Internal Consistency of Neutron Coherent Scattering Length Measurements from Neutron Interferometry and from Neutron Gravity Reflectometry for Exotic Yukawa Analyses

Abstract

Many theories beyond the Standard Model postulate short-range modifications to gravity which produce deviations of Newton's gravitational potential from a strict $1/r$ dependence. It is common to analyze experiments searching for these modifications using a potential of the form $V^{\prime }(r)=-\frac{GMm}{r}[1+\alpha \exp (-r/\lambda )]$. The best present constraints on $\alpha$ for $\lambda <100$\,nm come from neutron scattering and often employ comparisons of different measurements of the coherent neutron scattering amplitudes $b$. We analyze the internal consistency of existing data from two different types of measurements of low energy neutron scattering amplitudes: neutron interferometry, which involves squared momentum transfers $q^2=0$, and neutron gravity reflectometry, which involves squared momentum transfers $q^2=8m{V}_{opt}$ where $m$ is the neutron mass and $V_{opt}$ is the neutron optical potential of the medium. We show that the fractional difference $\frac{\Delta b}{|b|}$ averaged over the 7 elements where high precision data exists on the same material from both measurement methods is $[2.2\pm 1.4]\times 10^{-4}$. We also show that $\frac{\Delta b}{|b|}$ for this data is insensitive both to exotic Yukawa interactions and also to the electromagnetic neutron-atom interactions proportional to the neutron-electron scattering length $b_{ne}$ and the neutron polarizability scattering amplitude $b_{pol}$. This result will be useful in any future global analyses of neutron scattering data to determine $b_{ne}$ and bound $\alpha$ and $\lambda$. We also discuss how various neutron interferometric and scattering techniques with cold and ultracold neutrons can be used to improve the precision of $b$ measurements and make some specific proposals.

13 pages, 1 figure

References in corpus (19)

• Tests of the Gravitational Inverse-Square Law below the Dark-Energy Length Scale
• Improved constraints on non-Newtonian forces at 10 microns
• Neutron scattering and extra short range interactions
• Review of short-range gravity experiments in the LHC era
• Gravity Resonance Spectroscopy Constrains Dark Energy and Dark Matter Scenarios
• A New Constraint for the Coupling of Axion-like particles to Matter via Ultra-Cold Neutron Gravitational Experiments
• Neutron Interferometry constrains dark energy chameleon fields
• Acoustic Rabi oscillations between gravitational quantum states and impact on symmetron dark energy
• Experiments in Fundamental Neutron Physics
• Constraints on New Gravitylike Forces in the Nanometer Range
• Limits on the Axial Coupling Constant of New Light Bosons
• Constraints on new interactions from neutron scattering experiments
• New source for ultracold neutrons at the Institut Laue-Langevin
• New constraints for CP-violating forces between nucleons in the range 10-4 cm - 1 cm
• A Neutron Interferometric Method to Provide Improved Constraints on Non-Newtonian Gravity at the Nanometer Scale
• Bounds on new light particles from high-energy and very small momentum transfer np elastic scattering data
• Prospects for Searching Thermal Effects, Non-Newtonian Gravity and Axion-Like Particles: Cannex Test of the Quantum Vacuum
• Constraining Spacetime Nonmetricity with Neutron Spin Rotation in Liquid He-4
• Comment about constraints on nanometer-range modifications to gravity from low-energy neutron experiments

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