First direct constraints on Fierz interference in free-neutron $\beta$ decay

Precision measurements of free-neutron $\beta$ decay have been used to precisely constrain our understanding of the weak interaction. However, the neutron Fierz interference term $b_n$, which is particularly sensitive to beyond-standard-model tensor currents at the TeV scale, has thus far eluded measurement. Here we report the first direct constraints on this term, finding $b_n=0.067\pm 0.{005}_{\text{stat}}{}_{-0.061}^{+0.090}{}_{\text{sys}}$, consistent with the standard model. The uncertainty is dominated by absolute energy reconstruction and the linearity of the $\beta$ spectrometer energy response.

Figure 1

Schematic diagram of the UCNA spectrometer.

Figure 2

Top: Reconstructed kinetic energy vs true kinetic energy for the conversion electron calibration sources. Uncertainty bands for the quadratic energy response functions used in the Monte Carlo estimate of systematic uncertainty in $b_n$ are also shown but barely visible due to the well-characterized response. Bottom: $\mathrm{\Delta }E$, the difference between true energy and reconstructed energy vs true energy. The bands are the same as for the top plot. The mean energies of conversion electron sources and their corresponding $1\sigma$ uncertainty in $\mathrm{\Delta }\mathrm{E}$ are also shown.

Figure 3

Distribution of fitted values of $b_n$ for the simulations with adjusted energy response.

Figure 4

Top: Measured energy spectrum compared with the full geant4 Monte Carlo spectrum for $b_n=0$ which includes the detector response. The dashed line is the predicted standard-model spectrum in the absence of detector response. Bottom: Measured shape factor (as defined in text) with statistical uncertainties. The solid line is the best-fit value for $b_n$ for the energy range of 150 $<E_R<$ 650 keV. The approximate $1\sigma$ and $2\sigma$ uncertainty range due to energy response is shown, using Monte Carlo simulations with nonzero $b_n$ sampled from Fig. 3 at the appropriate confidence levels. The minimum in the uncertainty bands occurs since only $b_n$ is varied in the simulations which produces a simple shift in the spectrum after normalization.