Search for an anomalous excess of charged-current quasielastic ${\nu }_e$ interactions with the MicroBooNE experiment using Deep-Learning-based reconstruction

We present a measurement of the ${\nu }_e$-interaction rate in the MicroBooNE detector that addresses the observed MiniBooNE anomalous low-energy excess (LEE). The approach taken isolates neutrino interactions consistent with the kinematics of charged-current quasielastic (CCQE) events. The topology of such signal events has a final state with one electron, one proton, and zero mesons ($1e1p$). Multiple novel techniques are employed to identify a $1e1p$ final state, including particle identification that use two methods of Deep-Learning-based image identification and event isolation using a boosted decision-tree ensemble trained to recognize two-body scattering kinematics. This analysis selects 25 ${\nu }_e$-candidate events in the reconstructed neutrino energy range of 200–1200 MeV, while $29.0\pm 1.9_{(\mathrm{sys})}\pm 5.4_{(\mathrm{stat})}$ are predicted when using ${\nu }_{\mu }$ CCQE interactions as a constraint. We use a simplified model to translate the MiniBooNE LEE observation into a prediction for a ${\nu }_e$ signal in MicroBooNE. A $\mathrm{\Delta }{\chi }^2$ test statistic, based on the combined Neyman–Pearson ${\chi }^2$ formalism, is used to define frequentist confidence intervals for the LEE signal strength. Using this technique, in the case of no LEE signal, we expect this analysis to exclude a normalization factor of 0.75 (0.98) times the median MiniBooNE LEE signal strength at 90% ($2\sigma$) confidence level, while the MicroBooNE data yield an exclusion of 0.25 (0.38) times the median MiniBooNE LEE signal strength at 90% ($2\sigma$) confidence level.

Figure 1

A typical selected data event from this analysis, showing time tick vs wire number from the TPC. (a) Pixel intensity images with annotation indicating the electron and proton. (b) Pixel labeling from the Deep-Learning-based semantic segmentation algorithm, discussed in Sec. 5.

Figure 2

MicroBooNE LEE model weights, based on unfolding the MiniBooNE electronlike excess assuming a ${\nu }_e$ hypothesis. These weights are applied to the beam-intrinsic CC ${\nu }_e$ prediction in order to obtain the MiniBooNE median LEE model prediction used in this analysis, which is added to the background contributions. In this analysis, LEE model weights above a true neutrino energy of 800 MeV are set explicitly to zero.

Figure 3

The fractional error distribution of the neutrino energy reconstruction for simulated ${\nu }_e$ CCQE events that pass $1e1p$ selection criteria and reconstruct with $200<E_{\nu }<1200\mathrm{MeV}$.

Figure 4

$E_{\nu }$ distribution comparing data (black points) to the unconstrained prediction (stacked histogram) in the $200<E_{\nu }<1200\mathrm{MeV}$ region. The green contribution represents the prediction from the background fit described in Sec. 6a3, and the dashed blue line gives the prediction of the unfolded median MiniBooNE excess model described in Sec. 4a. The ${\chi }_{\mathrm{CNP}}^2/\mathrm{d}.\mathrm{o}.\mathrm{f}.$ is $23.02/10$, corresponding to $p_{\mathrm{val}}=0.024$. The prediction is presented in terms of both interaction type (a) and topology (b). The numbers in parentheses indicate the integrated number of events over the range shown.

Figure 5

$1e1p$ BDT ensemble average score distribution comparing data (black points) to the unconstrained prediction (stacked histogram) in the [0.95, 1.0] region. The green background contribution comes directly from our simulation sample, and the dashed blue line gives the prediction of the unfolded median MiniBooNE excess model described in Sec. 4a. The ${\chi }_{\mathrm{CNP}}^2/\mathrm{d}.\mathrm{o}.\mathrm{f}.$ is $11.06/10$, corresponding to $p_{\mathrm{val}}=0.43$.

Figure 6

The fit to the ${\nu }_{\mu }$ background distribution to the $1e1p$ analysis. The shape fit is performed at a loose BDT score cutoff of 0.7 (a) and scaled to the signal cutoff of 0.95 (b). Blue points represent the prediction from the simulation, with error bars representing the Gaussian approximation of the statistical error (quadrature sum of event weights). The orange line and corresponding shaded region represent prediction and uncertainty, respectively, coming from the $\mathrm{Landau}+\mathrm{linear}$ fit.

Figure 7

The data and MC prediction for events with a BDT score inside [0.7, 0.95]. The ${\chi }_{\mathrm{CNP}}^2/\mathrm{d}.\mathrm{o}.\mathrm{f}.$ for this distribution is $11.35/10$, corresponding to $p_{\mathrm{val}}=0.38$. This indicates good agreement between observed data and prediction. The prediction incorporating the $\mathrm{Landau}+\mathrm{linear}$ background fit is shown by the red line.

Figure 8

The reconstructed neutrino energy spectrum of the data and simulation for events passing the $1\mu 1p$ selection, calculated using the track lengths of the proton and muon. The ${\chi }_{\mathrm{CNP}}^2/19(\mathrm{d}.\mathrm{o}.\mathrm{f}.)=1.314$ with a $p$ value of 0.162.

Figure 9

For comparison to Fig. 8, the reconstructed neutrino charged-current quasielastic energy spectrum of the data and prediction for events passing the $1\mu 1p$ selection. This is calculated using Eq. (4). The ${\chi }_{\mathrm{CNP}}^2/14(\mathrm{d}.\mathrm{o}.\mathrm{f}.)=0.950$ with a $p$ value of 0.522.

Figure 10

The ${\pi }^0$ mass test variable for events passing the ${\pi }^0$ selection criteria. The colored stacked histograms represent the standard simulation (MC) prediction. The red dashed line is the total weighted (wMC) prediction. The data points are shown by the black points. The lower two panels show the data/MC ratio and data/wMC ratio, respectively. The ${\chi }_{\mathrm{CNP}}^2/20(\mathrm{d}.\mathrm{o}.\mathrm{f}.)=0.709$ with a $p$ value of 0.821 for the MC prediction. The ${\chi }_{\mathrm{CNP}}^2/20(\mathrm{d}.\mathrm{o}.\mathrm{f}.)=0.778$ with a $p$ value of 0.744 for the wMC prediction.

Figure 11

Reconstructed ${\pi }^0$ momenta for the CC (a) and NC (b) samples. The colored stacked histograms represent the standard simulation (MC) prediction. The red dashed line is the total weighted (wMC) prediction. The data points are shown by the black points. The lower two panels of each figure show the data/MC ratio and data/wMC ratio, respectively. In the CC sample, the ${\chi }_{\mathrm{CNP}}^2/20(\mathrm{d}.\mathrm{o}.\mathrm{f}.)=0.619$ with a $p$ value of 0.902 for the MC prediction and the ${\chi }_{\mathrm{CNP}}^2/20(\mathrm{d}.\mathrm{o}.\mathrm{f}.)=0.405$ with a $p$ value of 0.991 for the wMC prediction. In the NC sample, the ${\chi }_{\mathrm{CNP}}^2/20(\mathrm{d}.\mathrm{o}.\mathrm{f}.)=0.555$ with a $p$ value of 0.944 for the MC prediction and the ${\chi }_{\mathrm{CNP}}^2/20(\mathrm{d}.\mathrm{o}.\mathrm{f}.)=0.490$ with a $p$ value of 0.972 for the wMC prediction.

Figure 12

The Michel electron energy spectrum. The data observation is given by the black points, and the prediction is given by the stacked histogram. The systematic error here corresponds only to the statistical uncertainty on the simulated events. The ${\chi }_{\mathrm{CNP}}^2/\mathrm{d}.\mathrm{o}.\mathrm{f}.$ for this distribution is $5.9/10$.

Figure 13

Fractional uncertainties on the prediction for the $1e1p$ (a) and $1\mu 1p$ (b) event selections as a function of reconstructed neutrino energy.

Figure 14

Total fractional covariance (a) and correlation (b) matrices for the $1e1p$ and $1\mu 1p$ selections. The $1e1p$ events are on the lower left and are binned from 200–1200 MeV in 100 MeV bins. The $1\mu 1p$ events are on the upper right and are binned from 250–1200 MeV in 50 MeV bins. The solid bold lines indicate the boundaries between the $1e1p$ and $1\mu 1p$ selections.

Figure 15

Fractional systematic uncertainties for the $1e1p$ prediction as a function of reconstructed neutrino energy, before and after the $1\mu 1p$ constraint. The black curve is the same as the total systematic uncertainty shown in Fig. 13.

Figure 16

The final constrained prediction for ${\nu }_e$ signal and ${\nu }_{\mu }$ background events compared with the observed data events in the analysis range ($200<E_{\nu }<1200\mathrm{MeV}$). The final prediction before the constraint is shown by the black line, and the final constrained systematic errors are shown by the gray band. The ${\chi }_{\mathrm{CNP}}^2/\mathrm{d}.\mathrm{o}.\mathrm{f}.$ is $25.28/10$, corresponding to $p_{\mathrm{val}}=0.014$.

Figure 17

Comparison between data (black points) and simulation in the $E_{\nu }^{\mathrm{QE}-\ell }$ distribution. The stacked histograms give the prediction directly from our simulation sample, and the dashed line gives the prediction of the unfolded median MiniBooNE excess model described in Sec. 4a. The ${\chi }_{\mathrm{CNP}}^2/\mathrm{d}.\mathrm{o}.\mathrm{f}.$ is $11.46/10$, corresponding to $p_{\mathrm{val}}=0.52$.

Figure 18

Comparison between data (black points) and simulation for the $E_{e^{-}}$ distribution. The stacked histograms give the prediction directly from our simulation sample. and the dashed line gives the prediction of the unfolded median MiniBooNE excess model described in Sec. 4a. The ${\chi }_{\mathrm{CNP}}^2/\mathrm{d}.\mathrm{o}.\mathrm{f}.$ is $10.68/10$, corresponding to $p_{\mathrm{val}}=0.42$.

Figure 19

Comparison between data (black points) and simulation (stacked histograms) for the $E_p$ distribution. The stacked histograms are as described in Fig. 18. The ${\chi }_{\mathrm{CNP}}^2/\mathrm{d}.\mathrm{o}.\mathrm{f}.$ is $5.77/10$, corresponding to $p_{\mathrm{val}}=0.80$.

Figure 20

Comparison between data (black points) and simulation (stacked histograms) for the ${\theta }_{e^{-}}$ distribution. The stacked histograms are as described in Fig. 18. The distribution is not peaked at a small angle due to the opening angle requirement for vertex-finding described in Sec. 5d. The ${\chi }_{\mathrm{CNP}}^2/\mathrm{d}.\mathrm{o}.\mathrm{f}.$ is $10.19/10$, corresponding to $p_{\mathrm{val}}=0.48$.

Figure 21

(Top) Pixel intensity. (Bottom) sparsessnet labels. (Left to Right) $U$, $V$, $Y$ planes. The white circle indicates the reconstructed vertex.

Figure 22

Results of the two-hypothesis test comparing the $1e1p$ observation to the constrained $H_0$ and $H_1$ predictions. The hatched red (blue) histogram shows the distribution of the $\mathrm{\Delta }{\chi }^2$ test statistic under the $H_0$ ($H_1$) hypothesis. The cyan vertical line indicates the data value of $-11.08$.

Figure 23

Confidence level at which we rule out values of $x_{\mathrm{LEE}}$, based on the Feldman–Cousins procedure (solid black curve) and Wilks’ theorem (dotted gray curve). The shaded dark green region is the $1\sigma$ confidence interval determined using the Feldman–Cousins procedure. The light green region is the 90% interval. The yellow region is the $2\sigma$ interval. The dashed blue vertical line indicates the best-fit value at $x_{\mathrm{LEE}}=0$. The solid red vertical line is the median MiniBooNE signal model at $x_{\mathrm{LEE}}=1$; the hatched red (orange) region is the estimated MiniBooNE $1\sigma$ confidence interval without (with) systematic uncertainties.

Figure 24

(Top) pixel intensity. (Bottom) sparsessnet labels. (Left to right) $U$, $V$, $Y$ planes. The white circle indicates the reconstructed vertex.

Figure 25

(Top) pixel intensity. (Bottom) sparsessnet labels. (Left to right) $U$, $V$, $Y$ planes. The white circle indicates the reconstructed vertex.

Figure 26

(Top) pixel intensity. (Bottom) sparsessnet labels. (Left to right) $U$, $V$, $Y$ planes. The white circle indicates the reconstructed vertex.

Figure 27

(Top) pixel intensity. (Bottom) sparsessnet labels. (Left to right) $U$, $V$, $Y$ planes. The white circle indicates the reconstructed vertex.

Figure 28

(Top) pixel intensity. (Bottom) sparsessnet labels. (Left to right) $U$, $V$, $Y$ planes. The white circle indicates the reconstructed vertex.

Figure 29

(Top) pixel intensity. (Bottom) sparsessnet labels. (Left to right) $U$, $V$, $Y$ planes. The white circle indicates the reconstructed vertex.

Figure 30

(Top) pixel intensity. (Bottom) sparsessnet labels. (Left to right) $U$, $V$, $Y$ planes. The white circle indicates the reconstructed vertex.

Figure 31

(Top) pixel intensity. (Bottom) sparsessnet labels. (Left to right) $U$, $V$, $Y$ planes. The white circle indicates the reconstructed vertex.

Figure 32

(Top) pixel intensity. (Bottom) sparsessnet labels. (Left to right) $U$, $V$, $Y$ planes. The white circle indicates the reconstructed vertex.

Figure 33

(Top) pixel intensity. (Bottom) sparsessnet labels. (Left to right) $U$, $V$, $Y$ planes. The white circle indicates the reconstructed vertex.

Figure 34

(Top) pixel intensity. (Bottom) sparsessnet labels. (Left to right) $U$, $V$, $Y$ planes. The white circle indicates the reconstructed vertex.

Figure 35

(Top) pixel intensity. (Bottom) sparsessnet labels. (Left to right) $U$, $V$, $Y$ planes. The white circle indicates the reconstructed vertex.

Figure 36

(Top) pixel intensity. (Bottom) sparsessnet labels. (Left to right) $U$, $V$, $Y$ planes. The white circle indicates the reconstructed vertex.

Figure 37

(Top) pixel intensity. (Bottom) sparsessnet labels. (Left to right) $U$, $V$, $Y$ planes. The white circle indicates the reconstructed vertex.

Figure 38

(Top) pixel intensity. (Bottom) sparsessnet labels. (Left to right) $U$, $V$, $Y$ planes. The white circle indicates the reconstructed vertex.

Figure 39

(Top) pixel intensity. (Bottom) sparsessnet labels. (Left to right) $U$, $V$, $Y$ planes. The white circle indicates the reconstructed vertex.

Figure 40

(Top) pixel intensity. (Bottom) sparsessnet labels. (Left to right) $U$, $V$, $Y$ planes. The white circle indicates the reconstructed vertex.

Figure 41

(Top) pixel intensity. (Bottom) sparsessnet labels. (Left to right) $U$, $V$, $Y$ planes. The white circle indicates the reconstructed vertex.

Figure 42

(Top) pixel intensity. (Bottom) sparsessnet labels. (Left to right) $U$, $V$, $Y$ planes. The white circle indicates the reconstructed vertex.

Figure 43

(Top) pixel intensity. (Bottom) sparsessnet labels. (Left to right) $U$, $V$, $Y$ planes. The white circle indicates the reconstructed vertex.

Figure 44

(Top) pixel intensity. (Bottom) sparsessnet labels. (Left to right) $U$, $V$, $Y$ planes. The white circle indicates the reconstructed vertex.

Figure 45

(Top) pixel intensity. (Bottom) sparsessnet labels. (Left to right) $U$, $V$, $Y$ planes. The white circle indicates the reconstructed vertex.

Figure 46

(Top) pixel intensity. (Bottom) sparsessnet labels. (Left to right) $U$, $V$, $Y$ planes. The white circle indicates the reconstructed vertex.

Figure 47

(Top) pixel intensity. (Bottom) sparsessnet labels. (Left to right) $U$, $V$, $Y$ planes. The white circle indicates the reconstructed vertex.