A summary of the Planck constant measurements using a watt balance with a superconducting solenoid at NIST

TL;DR

This paper reports a corrected and combined measurement of the Planck constant using a watt balance at NIST, addressing previous discrepancies and systematic errors to refine the value with improved accuracy.

Contribution

The paper provides a corrected measurement of the Planck constant with a systematic uncertainty adjustment and guidance on combining conflicting measurements.

Findings

Final value of h: 6.62606936(37)×10⁻³⁴ J·s

Measurement is 77(57)×10⁻⁹ higher than h₉₀

Added systematic uncertainty to account for discrepancies

Abstract

Researchers at the National Institute of Standards and Technology have been using a watt balance, NIST-3, to measure the Planck constant $h$ for over ten years. Two recently published values disagree by more than one standard uncertainty. The motivation for the present manuscript is twofold. First, we correct the latest published number to take into account a recently discovered systematic error in mass dissemination at the Bureau International des Poids et Mesures (BIPM). Second, we provide guidance on how to combine the two numbers into one final result. In order to adequately reflect the discrepancy, we added an additional systematic uncertainty to the published uncertainty budgets. The final value of $h$ measured with NIST-3 is $h = 6.626\,069\,36(37)\times 10^{-34}\,\mbox{J\,s}$. This result is $77(57) \times 10^{-9}$ fractionally higher than $h_{\mathrm{90}}$. Each number in parentheses gives the value of the standard uncertainty in the last two digits of the respective value and $h_{\mathrm{90}}$ is the conventional value of the Planck constant given by $h_{\mathrm{90}}\equiv 4 /( K_{\mathrm{J-90}}^2 R_{\mathrm{K-90}})$, where $K_{\mathrm{J-90}}$ and $R_{\mathrm{K-90}}$ denote the conventional values of the Josephson and von Klitzing constants, respectively.