# Presentation: 916335

## A Short-Range Test of Newton’s Gravitational Inverse-Square Law

- A torsion-balance measurement
- from the Eöt-Wash Group,
- Center for Experimental Nuclear Physics and
- Astrophysics (CENPA)
- at the University of Washington
-  Eric Adelberger
-  Ted Cook
-  Jens Gundlach
-  Blayne Heckel
-  C.D. Hoyle
-  Erik Swanson
-  Dan Kapner – currently at KICP @
-  University of Chicago

- Coulomb’s torsion balance, 1785

## Isaac Newton’s Gravitational Inverse-Square Law (ISL)

-  Measured over a huge range of scales in search of new physics :

## Dark Energy and the ISL

- Gravity is an *attractive *force that acts between all mass/energy in the Universe.
- Expect the expansion of the Universe to slow.
- The expansion is accelerating, which implies a dark energy density :

- This length scale is unknown, but should be > 20μm.

- And a natural length scale :

- A modified ISL could potentially
- link the dark energy density with
- vacuum fluctuations, a much
- higher energy density. Gravity
- might be blind to small-scale
- (high-energy) physics.

## String Theory and the ISL

**String Theory – meant to unify all forces**
- Replaces point-like particles with one-dimensional strings or n-dimensional “branes”
- Requires 6 or 7 extra spatial dimensions
- Conventionally, thought to be observable at Planck scale
**May have observable consequences in short-range gravity:**
- Large extra dimensions may explain why gravity is so weak relative to other forces
- 	 *-Arkani-Hamed, Dimopoulos, Dvali*
- 	(Gauge Hierarchy Problem)
- New scalar fields may mediate macroscopic forces with strengths near gravity’s: radion, dilaton, other moduli...
**Chameleon Scalar Fields:**
- Self-interacting scalar fields acquire mass near local densities, hiding long-range interactions as short-range.
- 	- *Amol Upadhye, Steven S. Gubser, Justin Khoury** *hep-ph/0608186v1 – calculates effect for this experiment

- Figure courtesy Savas Dimopoulos

## Current Constraints

- Yukawa potential is the standard
- parameterization of ISL-violation

## General Torsion Oscillator

- 	: gravitational

-   : linear response

- fiber

- mirror

- detector
- mass

- attractor
- mass

## Short-Range Torsion Oscillator

- tungsten fiber, 20m diameter, 80cm length

- 21-fold axial symmetry, molybdenum disc, 1mm thick

- Attractor :** rotating pair** of discs, rotated out of phase with each other to **cancel Newtonian gravity**

- not pictured, 10m thick Au-coated BeCu membrane, electrostatic shield

- 3 aluminum calibration spheres

- 4 mirrors for tracking angle of deflection

- leveling mechanism

- “s”

- 7cm

## Short-Range Torsion Oscillator

## Noise

- optics noise

- data

- Predicted thermal noise for Q = 3500
- (internal dissipation)

## Calibration

- Error Budget :
- Pendulum sphere location [±13 μm]  : 2e-2 fNm
- Attractor sphere location   [±13 μm]  : 3e-3 fNm
- Z calibration centering    [±100 μm]  : 3e-4 fNm
- X-Y centering  	     [±160 μm] : 1e-5 fNm
- Pendulum sphere mass       [±20 μg]  : 2e-4 fNm
- Attractor sphere mass	      [±1.7 mg]  : 1e-5 fNm
- Total		     8.835   +/-   0.02 fNm
- Statistical uncertainty		 0.003 fNm.

## Apparatus

- -top – (x,y,z, ) stages to control position of fiber suspension
- vacuum vessel; turbo pumped, ~10-6 torr
- 3 leveling legs, ~3mrad/turn
- Autocollimator – laser and detector to track pendulum twist
- calibration turntable
- Thermal enclosure
- radiator
- All within a cleanroom

## Aligning Attractor to Bearing Rotation Axis

- 1μm indicator resolution
- Attractors held in copper cup
- Brass screws adjust alignment
- Vacuum-compatible bearing assembly with non-magnetic rotating components

## Align Bearing to Conducting Membrane

- Can adjust to make these two surfaces parallel

## Conducting Membrane

- 10μm thick Au-coated BeCu stretched foil shields electrostatic effects.
- Placed 12 μm above rotating attractor

## Pendulum-to-Horizon Alignment

- Intentional tilt ± 1.2 mrad

- Residual tilt ≤ 80 μrad

- Pendulum twists on fiber 180o, differential capacity changes sign

## Final Assembly

- Pendulum is Au-coated; conducting membrane and     Au-coated magnetic shield (not shown) surround it to minimize electrostatic interactions.

## Pendulum-to-Membrane Alignment

- Fit minimum to ≤ 16 μrad

- Total pendulum-to-attractor misalignment ≤ 70 μrad
- (≤ 5 μm height variation across rings)

## Pendulum-to-Membrane Separation

- pendulum-to-membrane separation determined by fit of capacitance vs. *z *to finite-element calculation

- Figure and Calculation - Ted Cook

## Newtonian Force Model

*t*

*F**t* at vertical  separation of 50μm

- Precision requirement

- Interpolation error

- Integration error

## Newtonian Torque Model - Cancelation

- Use tabulated horizontal forces *F**t *(*t,s*) to calculate torques.
*s *is vertical separation between pendulum and attractor rings

- upper-attractor contribution

- lower-attractor contribution

- total 21ω torque (×10)

## Upper-Attractor-Only Data

- Data runs with only the upper attractor help independently determine fit parameters.
- 21ω errors blow up at small distances due to calibration uncertainty, micrometer readout – closer points not worthwhile
- No departure from Newtonian gravity (*s *≥ 1mm)

- 21ω

- 42ω×30

- 63ω×20

## Newtonian Torque Model – Two Attractors

- 21ω

- 63ω

- 42ω

- Multiple harmonics (21, 42, 63): gravitational potential from attractors is not purely sinusoidal
- Function depends on physical characteristics of attractors:
- missing masses of holes
- positions and sizes of holes
- relative angles of attractors
- relative position of pendulum and attractors

## Allowable Range for New Physics

- short-range interactions show up predominantly at 21ω
- purple lines indicate previously- allowed range for deviations
- our statistical sensitivity :
- σ ≈ 0.003 fNm
-  (≈ thickness of lines)*
- *nominal : more later

## Two-Attractor Data and Newtonian Fit

- Substantial improvement over previous constraints
- Data taken down to *s* = 65 μm
- Good agreement with Newtonian gravity at *s* ≥ 100 μm
-  Showed repulsive deviation at scales smaller than 100 μm
* **status as of 06/2005*

## Successive Measurements

- Original measurement:
- Ignoring 3rd harmonic to be consistent with  further measurements.

## Successive Measurements

- 2nd measurement :
-  thinned lower attractor
-  flattened detector ring to better than 1μm (was 4μm)
-  went from 20μm to 17μm diameter fiber and changed turntable speeds to give better noise performance

## Successive Measurements

- 3rd measurement :
-  improved gold coatings
-  detector ring bent to 4μm again (inadvertently)
-  back to 20μm diameter fiber
-  independent measurements of attractor rings with same fiber

## Systematic and Other Effects

- Considered thermal, magnetic and mechanical systematic effects
- All were well below our statistical resolution
- Considered misalignments and imperfections
- if important, included as adjustable, constrained fit parameters
- 	(e.g. pendulum-ring curvature, gap between attractors, angle between attractors)
- Unshielded component of finite-temperature Casimir Effect?
- - Several different calculations show that this is negligible.

## New 95% Exclusion Constraints

## Results

- Fitting all 3 experiments gives 2 = 407 for  = 421
- Best-fit Yukawa (α , λ) = (.0037, 2mm) improves 2 by 3.5
- At any λ, Yukawa interaction is constrained to be ****** ******
- At 95%, a gravitational-strength force must have λ ≤ 56 μm
- For 2 large extra dimensions to solve gauge hierarchy problem, M*  ≥ 3.2TeV/c2
- 4 self-interacting scalar of Upadhye et al. excluded for “natural” values of self-interaction and coupling to matter.
- No evidence for new physics.
- Tests of the Gravitational Inverse-Square Law below the Dark-Energy Length Scale
- D.J. Kapner, T.S. Cook, E.G. Adelberger, J.H. Gundlach, B.R. Heckel, C.D. Hoyle, H.E. Swanson
- Phys.Rev.Lett. 98 (2007) 021101
- arXiv:hep-ph/0611184v1
- Particle Physics Implications of a Recent Test of the Gravitational Inverse Square Law
- E.G. Adelberger, B.R. Heckel, S. Hoedl, C.D. Hoyle, D.J. Kapner, A. Upadhye
- arXiv:hep-ph/0611223v3

## Future Plans

- New Experimental Design – Ted Cook’s thesis project
- higher symmetry, denser & thinner material → smaller Newtonian background→ less sensitive to imperfections
- wedges vs. holes → more sensitive to short-range interactions
- lighter pendulum → thinner fiber possible → lower thermal noise
- different set of systematics

- Plan view of tungsten foil detector and attractor rings.

## Next Generation Sensitivity

## Acknowledgements

- Eöt-Wash Group :
- 	  Eric Adelberger
- 	  Jens Gundlach
- 	  Blayne Heckel
- 	  Erik Swanson
- 	  Seth Hoedl
- 	  C.D. Hoyle
- 	  Stephan Schlamminger
- 	  Ki-Young Choi
- 	  Ted Cook
- 	  Claire Cramer
- 	  Charlie Hagedorn
- 	  Frank Marcoline
- 	  Chris Spitzer
- 	  Todd Wagner
- 	  Rogan Carr
- 	  Rob Kyle
- 	  Chiara Losh - REU

- CENPA machine shops :
- 	  Hank Simons
- 	  Jim Elms
- 	  David Hyde
- Physics Shop :
-  	  Mike Vinton
- 	  Ted Ellis
- 	  Brent Robinett

- NSF
- 	PHY-0355012
- DOE Office of Science