The MOMENT to search for CP violation

In this letter, we analyze for the first time the physics reach in terms of sensitivity to leptonic CP violation of the proposed MuOn-decay MEdium baseline NeuTrino beam (MOMENT) experiment, a novel neutrino oscillation facility that would operate with neutrinos from muon decay. Apart from obtaining a sufficiently intense flux, the bottlenecks to the physics reach of this experiment will be achieving a high enough suppression of the atmospheric background and, particularly, attaining a sufficient level of charge identification. We thus present our results as a function of these two factors. As for the detector, we consider a very massive Gd-doped Water Cherenkov detector. We find that MOMENT will be competitive with other currently planned future oscillation experiments if a charge identification of at least 80 % can be achieved at the same time that the atmospheric background can be suppressed by at least a factor of ten. We also find a large synergy of MOMENT with the current generation of neutrino oscillation experiments, T2K and NOvA, which significantly enhances its final sensitivity.


Introduction
The violation of the charge-parity (CP) symmetry in Nature holds a very particular role in the development of modern theoretical physics. In the quark sector, the violation was observed in the decays of neutral kaons in 1964 [1] and was fundamental in the prediction of the third generation of quarks [2]. Furthermore, CP-violation is also one of the Sakharov conditions [3], which describe the necessary ingredients for creating a baryon asymmetry in the early Universe. With the amount of CP-violation in the quark sector being too small to account for the observed baryon asymmetry [4,5], the discovery of a different source of CP-violation could prove crucial to further our understanding of the genesis of matter over anti-matter.
Possible additional sources of CP-violation can be found in the lepton sector, once the Standard Model (SM) is extended in order to include neutrino masses. The mixing of massive neutrinos in the flavor basis allows for the inclusion of non-trivial complex phases in the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix [6][7][8][9][10], in an analogous manner to what is done in the quark sector. Assuming that there are only three neutrino families the PMNS matrix will contain one or three such phases, depending on whether neutrinos are Dirac or Majorana particles. Although neutrino oscillation experiments are insensitive to the two Majorana CP-violating phases, they can probe the Dirac CP-violating phase.
In the last few years, new results from the latest generation of neutrino oscillation experiments have started to provide precision measurements of the parameters describing the masses and mixing of neutrinos. In particular, with the measurements of the size of the PMNS matrix element U e3 provided by accelerator and reactor neutrino experiments [11][12][13][14][15], it is plausible that CP-violation in the lepton sector may be found in the not so distant future. The current hints of maximal lepton CP-violation [16][17][18] provide further indication that this discovery may be right around the corner.
In the next generation of neutrino oscillation experiments, the front runners in the hunt for leptonic CP-violation are the proposed Deep Underground Neutrino Experiment (DUNE) [19] and the Tokai to Hyper-Kamiokande (T2HK) experiment [20]. Both of them propose to use conventional accelerator neutrino beams from pion decay. In contrast, the MuOn-decay MEdium baseline NeuTrino beam facility (MOMENT) [21] proposes to observe a neutrino beam produced from decaying muons at relatively low energies. By using this type of beam, some of the technical difficulties related to the construction of the more futuristic neutrino factory could be avoided [22][23][24]. The aim of this letter is to study the capabilities of the MOMENT experiment and put it into context in the global experimental effort in neutrino physics.

Implementation
The MOMENT design is still not fully developed and is therefore subject to large uncertainties. As a first step towards studying its physics potential and the requirements it would need to meet to reach a competitive performance with respect to other future neutrino oscillation experiments, some assumptions regarding both the beam and detector performance have to be made. However, in our analysis we leave the most relevant parameters free in order to explore their impact on the expected sensitivities. One of the main challenges for MOMENT will be to deliver a sufficiently intense muon flux. This issue is already being investigated, and we refer the interested reader to Ref. [21]. Instead, in this work we will assume that the muon and electron neutrino fluxes presented in Refs. [21,25] at 150 km from the source are achievable, and that alternating between muon polarities with a similar flux intensity is also possible. The neutrino fluxes used in this work have their maximum at energies around 150 MeV with maximum intensity of ∼ 10 9 MeV −1 m −2 year −1 , and have been taken from Ref. [25]. Five years of running time per polarity are assumed.
In principle, the MOMENT setup would allow the study of the ν e → ν e , ν µ → ν e , ν e → ν µ and ν µ → ν µ oscillation channels as well as their corresponding CP-conjugate partners. However, since the original flux is composed of ν µ andν e from µ − decay, both good flavour and charge identification capabilities are needed in order to be sensitive to a possible CP-violating signal. The neutrino flux for this facility would peak at low energies around 150-200 MeV. Therefore, a very massive detector would be required in order to compensate the low interaction cross section at these energies and reach large enough statistics. The detector technology for MOMENT has not yet been decided, but a massive Water Cherenkov detector has been suggested due to its excellent flavour identification capabilities and performance at low energies. The drawback of using a Water Cherenkov in combination with the MOMENT beam is its inability to distinguish neutrinos and antineutrinos. Nevertheless, this problem may be solved (at least partially) by doping the water with Gd [26] at the 0.1-0.2% level. We will thus adopt a Mton class (500 kton fiducial) Gd-doped Water Cherenkov detector as baseline detector for our analysis.
In this study, the detector response has been implemented following Ref. [27]. Migration matrices, describing both the detection efficiencies and energy reconstruction, are used for all four relevant oscillation channels (and their CP-conjugates). The most relevant backgrounds come from charge mis-identification (charge mis-ID) of events coming from the intrinsic contamination of the beam, flavour mis-identification and neutral current (NC) backgrounds mis-identified as charged current (CC) events. Since charge mis-ID will be one of the bottlenecks for the physics performance of the facility, our results will be presented as a function of this parameter. In Ref. [28] it was estimated that Gd-doping alone (at the 0.1-0.2 % level) could bring charge separation up to the 80 % level. Be-sides Gd-doping, some statistical neutrino/antineutrino discrimination could be achieved from other distinctive features [28], such as the angular distribution between the charged lepton and the incident neutrino/antineutrino, or the different lifetimes of the outgoing muons/antimuons produced in ν µ /ν µ interactions. Since it is uncertain how much extra charge-identification efficiency these extra handles would eventually bring to the table 1 , we will show how much the performance of the setup would improve if the total chargeidentification efficiency surpasses the 70 % level, which is taken as a (conservative) lower threshold [30].
Another important limiting factor could be the potentially large atmospheric neutrino background expected. Such background could be largely reduced by sending the neutrino flux in short bunches, so that a time cut can be efficiently applied. This is usually parametrized in terms of a suppression factor (SF), i.e., the ratio between the length of each bunch to the distance between bunches. In neutrino oscillation experiments using pion decay beams, the achieved SF is typically around 10 −3 [24]. In the current work, we will explicitly consider the atmospheric background, computed as in Ref. [31], applying a SF ranging from 1 to 5 · 10 −3 in order to quantify its impact on the final sensitivities. Finally, we also include an overall 5 % (10 %) normalization systematic error, uncorrelated between all signal (background) channels. All of our numerical simulations have been implemented using the GLoBES software [32,33].
For convenience, Tab. 1 summarizes the total expected event rates in the energy range between 0 and 1.6 GeV, for all oscillation channels under consideration, after efficiencies are accounted for. The signal and background rates are provided separately for each channel, assuming a charge separation efficiency of 70 % and a suppression factor SF = 10 −1 for the atmospheric neutrino background. These number of events have been obtained assuming that the true values of the oscillation parameters correspond to the best-fit values from Ref. [34], with the sole exception of the CP-violating phase which is set to δ = 0. A normal ordering of the neutrino masses (m 1 < m 2 < m 3 ) has also been assumed. Only those events with reconstructed neutrino energy between 0.1 and 1 GeV are considered for the χ 2 analysis.

Results and conclusions
In its most conservative incarnation, with a 70 % charge ID and no suppression of the atmospheric background, we find that the MOMENT facility, on its own, barely improves over what the presently running experiments T2K and NOνA will achieve in the coming years. However, we have found that combining the data from the three facilities can be quite complementary, leading to a significant improvement of their individual physics reaches beyond that due to a simple increase in statistics. In the following, we have simulated the sensitivity from the NOνA experiment as in Ref. [35], using 3 years of data taking per polarity and 6.0 × 10 20 protons on target (PoT) per year. This is then combined with a  Table 1.  simulation of T2K data using neutrino data corresponding to approximately 3 × 10 20 PoT. The T2K fluxes have been taken from Ref. [36] and the signal and background efficiencies have been set to approximately match the results from Ref. [37] for the same exposure.
The complementarity between MOMENT and the current generation of neutrino oscillation experiments is shown for a particular point in the θ 23 -δ parameter space in Fig. 1. In each panel, the shaded areas show the confidence regions obtained in the θ 23 − δ plane for the correct neutrino mass ordering, while the dashed lines show the allowed regions for the opposite mass ordering (a.k.a., sign degeneracies [38]). Each panel corresponds to the expected results for a given facility (or combination thereof), as indicated in the legend. As can be seen from a comparison between the left and central panels, the sign degeneracies affect both the T2K+NOνA and the MOMENT setup, but appear at completely different values of δ due to the much weaker matter effects that characterize the latter. Furthermore, the octant degeneracy also plays an important role at MOMENT, while it is solved at T2K+NOνA (for this particular point in parameter space).
We found that, even though both theν e →ν µ and ν µ → ν e channels are available at MOMENT for µ − running, the former channel dominates the physics reach unless very optimistic charge ID is assumed. This can be understood as follows. On one hand, the "wrong sign" electrons fromν e disappearance completely overwhelm the signal in the ν µ → ν e channel. On the other hand, the ν µ present in the beam are less of an issue for thē ν e →ν µ channel, since most them have already oscillated to ν τ when they reach the detector and therefore do not contribute to the muon-like CC sample. Thus, the physics reach from MOMENT and T2K+NOνA is dominated by different and complementary channels. The right panel of Fig. 1 shows how the combination of the three facilities is able to solve all degeneracies unambiguously and determine the correct value of θ 23 and δ with an allowed region which is significantly reduced compared to the individual fits.
Since by the time the MOMENT facility is built the T2K and NOνA facilities will have already finished taking data, we will present our results for the combination of MO-MENT+T2K+NOvA only. Notice that this essentially improves the overall performance for the most conservative choices for the charge ID and SF of MOMENT, while it has little impact in the optimistic scenarios. Similarly, the physics reach of DUNE or T2HK is mildly affected after combination with T2K+NOνA, since their observations are less complementary and do not lead to further degeneracy solving besides a small increase in statistics. For this reason, when comparing the reach of MOMENT to that of T2HK or DUNE, we will take the expected physics reach for the latter from their respective proposals.
We have also explored the effect of changing the baseline of the MOMENT detector. Indeed, it has been shown that, given the relatively large value of θ 13 , if the neutrino flux is centered around the second oscillation peak, the sensitivity to δ [39,40] improves considerably. This has been studied in depth for a similar low-energy neutrino beam, the ESSνSB [41], also in combination with a Water Cherenkov detector. In the case of MOMENT, we find that when the most conservative assumptions are made, the optimal baseline is around L = 150 km. However, when the most optimistic assumptions are adopted, the sensitivity becomes almost independent of the baseline as it is increased from the first to the second peak. This is mainly due to the strong dependence on δ at longer baselines, which compensates for the lower statistics. Thus, in the following we will only consider a L = 150 km baseline, since the performance of the detector is still uncertain.
Our main results are shown in Fig. 2 for which the combination of MOMENT+T2K+NOνA would allow a 3σ (5σ) discovery of leptonic CP violation. Our results are shown as a function of the achievable charge-ID and atmospheric suppression factor. As can be seen, if a ∼ 80 % charge-ID can be achieved, a 3 (5) σ discovery of CP violation would be possible for roughly 60 % (20 %) of the values of δ, as long as the atmospheric suppression factor remains below SF 0.1. This is similar to the sensitivity reach expected for DUNE [19] with an exposure of 300 MW·kt·yr (corresponding to ∼ 3.5 years running per polarity). Conversely, if the charge identification cannot be improved beyond ∼ 70 %, less than 10 % of the values of δ would lead to a 5σ discovery regardless of the value of SF. As a comparison, T2HK [42] with a 10-year run using a beam power of 750 MW would allow to cover ∼ 75 % (∼ 55 %) of the values of δ for a 3 (5σ) discovery. MOMENT would require a charge ID of ∼ 98 % and SF < 5 · 10 −2 to achieve a similar performance.
In conclusion, we have studied for the first time the physics reach attainable at MO-MENT in terms of its CP violation discovery potential. We find that the main limiting factors to its performance are the charge identification and atmospheric background suppression. With a conservative assumption of 70 % charge identification and no atmospheric background suppression, MOMENT would not improve significantly over the results expected at the end of the running period of T2K and NOνA, even after a 10 year run with a Mton Water Cherenkov detector. However, its combination with present facilities is able to lift several degeneracies and significantly improve the combined physics reach over a simple addition of statistics.
In order to compete with other future neutrino oscillation facilities, more demanding detection capabilities would be necessary. We find that the physics reach of MOMENT would be similar to a 7 year run of DUNE if a charge identification of ∼ 80 % and atmospheric suppression by a factor of 10 is achieved. To compete with 10 years of T2HK with a 750 MW beam, the background suppression factor should improve by a factor 20 keeping charge identification capabilities at the level of ∼ 98 %. In order to satisfy this requirement, a different detector technology would most likely be required in this case.