Search for Neutrino-Induced Neutral Current $\Delta$ Radiative Decay in MicroBooNE and a First Test of the MiniBooNE Low Energy Excess Under a Single-Photon Hypothesis

We report results from a search for neutrino-induced neutral current (NC) resonant $\Delta$(1232) baryon production followed by $\Delta$ radiative decay, with a $\langle0.8\rangle$~GeV neutrino beam. Data corresponding to MicroBooNE's first three years of operations (6.80$\times$10$^{20}$ protons on target) are used to select single-photon events with one or zero protons and without charged leptons in the final state ($1\gamma1p$ and $1\gamma0p$, respectively). The background is constrained via an in-situ high-purity measurement of NC $\pi^0$ events, made possible via dedicated $2\gamma1p$ and $2\gamma0p$ selections. A total of 16 and 153 events are observed for the $1\gamma1p$ and $1\gamma0p$ selections, respectively, compared to a constrained background prediction of $20.5 \pm 3.65 \text{(sys.)} $ and $145.1 \pm 13.8 \text{(sys.)} $ events. The data lead to a bound on an anomalous enhancement of the normalization of NC $\Delta$ radiative decay of less than $2.3$ times the predicted nominal rate for this process at the 90% confidence level (CL). The measurement disfavors a candidate photon interpretation of the MiniBooNE low-energy excess as a factor of $3.18$ times the nominal NC $\Delta$ radiative decay rate at the 94.8% CL, in favor of the nominal prediction, and represents a greater than $50$-fold improvement over the world's best limit on single-photon production in NC interactions in the sub-GeV neutrino energy range

We report results from a search for neutrino-induced neutral current (NC) resonant ∆(1232) baryon production followed by ∆ radiative decay, with a 0.8 GeV neutrino beam. Data corresponding to MicroBooNE's first three years of operations (6.80×10 20 protons on target) are used to select single-photon events with one or zero protons and without charged leptons in the final state (1γ1p and 1γ0p, respectively). The background is constrained via an in-situ high-purity measurement of NC π 0 events, made possible via dedicated 2γ1p and 2γ0p selections. A total of 16 and 153 events are observed for the 1γ1p and 1γ0p selections, respectively, compared to a constrained background prediction of 20.5 ± 3.65(sys.) and 145.1 ± 13.8(sys.) events. The data lead to a bound on an anomalous enhancement of the normalization of NC ∆ radiative decay of less than 2.3 times the predicted nominal rate for this process at the 90% confidence level (CL). The measurement disfavors a candidate photon interpretation of the MiniBooNE low-energy excess as a factor of 3.18 times the nominal NC ∆ radiative decay rate at the 94.8% CL, in favor of the nominal prediction, and represents a greater than 50-fold improvement over the world's best limit on single-photon production in NC interactions in the sub-GeV neutrino energy range.
For over two decades, the anomalous signals consisting of MiniBooNE's low-energy excess (LEE) [1][2][3] and the prior LSND [4] ν e appearance results have been at the forefront of neutrino physics. Each has been interpreted as evidence for new types of neutrinos or other physics beyond the Standard Model (SM). The existence of new particles would be the first evidence for a new paradigm of physics associated with the neutrino sector since the discovery of neutrinos mass via their observed oscillations, and would have profound ramifications for all particle physics, astrophysics, and cosmology. At the heart of this puzzle of anomalies in need of interpretation is the fact MiniBooNE could not differentiate neutrino interactions producing an electron (such as from ν e appearance due to light sterile neutrinos) from those with a single photon in the final state. Thus, both types of interactions must be examined independently as a source of the LEE.
Neutrino-induced neutral current (NC) production of the ∆(1232) baryon resonance with subsequent ∆ radiative decay is predicted to be the dominant source of single photons in neutrino-argon scattering below 1 GeV [5]. Although ∆ radiative decay is predicted in the SM, and measurements of photoproduction [6] and virtual compton scattering [7] are well described by theory, this process has never been directly observed in neutrino scattering. Previous searches have been performed by the T2K [8] and NOMAD [9] experiments with average incident neutrino energies, E ν , of 0.85 and 25 GeV, respectively, resulting in leading limits on this process. Although on a different target, T2K's result is closest in E ν to that of the MiniBooNE beam. However, the 90% con-fidence level (CL) limit is ∼ 100 times the theoretically predicted rate of NC ∆ radiative decay.
In this letter, we present the world's most sensitive search for NC ∆ → N γ, where N = p, n, using neutrinoargon scattering data collected by the MicroBooNE detector [10]. MicroBooNE is an 85 metric ton active volume liquid argon time projection chamber (LArTPC) situated at a similar baseline in the same muon neutrino dominated Booster Neutrino Beam (BNB) at Fermilab [11] as MiniBooNE, with E ν = 0.8 GeV. The measurement makes use of data corresponding to a BNB exposure of 6.80 × 10 20 protons on target (POT), collected during 2016-2018. LArTPC technology allows Mi-croBooNE to distinguish electromagnetic showers originating from electrons or photons based on ionization energy deposition (dE/dx) at the start of the shower, and the non-zero conversion distance of the photon relative to the interaction vertex.
This search represents a first for this process with argon as the neutrino target, and also constitutes the first test of the MiniBooNE LEE under a single-photon interpretation. In a fit to the radial distribution of the Mini-BooNE data with statistical errors only, an enhancement of NC ∆ → N γ (as predicted by the NUANCE [12] neutrino event generator on CH 2 ) by a normalization factor of x MB = 3.18 (quoted with no uncertainty) was found to provide the best fit for the observed LEE [3]. We perform an explicitly model-dependent test of this interpretation, cast as a factor of 3.18 enhancement to the predicted NC ∆ → N γ rate in MicroBooNE, under a two-hypothesis ∆χ 2 test between the enhanced rate and the nominal NC ∆ → N γ prediction.
MicroBooNE uses a custom tune [13] of the genie neutrino event generator v3.0.6 [14,15] to simulate neutrinoargon interactions. At BNB energies, the dominant source of single-photon production with no charged leptons or pions in the final state is NC ∆(1232) → N γ. This process is included in the MicroBooNE nominal prediction exactly as modeled in genie. Heavier resonances and non-resonant processes, including coherent singlephoton production [16], are not currently included in the simulation, but are each estimated to contribute at the 10% level or less. Both these processes would produce slightly higher-energy photons than the ∆(1232) resonance, and a more forward (in the direction of the neutrino beam) photon in the case of coherent production. Although such events may be selected by this analysis, we do not explicitly quantify their selection efficiency and in this letter we focus on the dominant NC ∆(1232) → N γ process.
The MicroBooNE NC ∆ → N γ search exclusively targets events with a single, photon-like electromagnetic shower and either no other visible activity or one visible final-state proton. These are referred to as 1γ0p and 1γ1p events and primarily probe ∆ → nγ and ∆ → pγ decays, respectively. The analysis selects and simultaneously fits 1γ1p and 1γ0p data-to-Monte Carlo (MC) simulated distributions together with two additional, mutually exclusive but highly correlated event samples: 2γ1p, and 2γ0p. The signal, defined as all true NC ∆ → N γ events whose true interaction vertex is inside the active TPC, contributes predominantly to the 1γ event samples. The high-statistics 2γ samples are enhanced in NC ∆ → N π 0 production, which is the dominant source of mis-identified background to the 1γ1p and 1γ0p event samples.
Reconstruction of all four event samples makes use of the Pandora framework [17]. Reconstructed ionization charge hits are clustered and matched across three 2D projected views of the MicroBooNE active TPC volume into 3D reconstructed objects. These are then classified as tracks or showers based on a multivariate classifier score and aggregated into candidate neutrino interactions. The topological selection of interactions with exactly one shower and zero or one tracks represents the basis of the 1γ selections. Subsequently, pre-selection requires that the reconstructed vertex, shower-start point and track (as applicable) are all fully contained within the detector fiducial volume. A minimum energy requirement is imposed on the shower, ensuring good reconstruction performance, and a maximum track length requirement is imposed on the track, rejecting obvious muon backgrounds. Tracks are also required to have a high dE/dx consistent with that of a proton. Finally, an opening angle requirement between the track and shower directions is applied to eliminate co-linear events where the start of a shower can be mis-reconstructed as a track.
The pre-selected events are fed into a set of boosted decision trees (BDTs), each designed to reject a distinct background and select NC ∆ → N γ events. The gradient boosting algorithm XGBoost [18] is used to train the BDTs. A cosmic BDT rejects cosmogenic backgrounds and is trained on cosmic ray data events collected when no neutrino beam was present. Track calorimetry is used to reject cosmic muons, with track and shower directionality-based variables proving powerful discriminators. A NC π 0 BDT compares the relationship of the reconstructed shower and track to those expected from π 0 decay kinematics to separate true single-photon events from those containing a π 0 decay where a second photon is not reconstructed. A charged current (CC) ν e BDT targets the intrinsic ν e background events. Here, the photon conversion distance and shower calorimetry play important roles. A fourth BDT is designed to veto events in which a second shower from a π 0 decay deposits some charge, but fails 3D shower reconstruction. Such events can result in 2D charge hits near the neutrino interaction that are not associated with a 3D object. A planeby-plane clustering algorithm, DBSCAN [19], is used to group these unassociated hits, and properties including direction, shape and energy of the cluster are used to determine consistency with a second shower from a π 0 decay. A final CC ν µ -focused BDT removes any remaining backgrounds, primarily targeting the muon track through track calorimetry variables. The 1γ1p selection uses all five BDTs. The absence of a track in the 1γ0p sample means that the 1γ0p selection cannot use these BDTs identically, as it is limited to only shower variables. As such, it uses variations of the cosmic and NCπ 0 BDTs, and a third BDT merging the functionality of the CC ν e and CC ν µ -focused BDTs, targeting all remaining backgrounds. All BDTs are trained explicitly to select well-reconstructed NC ∆ → N γ events. While model-dependent, this leverages the kinematics and correlations between the track and shower associated with ∆(1232) resonance decay, particularly for the 1γ1p selection. The BDTs for the 1γ1p and 1γ0p selections are trained and optimized for each selection independently, through a scan over grids of their BDT classifier scores. The optimized BDT classifier score cuts correspond to the highest statistical significance of the NC ∆ → N γ signal over background in each sample. The topological, pre-selection, BDT selection, and combined signal efficiencies are summarized in Table I.
The number of predicted background (both from simulation and cosmic ray data) events and NC ∆ → N γ signal events after BDT selection are summarized in Table II. A significant background to the search for singlephoton events is NC π 0 events in which one of the decay photons is not reconstructed. This happens for a variety of reasons: (a) one of the photons from the π 0 decay may leave the detector active TPC volume before interacting, (b) the π 0 decay may be highly asymmetric leading to a secondary photon that is low in energy and not reconstructed, (c) both photons may be approximately co-linear and overlapping and thus reconstructed as a single shower, or (d) the secondary photon may fall in a region of unresponsive wires, leading to poor reconstruction efficiency. Motivated by the background contribution of NC π 0 events, the 2γ1p and 2γ0p event samples serve to constrain the rate of NC π 0 background. The 2γ samples follow the same topological, pre-selection and BDT selection scheme as the 1γ samples (see supplemental materials). The selected 2γ1p and 2γ0p events are shown in Fig. 1 as a function of reconstructed π 0 momentum, with a true NC 1π 0 event purity of 63.4% and 59.6%, respectively. The data-to-MC simulation ratio in the 2γ1p and 2γ0p samples is 0.80 ± 0.22(stat.⊕sys.) and 0.91 ± 0.19(stat.⊕sys.), respectively, showing an overall deficit but one that is within 1σ. The selected data and MC predictions are compared in a fit with a single free parameter corresponding to the normalization (x ∆ ) of the nominal rate of NC ∆ → N γ. A single bin is used for each of the 1γ1p and 1γ0p event samples, with reconstructed shower energy bin boundaries of 0-600 MeV and 100-700 MeV, respectively. The one-bin 1γ1p and 1γ0p event rates are fit simultaneously with the 2γ1p and 2γ0p distributions shown in Fig. 1. The fit makes use of a covariance matrix that encapsulates statistical and systematic uncertainties and bin-tobin correlations, allowing for both the expected rate and uncertainties of the NC π 0 backgrounds in the 1γ samples to be effectively constrained by the high-statistics data observed in the 2γ samples.
The normalization x ∆ can also be reinterpreted in various ways. First, it can be reinterpreted as a scaling of an effective branching fraction B eff (∆ → N γ), where the nominal prediction (x ∆ = 1) corresponds to an effective branching fraction of 0.6%. This effective branching fraction can be thought of as a metric to account for any uncertain nuclear effects that might modify the ∆ behavior inside the nuclear medium, as we cannot observe the true ∆ → N γ branching fraction directly. In addition, any BSM effect that can contribute as an NC ∆-like process (with a single photon-like shower in the final state) could lead to an effective modification to the observed branching fraction. Although genie prescribes a normalization uncertainty for B eff (∆ → N γ), this uncertainty is not included in the fit. In addition, with the knowledge that genie predicts a cross-section for NC ∆ → N γ production to be σ GENIE,Ar N C∆→N γ = 8.61 × 10 −42 cm −2 /nucleon, we can also reinterpret x ∆ as scaling on this production cross-section. The Feldman-Cousins [20] approach is followed to construct the confidence intervals for x ∆ given the best fit to the observed data, with a metric of ∆χ 2 defined using the Combined-Neyman-Pearson χ 2 [21] as an approximation of the log-likelihood ratio.
Systematic uncertainties include contributions from flux, cross-section modeling, hadron re-interactions, detector effects, and finite statistics used in the background predictions (both MC and cosmic ray data). The flux uncertainties incorporate hadron production uncertainties, uncertainties on pion and nucleon scattering in the beryllium target and surrounding aluminum magnetic horn, and mis-modeling of the horn current. Following [22], these are implemented by reweighting the flux prediction and studying the propagated effects on event distributions. The cross-section uncertainties incorporate modeling uncertainties on the genie prediction [13,15,23], evaluated also by reweighting tools. The hadron-argon re-interaction uncertainties are associated with the propagation of hadrons through the detector, as modeled in geant4 [24]. The detector modeling and response uncertainties are evaluated using a novel data-driven technique. This uses in-situ measurements of distortions in the TPC wire readout signals due to various detector effects, such as diffusion, electron drift lifetime, electric field, and electronics response, to parametrize these effects at the TPC wire level, and provides a detector model-agnostic way to study and evaluate their effects on event distributions [25]. Additional systematics varying the charge recombination model, the scintillation light yield, and space charge effects [26,27] are separately included. The uncertainty on photo-nuclear absorption of photons on argon was evaluated to be at the subpercent level, and is therefore omitted. There is also no assigned uncertainty for heavier resonances or coherent single-photon production, which are not simulated in genie. Finally, an inconsistency was identified in the genie v3.0.6 reweighing code used to evaluate a small subset of systematic uncertainties, but was found to have negligible impact on the analysis sensitivity and thus has been ignored.
The fractional systematic uncertainties on the 1γ1p and 1γ0p total background events are summarized in Table III. The genie cross-section uncertainties dominate. This stems from the uncertainties on NC π 0 production on argon, which forms the largest background and has not been measured to high precision to date. Both crosssection and flux uncertainties are strongly correlated between the 1γ and 2γ event samples. The simultaneous fit to the 1γ and 2γ samples is equivalent to a 1γ-only fit where the background and uncertainty are conditionally constrained [28] by the 2γ samples. Given the 2γ samples' statistics, this constraint effectively reduces the total background systematic uncertainty of the 1γ1p and 1γ0p samples by 40% and 50%, and the total background prediction by 24.1% and 12.3%, respectively. The 90% CL sensitivity is quantified for a Feldman-Cousins-corrected limit in the case of a background-only observation, x ∆ = 0, to be less than x ∆ = 2.5, corresponding to B eff (∆ → N γ) = 1.50% and σ Ar N C∆→N γ = 21.5×10 −42 cm −2 /nucleon . Under a two-hypothesis ∆χ 2 test, the expected sensitivity of the median experiment assuming the nominal prediction, to reject the LEE hypothesis (x MB = 3.18) in favor of the nominal hypothesis (x ∆ = 1) is 1.5σ; in the case of the median experiment assuming the LEE hypothesis, the sensitivity to reject the nominal hypothesis in favor of the LEE hypothesis is 1.6σ.
The reconstruction, selection, and fitting methods employed in this search were developed adhering to a signalblind analysis strategy, whereby the data was kept blind until the analysis was fully developed, with the exception of a small subset of the data consisting of 0.51 × 10 20 POT, used for analysis validation. After 1γ1p and 1γ0p event samples were unblinded, 16 data events with an expected constrained background of 20.5 ± 3.6(sys.) events were observed in the 1γ1p event sample, and 153 data events with an expected constrained background of 145.1 ± 13.8(sys.) events were observed in the 1γ0p event sample. The reconstructed shower energy distributions of selected 1γ1p and 1γ0p events are shown in Fig. 2. Overall, a systematic deficit of data relative to the unconstrained MC prediction is observed, which is within systematic and statistical uncertainties, and consistent with a similar deficit in the 2γ event samples. The expected signal and background predictions are summarized in Table IV and Fig. 3, and compared to the observed data, both before and after applying the 2γ conditional constraint. The 2γ constraint reduces the total background prediction, consistently with the data to MC simulation ratio observed in the 2γ event samples.
The best-fit value for x ∆ obtained from the fit is 0, with a χ 2 bf of 5.53 for 15 degrees of freedom (dof ). This measurement is in agreement with the nominal NC ∆ → N γ rate (corresponding to x ∆ = 1) within 1σ (67.8% CL) with a χ 2 of 6.47 for 16 dof . The Feldman-Cousins calculated confidence limit leads to a one-sided  shows the total background prediction with systematic uncertainty both before and after the 2γ constraint. The local significance of the data fluctuation in the 200-250 MeV bin of (b) corresponds to 1.6σ (χ 2 /dof = 3.66/1) before the 2γ constraint, and 2.7σ (χ 2 /dof = 8.54/1) after. From MC studies, the probability of any one bin across all 16 1γ bins giving rise to a constrained χ 2 ≥ 8.54 is 4.74%.   bound on the normalization of NC ∆ → N γ events of x ∆ < 2.3, corresponding to B eff (∆ → N γ) < 1.38% and σ Ar N C∆→N γ < 19.8×10 −42 cm −2 /nucleon, at 90% CL. This is summarized in Fig. 4.
This result represents the most stringent limit on neutrino-induced NC ∆ → N γ on any nuclear target [8,9], and a significant improvement over previous searches, in particular in the neutrino energy range below 1 GeV. Under a two-hypothesis test, the data rules out the interpretation of the MiniBooNE anomalous excess [29] as a factor of 3.18 enhancement to the rate of ∆ → N γ, in favor of the nominal prediction at 94.8% CL (1.9σ). While this is a model-dependent test of the Mini-BooNE LEE, and does not apply universally to all other photon-like interpretations, it provides an important constraint on this process and a first direct test of the Mini-BooNE LEE, and opens the door to further searches that focus on a broader range of models. Those include co-herent single-photon production [5], anomalous contributions of which could give rise to additional events and would be expected to leave an imprint in the 1γ0p selection, as well as more exotic beyond-SM processes that manifest as single-photon events, such as co-linear e + e − pairs from Z [30,31] or scalar [32] decays, among others. Follow-up MicroBooNE analyses will explicitly target and quantify sensitivity to these alternative hypotheses, as well as model-independent single-photon searches. The resulting ∆χ 2 curve after fitting to x∆ using the Feldman-Cousins procedure, showing extracted confidence intervals. The best fit is found to be at x∆ = 0 with a χ 2 bf = 5.53. Shown also is the reinterpretation of this scaling factor as both an effective branching fraction, B eff (∆ → N γ), and a cross-section, σ Ar N C∆→N γ . The default genie value corresponds to x∆ = 1. The error on the LEE model is estimated from the MiniBooNE result [3] with statistical and systematic uncertainty. It should be noted that this uncertainty does not account for systematic correlations between MiniBooNE and MicroBooNE.