Reanalysis of the $\beta -{\overline{\nu }}_e$ Angular Correlation Measurement from the aSPECT Experiment with New Constraints on Fierz Interference

On the basis of revisions of some of the systematic errors, we reanalyzed the electron-antineutrino angular correlation ($a$ coefficient) in free neutron decay inferred from the recoil energy spectrum of the protons which are detected in $4\pi$ by the aSPECT spectrometer. With $a=-0.10402\left(82\right)$ the new value differs only marginally from the one published in 2020. The experiment also has sensitivity to $b$, the Fierz interference term. From a correlated $(b,a)$ fit to the proton recoil spectrum, we derive a limit of $b=-0.0098\left(193\right)$ which translates into a somewhat improved 90% confidence interval region of $-0.041\le b\le 0.022$ on this hypothetical term. Tighter constraints on $b$ can be set from a combined [shown as superscript ($c$)] analysis of the PERKEO III ($\beta$ asymmetry) and aSPECT measurement which suggests a finite value of $b$ with $b^{\left(c\right)}=-0.0181\pm 0.0065$ deviating by $2.82\sigma$ from the standard model.