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

TL;DR

This paper assesses the internal consistency of neutron scattering measurements from interferometry and gravity reflectometry, showing their agreement and insensitivity to exotic interactions, which supports future constraints on short-range modifications to gravity.

Contribution

It demonstrates the high consistency between two different neutron scattering measurement methods and their robustness against exotic Yukawa interactions, aiding future analyses of neutron data.

Findings

Fractional difference in measurements is (2.2 ± 1.4) × 10^{-4}.

Measurement differences are insensitive to exotic Yukawa interactions.

Results support improved future neutron scattering experiments.

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 $q^{2}=8mV_{opt}$ 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.