Explaining the MiniBooNE Excess Through a Mixed Model of Oscillation and Decay S. Vergani, 1, * N.W. Kamp, 2, † A. Diaz, 2, ‡ C.A. Arg¨ uelles, 3, § J.M. Conrad, 2, ¶ M.H. Shaevitz, 4, ** and M.A. Uchida 1, †† 1 University of Cambridge, Cambridge CB3 0HE, United Kingdom 2 Dept. of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA 3 Dept. of Physics, Harvard University, Cambridge, MA 02138, USA 4 Dept. of Physics, Columbia University, New York, NY, 10027, USA (Dated: September 29, 2021) The electron-like excess observed by the MiniBooNE experiment is explained with a model com- prising a new low mass state (O(1) eV) participating in neutrino oscillations and a new high mass state (O(100) MeV) that decays to ν + γ. Short-baseline oscillation data sets are used to predict the oscillation parameters. Fitting the MiniBooNE energy and scattering angle data, there is a narrow joint allowed region for the decay contribution at 95% CL. The result is a substantial improvement over the single sterile neutrino oscillation model, with Δχ 2 /dof = 19.3/2 for a decay coupling of 2.8 × 10 -7 GeV -1 , high mass state of 376 MeV, oscillation mixing angle of 7 × 10 -4 and mass splitting of 1.3 eV 2 . This model predicts that no clear oscillation signature will be observed in the FNAL short baseline program due to the low signal-level. INTRODUCTION For the past 25 years, anomalies have been observed in short-baseline (SBL) neutrino oscillation experiments. These have been studied under a model called “3+1” that introduces a new non-interacting, hence “sterile,” state with mass of O(1 eV), in addition to the three Standard Model (SM) neutrino states. In this model, ν μ → ν e appearance, ν e disappearance, and ν μ disap- pearance searches should all point to neutrino oscillations at L/E ∼ 1 m/MeV, where L is the distance a neutrino of energy E travels, with a consistent set of flavor mixing parameters [1–4]. However, while individually the data appear to fit oscillations, global fits find a small proba- bility that all of the relevant data sets are explained by the same parameters [2, 3], as measured by the Param- eter Goodness of Fit (PGF) test [5, 6]. In particular, appearance data from MiniBooNE produces large ten- sion between appearance and disappearance in the 3+1 model. This is because the 3+1 best-fit parameters from the other data sets yield a poor fit to the lowest energy range of the MiniBooNE anomaly [7]. Therefore, there is significant interest in explanations for MiniBooNE be- yond the 3+1 model; for example, one can consider de- cays of a sterile neutrinos into active neutrinos and singlet scalars [8, 9]. The MiniBooNE anomaly is a 4.8σ excess of electron- like events observed in interactions from a predominantly muon neutrino beam in a Cherenkov detector [10], which cannot distinguish between electromagnetic showers from * sv408@hep.phy.cam.ac.uk † nwkamp@mit.edu ‡ diaza@mit.edu § carguelles@fas.harvard.edu ¶ conrad@mit.edu ** shaevitz@nevis.columbia.edu †† mauchida@hep.phy.cam.ac.uk electrons and photons. Hence, a favored alternative to the 3+1 model has been to introduce MeV-scale heavy neutral leptons (HNLs) that decay via N→ νγ within the detector, where the photon is then misidentified as an electron [11–18]; see Refs.[19–27] for misidentified di- electron scenarios. These initial studies of N -decay mod- els describe the MiniBooNE energy distribution well but omit the 3+1 oscillations predicted from fits to the other anomalies. In this work, we explore a combination of the two explanations by fitting the MiniBooNE energy and an- gle distributions using a combined model, 3+1+N -decay. The 3+1 oscillation component has been obtained by fit- ting SBL data sets other than MiniBooNE appearance. We will show that such a model explains the data well, identifying a highly limited range for the four model pa- rameters: the mixing angle, sin 2 2θ, and mass splitting, Δm 2 , for the oscillation; and the HNL mass, m N , and photon coupling, d, for the decay. MODEL The combination of eV-scale and MeV-scale mass states is motivated if the two are members of a family of N j where j =1, 2, 3. If the mass splittings are sim- ilar to the quark and charged-lepton sectors, then the family might also include a keV-scale member [28, 29]. All members may interact with photons at a weak level through a dipole portal interaction [17], also known as neutrino magnetic moment [30–35]. Thus, the N 1 = ν 4 can decay, but the lifetime is typically longer than the age of the Universe [31, 36]. The keV-scale mass state, N 2 , would have a lifetime that is too long to be observed through decay in terrestrial experiments but could ex- plain observed X-ray lines [28, 37]. Only the N≡N 3 would decay on length scales relevant to SBL experi- ments. Conversely, only the eV-scale mass state would have sufficiently small mass splitting with respect to the arXiv:2105.06470v5 [hep-ph] 27 Sep 2021