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A New Method to Search for CP violation in the Neutrino Sector

New low-cost, high-power proton cyclotrons open the opportunity for a novel precision search for CP violation in the neutrino sector. The accelerators can produce decay-at-rest neutrino beams located at multiple distances from a Gd-doped ultra-large water Cerenkov detector in order to search for CP violation in anti-nu_mu to anti-nu_e at short baseline. This new type of search complements presently proposed experiments, providing measurements that could lead to a substantially better exploration of CP violation in the neutrino sector.


I. INTRODUCTION
With the discovery of neutrino oscillations, particle physicists have been inspired to develop theories that explain very light neutrino masses. The most popular models invokes GUT-scale Majorana partners which can decay, producing a matter-antimatter asymmetry in the early universe through the mechanism of CP violation. Observation of CP violation in the light neutrino sector would be a strong hint that this theory is correct.
In Eq. 1, aside from δ CP , all but two of the parameters (θ 13 and the sign of ∆m 2 31 ) are well known. Further precision on these known parameters is expected in the near future (see Table I). With respect to θ 13 , global fits report a non-zero value at the ∼ 1σ level [2,3]. This parameter drives the amplitude for the CP violating terms in Eq. 1 and therefore sets the level of technical difficulty for observing CP violation. The unknown sign of ∆m 2 31 , referred to as "the mass hierarchy," affects the sign of term 3 in Eq. 1. Matter effects modify Eq. 1 and are sensitive to the mass hierarchy.
We propose a new method to search for CP violation by comparing absolute neutrino rates in a single detector that is illuminated by neutrino beam sources at multiple distances. This method explores the δ CP dependence inherent in Eq. 1 in a different way and with comparable precision than the planned long-baseline program.
The neutrino sources would be based on commerciallydeveloped, small (2.5 m diameter), high-power proton cyclotron accelerators that are under development [7]. A 250 MeV, 1 mA cyclotron is under construction at MIT and a GeV-energy, megawatt-class cyclotron is presently under design. When in production, because of new, inexpensive superconducting technology, these machines are expected to cost 5% of a conventional proton accelerator (< $20M). These machines will demonstrate the beam physics and engineering needed for this experiment.
This experiment utilizes an ultra-large water Cerenkov detector such as Hyper-K [8], MEMPHYS [9], or the detector proposed for the Deep Underground Science and Engineering Laboratory (DUSEL) [10]. We use a 300 kton DUSEL detector as our model. Water provides a target of free protons for the inverse beta decay (IBD) interaction:ν e + p → n + e + .
IBD interactions are identified via a coincidence signal. The first signal is from the Cerenkov ring produced by the positron. The second signal is from capture of the neutron. The signal from neutron capture on protons, which produces only a single 2.2 MeV γ, is too feeble to be efficiently observed in a large Cerenkov detector. For that reason, doping with gadolinium (Gd), which has a high capture rate and a short capture time, is proposed [11]. Neutron capture on Gd produces multiple photons totaling ∼8 MeV which can be observed with 67% efficiency [12]. Gd-doping of water is under development [13]. In IBD events, the energy of the neutrino is related to the energy of the positron and kinetic energy of the neutron, K, by The accelerators are placed at three separate baselines, L, for theν µ →ν e search (see Fig. 2). Each set of accelerators at the three sites runs for a 20% duty factor interspersed in time; the other 40% of the time is used to collect beam-off data. The longest baseline is L = 20 km, where ∼40 MeVν µ are at oscillation maximum for the measured value of ∆m 2 31 . In this case, term 2 of Eq. 1 will contribute while term 3 will not. A mid-baseline accelerator site is located at L = 8 km, where term 3 of Eq. 1 is non-zero. The shortest baseline accelerator site is at L =1.5 km, directly above the DUSEL detector. At this location, the neutrino-electron elastic scattering rates are sufficient to allow precision measurement of the neutrino flux normalization as discussed below. We propose multiple accelerators at the various locations (see Fig. 2), which is feasible because of the low cost per machine. For the L of a given event to be well-determined, the beams from each location are staggered in time.
Term 3 of Eq. 1 leads to an inherent ambiguity between δ CP and the mass hierarchy. We assume that on the timescale of the measurements presented here, the mass hierarchy will be measured using LBNE [10] or atmospheric neutrino measurements. [15]. For the sensitivity estimates, we choose the normal hierarchy as the example model.
We present a two-phase experiment, where the design has flexibility in the second phase. In our case, each phase represents five years. The first phase explores the oscillation space at ∼3σ and requires one accelerator at the near location, two at the mid-location and three at the far location. Once a signal for CP violation has been localized, the strategy for the second phase can be de-  termined. As an example for phase 2, we have chosen a design with one, two and seven accelerators. This design matches the sensitivity of a run of LBNE with 30 × 10 20 protons on target in neutrino mode followed by 30 × 10 20 protons on target in antineutrino mode [10]. This design is unique among proposals for CP violation searches and complementary to the present plans [6,10]. The measurement is done with antineutrinos, while all existing proposals rely heavily on neutrino data. The neutrino production systematics are different and well-controlled. Because of the low energy, the interaction systematics are also different. Varying L, while employing a single detector is novel and reduces systematics. A two-phase program which allows an optimized measurement strategy is powerful and potentially costsaving.

II. EVENT TYPES AND BACKGROUNDS
The energy range of the analysis is 20 < E ν < 55 MeV. The lower cut renders potential backgrounds from radioactive decay and spallation negligible. The upper cut is chosen because of the 52.8 MeV signal endpoint.
In this energy range, three types of interactions must be considered. First is the IBD signal, with an estimated reconstruction efficiency of recon = 67%, based on studies for Super-K [12]. Second is ν e + O → e − + F ("ν e O"), with a suppressed cross section relative to IBD due to nuclear effects [16,17] and no neutron capture. Third is neutrino-electron elastic scattering (ν e ES) ν e + e − → ν e + e − . This is separable from ν e O by angular cuts [18,19] and, so, can be used for the flux normalization. For ν e O and ν e ES events, we estimate recon = 75% [18].
Beam-off backgrounds arise from three sources: atmospheric ν µ p scatters with muons below Cerenkov threshold which stop and decay ("invisible muons"), atmospheric IBD events, and diffuse supernova neutrinos. These are all examples of correlated backgrounds; accidental beam-off backgrounds are estimated to be negligible. The rates of these correlated backgrounds are scaled from analyses for the GADZOOKS experiment [11]. The interaction rates of the beam-off backgrounds are wellmeasured during the 40% beam-off running fraction.
The beam-on backgrounds have both accidental and  correlated sources. The accidental backgrounds arise from the ν e in the beam which are followed by a neutronlike event. This background is estimated to be very small using the measurements from the Super-K Gd-doping study [12]. Correlated backgrounds are produced by the intrinsicν e content of the beam. This is reduced by careful design of the beam stop. We assume a long water target embedded in a copper absorber, surrounded by steel for each cyclotron. We target at 100 degrees from the detector to reduce decay-in-flight (DIF) backgrounds. For 2 GeV protons on target, the pion yields, π + /p (π − /p), are 0.43 (0.056). with a π + (π − ) DIF fraction of 0.017 (0.025). The decays of µ − 's are further reduced by a factor of 8.3 since the µ − will be captured before decaying. The compact design decreases theν e production compared to LAMPF/LANCE by a factor of 1.7. The beam has aν e /ν e ratio of 4 × 10 −4 .

III. SYSTEMATIC ERRORS
The multiple-DAR-source design is an elegant choice for precision oscillation physics because the beam and detector systematics are low. The shape of the DAR flux with energy is known to high precision and is common among the various distances, thus shape comparisons will have small uncertainties. The neutrino flux from the three distances is accurately determined from the direct measurement of the π + production rate using ν e ES events from the near accelerator. Existing proton rate monitors assure that relative proton intensities are understood to 0.1%. The interaction and detector systematic errors are low since all events are detected in a single detector. The IBD cross section for the signal is well-known [14]. The fiducial volume error on the IBD events is also small due to the extreme volume-to-surfacearea ratio of the ultra-large detector. The largest systematic errors arise from the ν e ES sample used to determine the absolute normalization of the flux. The error on this cross section is 0.5% due to a 0.7% uncertainty from the NuTeV sin 2 θ W measurement [20]. We assume a 2.1% energy scale error [21] which leads to a 1% error on the DAR flux when a E vis > 10 MeV cut on the events is applied. The ν e events on oxygen and IBD events with a missing neutron can be separated from the ν e ES sample since the angular distribution of ν e ES events is very forward-peaked, while these backgrounds have a broad distribution [19]. We take the uncertainty from contamination by these events to be negligible. The uncertainty of the electron-to-free-proton ratio in water is also very small. Adding the ν e ES systematics in quadrature, the systematic error on the IBD flux is expected to be 1.1%. For the total error on the IBD flux, one must then add the ν e ES statistical error in quadrature, which depends on the running period.  The other significant systematic error is on the efficiency for neutron detection in IBD events. To reduce uncertainties, neutrons are tagged via timing rather than position reconstruction. This leads to an inefficiency for neutrons outside of the timing window with a systematic uncertainty of 0.5% [12].

IV. OSCILLATION SENSITIVITIES
Sensitivity estimates were made by calculating the χ 2 for a given set of predicted events and investigating the χ 2 minimization and excursion, using a method similar to Ref. [6]. Matter effects were included in the fit, but are negligible due to the short baseline. Systematic uncertainties (see Sec. III and Table I) were constrained by pull-term contributions to the χ 2 of the form (k i − 1) 2 /σ 2 i , where σ 2 i are the uncertainties. Results are given for two scenarios (see Fig. 2): Phase 1 and Phase 1+2 combined. Table II gives the event samples associated with the combined phases, for the various classes of oscillation, background, and calibration events.
The sensitivity for observing a non-zero value for θ 13 at the 3 and 5σ CL as a function of δ CP is shown in Fig. 3 for combined two-phase running. This sensitivity meets that of LBNE, but is inverted in its δ CP dependence [10].
The combined two-phase running yields a 4.1σ measurement of δ CP at the test point of sin 2 2θ 13 = 0.05 and δ CP = −90 0 , as shown in Table III (top). The correlated measurement uncertainties are shown in Fig. 4 for 1 and 2σ contours. Table III (bottom), which provides the statistical uncertainty, indicates that the measurement is statistics-limited.

V. CONCLUSIONS
We have described a novel experiment to search for CP violation in the neutrino sector. This experiment is relatively low cost, employing multiple high-powered compact cyclotrons located at L = 1.5 km, 8 km and 20 km from a large water Cerenkov detector. Using the example of the DUSEL detector, for sin 2 2θ 13 = 0.05, the CP violation parameter δ CP can be measured to the level of LBNE (> 4σ) in a 2-phase 10-year run.
The complementary nature of this measurement makes it a compelling addition to the program. This experiment will probe for CP violation with antineutrinos, unlike the present program which relies heavily on neutrino interactions. The systematics are also quite different and low compared to present planned experiments. As a result, this experiment will provide a powerful input to our global search for new physics in the neutrino sector.