Reanalysis of the $\beta - \bar{\nu_e}$ 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 $a = -0.10402(82)$ 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 $b = -0.0098(193)$ which translates into a somewhat improved 90 \% CL region of $-0.041 \leq b \leq 0.022$ on this hypothetical term. Tighter constraints on $b$ can be set from a combined$^{(c)}$ analysis of the PERKEO~III ($\beta$ asymmetry) and aSPECT measurement which suggests a finite value of $b$ with $b^{(c)}$ = -0.0181 $\pm$ 0.0065 deviating by 2.82$\sigma$ from the standard model.