A new analysis of the MiniBooNE low-energy excess

We present the results of a new analysis of the data of the MiniBooNE experiment taking into account the additional background of photons from $\Delta^{+/0}$ decay proposed in arXiv:1909.08571. We show that the new background can explain part of the MiniBooNE low-energy excess and the statistical significance of the MiniBooNE indication in favor of short-baseline neutrino oscillation decreases from $5.1\sigma$ to $3.3\sigma$. We also consider the implications for short-baseline neutrino oscillations in the 3+1 active-sterile neutrino mixing framework. We show that the new analysis of the MiniBooNE data indicates smaller active-sterile neutrino mixing and may lead us towards a solution of the appearance-disappearance tension in the global fit of short-baseline neutrino oscillation data.

The MiniBooNE experiment [2] found a significant excess of low-energy ν e -like events that could be due to short-baseline ν µ → ν e oscillations generated by activesterile neutrino mixing [3][4][5] or to other physics beyond the Standard Model [6][7][8][9]. The size of the lowenergy MiniBooNE excess depends crucially on the estimated background. Among the different sources of background are the ∆ → N γ photons produced by the decay ∆ +/0 → p/n + γ of ∆ +/0 's produced in neutral-current ν µ interactions with the mineral oil (CH 2 ) of the detector. Since in the MiniBooNE detector a single photon cannot be distinguished from an electron, the photons from ∆ +/0 decay represent an intrinsic background in the search of ν e appearance from the ν µ beam. The Mini-BooNE collaboration estimated this background through the measurement of π 0 's that are produced by the decay ∆ +/0 → p/n + π 0 , using the branching fractions [10,11] Br(∆ +/0 → p/n + γ) = (6.0 ± 0.5) × 10 −3 , Br(∆ +/0 → p/n + π 0 ) 2/3.
Final state interactions (FSI) cause the absorption of a fraction of the π 0 's in the carbon nucleus that was estimated of about 20% by the MiniBooNE collaboration [12]. However, in Ref. [1] one of us noted that measurements of π 0 photoproduction on nuclei [13,14] indicate that the fraction of π 0 's that emerge from the nucleus and can be observed is given by where A is the mass number of the target nucleus A N , σ FSI denotes the measured cross section which includes final state interactions and σ 0 denotes the theoretical cross * carlo.giunti@to.infn.it † ara.ioannisyan@cern.ch ‡ gioacchino.ranucci@mi.infn.it section without final state interactions. Therefore, the number of ∆ +/0 produced in neutral-current ν µ interactions with 12 C and the number of γ's generated by their decay is a factor 12 1/3 2.3 larger than that obtained from the measurement of π 0 's without taking into account FSI. This enhancement of the ∆ → N γ background due to π 0 FSI is much larger than the 20% considered by the MiniBooNE collaboration [12].
The increase of the estimated ∆ → N γ background due to the reevaluation of π 0 FSI in 12 C can explain in part the low-energy MiniBooNE excess, because its largest contribution occur in the lowest energy bins, as one can see from Figures 1(a) and 1(b) that reproduce the MiniBooNE event histograms in neutrino and antineutrino mode in Refs. [2,15]. Taking into account the two protons in CH 2 , we obtain that the ∆ → N γ must be increases by a factor of about 1.8.
The effect of the ∆ → N γ background in MiniBooNE was studied theoretically in Ref. [16], where it was found that the ∆ → N γ background is a factor of about 2 larger than that estimated by the MiniBooNE collaboration. This is in rough agreement with our enhancement by a factor of about 1.8. On the other hand, the later theoretical studies in Refs. [17,18] found an agreement with the MiniBooNE estimate. Since our approach is phenomenological, based on the experimentally motivated ratio (3) and the branching fractions (1) and (2), it is independent of the theoretical calculations of the absolute rate of ∆ → N γ decays in MiniBooNE. Figure 1 shows a comparison of the standard Mini-BooNE event histograms (Figures 1(a) and 1(b)) with those obtained with our reevaluation of the effects of π 0 FSI (Figures 1(c) and 1(d)). One can see that in the reproductions 1(a) and 1(b) of the original MiniBooNE histograms the low-energy bins show a large excess with respect to the background prediction. The excess is significantly reduced with our reevaluation of π 0 FSI in 12 C that visibly increase the ∆ → N γ background. Only the first energy bin remains with a large visible excess.
The improvement of the fit of the MiniBooNE data arXiv:1912.01524v1 [hep-ph] 3 Dec 2019 is quantified by χ 2 /N DF = 32.4/22, corresponding to a goodness-of-fit of 7% obtained with A 1/3 π 0 FSI, compared to χ 2 /N DF = 53.0/22, corresponding to a goodness-of-fit of 0.02%, obtained in the standard analysis of MiniBooNE data. The reevaluation of the low-energy MiniBooNE excess has important implications for the interpretation of the MiniBooNE data in terms of short-baseline neutrino oscillations due to active-sterile neutrino mixing. In the following we consider the 3+1 scenario in which in addition to the three standard light massive neutrinos ν 1 , ν 2 , ν 3 , with respective masses m 1 , m 3 , m 3 , there is a heavier neutrino ν 4 with mass m 4 . The masses of the three standard light massive neutrinos have small separations, determined by the measurements of solar, atmospheric and long-baseline oscillations: ∆m 2 ν e oscillations that may explain the LSND and MiniBooNE anomalies, as well as other indications of short-baseline neutrino oscillations [3][4][5]. The probability of short-baseline where E is the neutrino energy, L is the source-detector distance, and sin 2 2ϑ eµ = 4|U e4 | 2 |U µ4 | 2 , where U is the 4 × 4 unitary mixing matrix. Figure 2 shows a comparison of the standard allowed regions in the (sin 2 2ϑ eµ , ∆m 2 41 ) plane obtained from the analysis of the MiniBooNE data and those obtained with our reevaluation of π 0 FSI in 12 C. The goodness-of-fit and the best-fit values of the oscillation parameters are listed in Table I, and the best fit event histograms are shown in Figure 1. The difference between the χ 2 min with oscillations and the χ 2 without oscillations is 30.2 and 13.6, without and with A 1/3 π 0 FSI, respectively. Taking into account that there is a difference of two degrees of freedom corresponding to the two fitted oscillation parameters sin 2 2ϑ eµ and ∆m 2 41 , the statistical significance of the MiniBooNE indication in favor of oscillation decreases from 5.1σ to 3.3σ with the introduction of the A 1/3 π 0 FSI (the corresponding χ 2 probabilities of the background-only fit relative to the best oscillation fit are 2.8 × 10 −7 and 1.1 × 10 −3 ) 1 .
1 In Ref. [2] the MiniBooNE collaboration obtained a probability of the background-only fit relative to the best oscillation fit of 6 × 10 −7 , which corresponds to 5.0σ. The small difference with our result is due to a different analysis of the data performed by the MiniBooNE collaboration with respect to that recommended in their data release [19]. In particular, they considered only the data below 1250 MeV because that upper limit "was chosen by the collaboration before unblinding the data in 2007" [2]. We have no reason to implement this restriction.
From Figure 2 one can see that the allowed regions in the (sin 2 2ϑ eµ , ∆m 2 41 ) plane change significantly by taking into account the effect of A 1/3 π 0 FSI. There is an extension of the allowed regions towards small values of the mixing parameter sin 2 2ϑ eµ . In particular, the best fit moves from a point with quasi-maximal mixing to a point with rather small mixing. This is beneficial, because large active-sterile mixing is disfavored by solar, atmospheric and long-baseline neutrino oscillation data [3][4][5].
The best-fit event histograms in Figure 1 show that the smaller number of signal events resulting from the smaller best-fit mixing that we obtained with A 1/3 π 0 FSI can fit well the data because of the increase of the background. Only the excess in the first bin is not well fitted. The values of the goodness-of-fit in Table I show that the fit of MiniBooNE data with A 1/3 π 0 FSI is better than the one without, although a close look at Figure 1 seems to indicate the opposite. The reason is that we fitted the data using the prescription of the MiniBooNE data release [19] where the covariance matrix takes into account the flux and cross section correlations between the uncertainties of the predicted It is interesting to compare the results of our new fit of the MiniBooNE data with the indication of the LSND experiment [20] in favor of short-baselineν µ →ν e oscillations. Figure 3 shows a comparison of the combined LSND and MiniBooNE allowed regions in the (sin 2 2ϑ eµ , ∆m 2 41 ) plane obtained without and with the effect of A 1/3 π 0 FSI. One can see that the changes are similar, but stronger, than those for MiniBooNE alone (shown in Figure 2): there is a clear shift of the allowed regions towards small mixing, with the absence of a 1σ allowed region at large mixing. Although the best-fit point is at a large value of ∆m 2 41 , there is a 1σ allowed region with the smallest mixing at ∆m 2 41 ≈ 2 eV 2 , that may be compatible with indications of short-baselineν e disappearance due to active-sterile neutrino mixing found in reactor experiments [4,[21][22][23].
For example, the 3σ upper limit from disappearance data in Figure 7 of Ref. [22] is about sin 2 2ϑ eµ 6 × 10 −4 at 3σ for ∆m 2 41 ≈ 1.3 eV 2 , that we can compare with the 3σ lower limit sin 2 2ϑ eµ 8 × 10 −4 in Figure 4 for the same value of ∆m 2 41 . It is clear that there is still a considerable appearance-disappearance tension, but it is significantly smaller than that obtained in Ref. [22].
The disappearance bound in Figure 5b of Ref. [3] is weaker than that obtained in Ref. [22], with an upper limit sin 2 2ϑ eµ 10 −3 at 3σ for ∆m 2 41 ≈ 1.3 eV 2 , that is compatible with the 3σ allowed region in Figure 4.
In conclusion, we have shown that a reassessment of the photon background from ∆ +/0 decay in the Mini-BooNE experiment taking into account the effect of A 1/3 π 0 FSI proposed in Ref. [1] can explain in part the lowenergy MiniBooNE excess and leads to a better fit of the data (with a goodness-of-fit of 7% compared to 0.02%, obtained in the standard analysis of MiniBooNE data) in absence of physics beyond the standard three-neutrino mixing. However, the MiniBooNE data are still fitted in a better way considering short-baseline ν e oscillations due to active-sterile neutrino mixing, albeit the statistical significance of the indication in favor of oscillation decreases from 5.1σ to 3.3σ. We have shown that in the 3+1 framework the new analysis of the MiniBooNE data prefers small values of active-sterile neutrino mixing, in contrast with the large values preferred by the standard analysis of MiniBooNE data. This shift towards small active-sterile neutrino mixing is beneficial towards a possible solution of the appearance-disappearance tension in the global fit of short-baseline neutrino oscillation data.