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Tests of Gravity at the 100 Micron Scale and Below Α /R 33rd SLAC Summer Institute on Particle Physics (SSI 2005), 25 July - 5 August 2005 Tests of Gravity at the 100 Micron Scale and Below Joshua Long Indiana University Cyclotron Facility, Bloomington, IN, USA Experimental limits allow for new forces in nature millions of times stronger than gravity at distance scales resolvable to the unaided eye, and trillions of times stronger than gravity at scales accessible to scanning probe microscopy. Recent theoretical work has led to specific predictions of new physics in these regimes, including possible signatures of extra spacetime dimensions. This presentation will review several experiments and proposals designed to be sensitive to new physics at these scales, with emphasis on an experiment in progress at Indiana University that probes the range from about 10 to 100 microns. 1. INTRODUCTION This presentation focuses on a series of table-top sized experiments designed to be sensitive to gravity and possible new physics at distance scales below 100 μm, with emphasis on an experiment in progress at Indiana University. This experiment is a continuation of one recently completed in the laboratory of Prof. John Price at the University of Colorado. The treatment is at the introductory level, and concentrates on experimental techniques and the sensitivity attainable with them. The first sections include a description of the parameters in terms of which these experiments commonly report their results, and a number of specific predictions of new effects these experiments can test. Following sections describe the experiments, starting with those sensitive in the range above a few microns. These include classical gravity measurements carried out with torsion pendulums, which are the most sensitive at 100 μm. Recently, experiments using high-frequency techniques (including the Colorado-Indiana project) have attained the most sensitivity at the short- distance end of this range. The final sections discuss experiments and proposals sensitive to the range below 1 μm, where the dominant background is the Casimir force. The presentation focuses mainly on active programs that have published results, and also highlights efforts at Stanford, the host institution of this conference, which has played a major role in both theoretical and experimental work in this field. 2. PARAMETER SPACE Short-range experiments are designed to be sensitive to new physics that manifests itself as a deviation from the Newtonian inverse-square law. The most popular parameterization of these deviations in the literature is in terms of the Yukawa potential, given by: mGm 21 − /r λ )r(V = ( +αe1 ) (1) r where G is the Newtonian Gravitational Constant, m1 and m2 are test masses, and r is their separation. The first term is the potential due to standard gravity and the second is the Yukawa potential. Here, α is the strength of a new interaction relative to gravity and λ is the range. The Yukawa interaction arises when the force between the test masses is mediated by a massive field; the range λ is given by the Compton wavelength of the mediating particle. In the absence of a signal of a new interaction (no such verifiable signal has been observed in any short range experiment to date), experimental results are commonly reported in terms of limits on the strength parameter α for a given range λ. They T032 1 33rd SLAC Summer Institute on Particle Physics (SSI 2005), 25 July - 5 August 2005 are often displayed on a log-log plot of one parameter versus the other, of which there are several examples in this presentation. 3. EXISTING LIMITS AND THEORETICAL MOTIVATION Fig. 1 is the first example. It shows the experimental limits in 1998, just after the Colorado project began, along with some theoretical predictions. Here, the range λ runs from 1 μm to 1 cm, the strength α runs from 10-6 times gravitational strength up to 1010. The experimentally excluded area is above and to the right of the solid black curves; each curve represents a 90% C. L. upper limit on α with the exception of the curve labeled “Irvine”, which is a 1σ upper limit. All of the limits are derived from torsion pendulum experiments. The Irvine curve is the result from an experiment in which a cylindrical test mass was suspended inside a long tube, nominally a null geometry for 1/r2 forces [1]. The curve labeled “Mitrofanov” is the result of a miniature version of the Cavendish experiment [2]. The curve labeled ``Lamoreaux'' derives from an experiment in which a torsion balance was used to measure the Casimir force between a spherical shell and flat disk [3]; the limits on new forces consistent with the experimental residuals of this experiment are derived in Refs. [4] and [5]. The experimental limits show that as of 1998, gravity itself had only been measured to length scales of about 1 mm. The limits allowed for new forces in nature several million times stronger than gravity at ranges of about 10 μm. Figure 1: Parameter space for short-range experiments in which the strength α of a hypothetical Yukawa interaction is plotted vs. the range λ. In addition to this very general motivation for new experiments, a number of specific theoretical predictions of new physics had appeared in this regime. These are represented by the fine and dashed lines in Fig. 1. Two recent comprehensive reviews on the subject can be found in Refs. [6] and [7]. The theoretical predictions tend to fall into T032 2 33rd SLAC Summer Institute on Particle Physics (SSI 2005), 25 July - 5 August 2005 three broad categories: signatures of compact extra dimensions, forces arising from the exchange of exotic scalar fields, and ideas motivated by the cosmological constant problem. The horizontal line labeled “Extra Dimensions” in Fig. 1 refers to the extra dimensions of string theories. String theories are the leading candidates for a unified description of gravity and the other fundamental forces, and have to be formulated in more than 3 spatial dimensions. In the original formulations of string theory the extra dimension were taken to be compacted at lengths on the order of the Planck scale 19 -35 (MP ~ 10 GeV or 10 m) and presumably undetectable by any practical experiment. In 1998 a class of models was discovered in which the weakness of gravity relative to the other fundamental forces is explained by two or more of these extra dimensions remaining large and accessible only to gravity; the spreading of the gravitational interaction into the extra dimensions appears to dilute its strength. The original model, termed the ADD model after its authors [8], relates the size R of the extra dimensions to their number n according to the expression: n 2 +∗ )n2( = P M/MR , (2) Where M* is the actual scale of the gravitational interaction. Assuming the weak scale MW to be the only short-distance scale in nature (and effectively eliminating the hierarchy problem), choosing M* ~ MW ~ 1 TeV in Eq. 2 yields R ~ 1 mm for n = 2. The consequence is that gravitational experiments approaching this range should be sensitive to potentials dictated by the appropriate Gauss’ law in 5 spatial dimensions, or forces varying as r-4. Detailed phenomenological investigations of these models predict Yukawa-type corrections to the Newtonian power law as the scale R ~ λ of the extra dimensions is approached from above [9, 10]; the model in Fig. 1 predicts α = 4 for n = 2. The scale M*, now a free parameter in these models, need not be fixed at 1 TeV; the range of the prediction in Fig. 1 represents a variation in the scale from about 1 TeV at λ ~ 1 mm to 20 TeV at λ ~ 1 μm. Scalar fields giving rise to new forces include moduli, dilatons, and axions. Moduli are gravitationally-coupled scalars that parameterize the size and shape of extra dimensions in string theories. They can acquire masses in the meV range via a number of scenarios, whereby they are predicted to mediate forces in the range of a few microns with a wide range of couplings [11, 12]. The dilaton is another scalar in string theory, the vacuum expectation value of which determines the strength of the interaction between strings. The coupling of the dilaton has been estimated to lie in a wide range above gravitational strength, but the mass has been constrained only by experiment [13, 14]. The axion is a light pseudoscalar field intended to explain the apparent absence of CP-violating effects in strong (QCD) interactions. It is also predicted to mediate sub-millimeter range forces between unpolarized test masses, though at an extremely feeble level [15, 16]. Finally, another class of predictions arises in attempts to address the cosmological constant (Λ) problem, the vast discrepancy between the observed curvature of the universe and the amount expected from vacuum energy contributions of the standard model fields. The vertical bars in Fig. 1 arise from models that postulate new fields with interaction ranges on the order of Λ-1/4 ~ 100 μm that act to suppress the vacuum contributions [17, 18]. 4. EXPERIMENTAL CHALLENGES With all of this motivation for short-range tests of gravity in the late 1990s, it may strike as odd why a number of experiments did not begin publishing right away. After all, the Cavendish experiment, published in 1798, represented a very sensitive measurement of Newton’s Constant with test mass separations of a few centimeters. The principle T032 3 33rd SLAC Summer Institute on Particle Physics (SSI 2005), 25 July - 5 August 2005 challenge to gravitationally sensitive experiments at short range is the scaling of the signal force with the size of the test masses. If all dimensions of the test masses are scaled by the same factor L, the signal varies as L4 and becomes extremely small at short ranges.
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