data compared to the residual Newtonian constant ansatz by $\Delta \chi^2 = -15$. Similar improved fits, also occur in about $10\%$ of Monte Carlo realizations of Newtonian data. Thus, the significance level of this improved fit is at a level of not more than $2\sigma$. The energy scale corresponding to this best fit wavelength is identical to the dark energy length scale $\lambda_{de} \equiv\sqrt[4]{\hbar c/\rho_{ de}}\approx 0.1mm$.

Electrostatic Positioning System for a free fall test at drop tower Bremen and an overview of tests for the Weak Equivalence Principle in past, present and future

The Weak Equivalence Principle (WEP) is at the basis of General Relativity – the best theory for gravitation today. It has been and still is tested with different methods and accuracies. In this paper an overview of tests of the Weak Equivalence Principle done in the past, developed in the present and planned for the future is given. The best result up to now is derived from the data of torsion balance experiments by Schlamminger et al. (2008). An intuitive test of the WEP consists of the comparison of the accelerations of two free falling test masses of different composition. This has been carried through by Kuroda & Mio (1989, 1990) with the up to date most precise result for this setup. There is still more potential in this method, especially with a longer free fall time and sensors with a higher resolution. Providing a free fall time of 4.74s (9.3s using the catapult) the drop tower of the Center of Applied Space Technology and Microgravity (ZARM) at the University of Bremen is a perfect facility for further improvements. In 2001 a free fall experiment with high sensitive SQUID (Superconductive QUantum Interference Device) sensors tested the WEP with an accuracy of 10-7 (Nietzsche, 2001). For optimal conditions one could reach an accuracy of 10-13 with this setup (Vodel et al., 2001). A description of this experiment and its results is given in the next part of this paper. For the free fall of macroscopic test masses it is important to start with precisely defined starting conditions concerning the positions and velocities of the test masses. An Electrostatic Positioning System (EPS) has been developed to this purpose. It is described in the last part of this paper.

Fundamental limitations to high-precision tests of the universality of free fall by dropping atoms

Tests of the universality of free fall and the weak equivalence principle probe the foundations of General Relativity. Evidence of a violation may lead to the discovery of a new force. The best torsion balance experiments have ruled it out to 10^-13. Cold-atom drop tests have reached 10^-7 and promise to do 7 to 10 orders of magnitude better, on the ground or in space. They are limited by the random shot noise, which depends on the number N of atoms in the clouds. As mass-dropping experiments in the non-uniform gravitational field of Earth, they are sensitive to the initial conditions. Random accelerations due to initial condition errors of the clouds are designed to be at the same level as shot noise, so that they can be reduced with the number of drops along with it. This sets the requirements for the initial position and velocity spreads of the clouds with given N. In the STE-QUEST space mission proposal aiming at 2x10^-15 they must be about a factor 8 above Heisenberg's principle limit, and the integration time required to reduce both errors is 3 years, with a mission duration of 5 years. Instead, offset errors at release between different atom clouds are systematic and give rise to a systematic effect which mimics a violation. Such offsets must be demonstrated to be as small as required in all drops, must be small by design and must be measured. For STE-QUEST to meet its goal they must be several orders of magnitude smaller than the size of each individual cloud, which in its turn must be at most 8 times larger than the uncertainty principle limit. Even if all technical problems are solved and the clouds are released with negligible systematic errors, still they must be measured. Then, Heisenberg's principle dictates that the measurement lasts as long as the experiment and the systematic nature of the effect requires many measurements for it to be ruled out as a source of violation.

Constraining models of extended gravity using Gravity Probe B and LARES experiments

We consider models of extended gravity and in particular, generic models containing scalar-tensor and higher-order curvature terms, as well as a model derived from noncommutative spectral geometry. Studying, in the weak-field approximation (the Newtonian and post-Newtonian limit of the theory), the geodesic and Lense-Thirring processions, we impose constraints on the free parameters of such models by using the recent experimental results of the Gravity Probe B (GPB) and Laser Relativity Satellite (LARES) satellites. The imposed constraint by GPB and LARES is independent of the torsion-balance experiment, though it is much weaker.

Precision torsion balance experiments and its applications

As an old and classical scientific instrument, the torsion balance was widely used in the field of precision measurement and fundamental physical experiments because of its extremely high sensitivity. In this paper, we briefly describe the basic principle of the torsion balance and the essential properties determining the accuracy of a torsion balancey experiment, and then introduce its typical applications at our laboratory, such as precision measurement of the gravitational constant <italic>G</italic> by the time-of-swing method, testing of the Newtonian gravitational inverse square law at short ranges by the dual-frequency modulation method, and measuring the upper limit on the photon mass by a rotating torsion balance.

Testing the weak equivalence principle with macroscopic proof masses on ground and in space: A brief review

General relativity is founded on the experimental fact that in a gravitational field all bodies fall with the same acceleration regardless of their mass and composition. This is the weak equivalence principle, or universality of free fall. Experimental evidence of a violation would require either that general relativity is to be amended or that another force of nature is at play. In 1916 Einstein brought as evidence the torsion balance experiments by Eötvös, to 10-8–10-9. In the 1960s and early 70s, by exploiting the "passive" daily rotation of the Earth, torsion balance tests improved to 10-11 and 10-12. More recently, active rotation of the balance at higher frequencies has reached 10-13. No other experimental tests of general relativity are both so crucial for the theory and so precise and accurate. If a similar differential experiment is performed inside a spacecraft passively stabilized by 1 Hz rotation while orbiting the Earth at ≃ 600 km altitude the test would improve by 4 orders of magnitude, to 10-17, thus probing a totally unexplored field of physics. This is unique to weakly coupled concentric macroscopic test cylinders inside a rapidly rotating spacecraft.

Constraints on noncommutative spectral action from Gravity Probe B and torsion balance experiments

Noncommutative spectral geometry offers a purely geometric explanation for the standard model of strong and electroweak interactions, including a geometric explanation for the origin of the Higgs field. Within this framework, the gravitational, the electroweak and the strong forces are all described as purely gravitational forces on a unified noncommutative space-time. In this study, we infer a constraint on one of the three free parameters of the model, namely the one characterising the coupling constants at unification, by linearising the field equations in the limit of weak gravitational fields generated by a rotating gravitational source, and by making use of recent experimental data. In particular, using data obtained by Gravity Probe B, we set a lower bound on the Weyl term appearing in the noncommutative spectral action, namely β≳10−6m−1. This constraint becomes stronger once we use results from torsion balance experiments, leading to β≳104m−1. The latter is much stronger than any constraint imposed so far to curvature squared terms.

GROUND-BASED EXPERIMENTS TO DETECT GRAVITO-MAGNETIC FORCE

Based on Maxwell-type linearized Einstein Eqs of gravity, new ground-base torsion balance experiments are proposed to detect gravito-magnetic forces due to the rotation of the Earth. An optic system is employed to enlarge the effects so that the predicted effects are measurable by the proposed ground-based experiments.

Further Support of the Reliability of the Limit on Photon Mass Given by the Rotating Torsion Balance Experiment

We consider there is a vacancy in the plasma in the solar system, and calculate the vector potential produced by the magnetic field frozen in the plasma. The result shows that, in the vacancy, the vector potential produced by the magnetic field frozen in the plasma is much less than the large scale cosmic vector potential. This means if our earth is in such a vacancy, the total vector potential on the surface of the earth is dominated by the cosmic magnetic vector potential, which gives a further support of the reliability of the limit on photon mass given by rotating torsion balance experiment [Phys. Rev. Lett. 90 (2003) 081801].

Limits on aCP-violating scalar axion-nucleon interaction

Axions or similar hypothetical pseudoscalar bosons may have a small CP-violating scalar Yukawa interaction g_s(N) with nucleons, causing macroscopic monopole-dipole forces. Torsion-balance experiments constrain g_p(e) g_s(N), whereas g_p(N) g_s(N) is constrained by the depolarization rate of ultra-cold neutrons or spin-polarized nuclei. However, the pseudoscalar couplings g_p(e) and g_p(N) are strongly constrained by stellar energy-loss arguments and g_s(N) by searches for anomalous monopole-monopole forces, together providing the most restrictive limits on g_p(e) g_s(N) and g_p(N) g_s(N). The laboratory limits on g_s(N) are currently the most restrictive constraints on CP-violating axion interactions.

Constraining photon mass by energy-dependent gravitational light bending

In the standard model of particle physics, photons are massless particles with a particular dispersion relation. Tests of this claim at different scales are both interesting and important. Experiments in territory labs and several exterritorial tests have put some upper limits on photon mass, e.g., torsion balance experiment in the lab shows that photon mass should be smaller than 1.2 × 10−51g. In this work, this claim is tested at a cosmological scale by looking at strong gravitational lensing data available and an upper limit of 8.71 × 10−39g on photon mass is given. Observations of energy-dependent gravitational lensing with not yet available higher accuracy astrometry instruments may constrain photon mass better.