Neutrino experiments : highlights of accelerator and reactor results

We present a summary of recent accelerator and reactor results in the field of neutrino experiments. Having established neutrino oscillations in a variety of experimental configurations, it is remarkable that practically all the observations fit within a well defined paradigm, where the neutrino mixing matrix PMNS plays a central role. The experimental task is today to precisely measure the parameters of this matrix and to make precision tests of this paradigm. Various experimental results, in particular the θ13 measurement at reactor experiments, are shown which illustrate that the few percent precision level has been reached or will be soon reached. This opens up a new realm of sensitivity to subleading effects in the oscillation phenomena. Moreover, the study of νμ → νe appearance at accelerator experiments provides very preliminary indications related to the CP violation parameter δCP. The full exploration of CP violation in the lepton sector is the goal for the future studies, with a contribution from various experiments, currently running or planned for the next decade.


Introduction
Neutrino physics has already provided us important discoveries and surprising results in the last decade. First, thanks to the discovery of neutrino oscillations it is now an established fact that neutrinos are massive. However, their mass is extremely low, certainly below the eV scale. This sets neutrinos aside from the other Standard Model fermions and requires an explanation. Indeed, the mere existence of a neutrino mass term points to physics beyond the Standard Model that needs to be understood. Second, there is now relatively good knowledge of the neutrino mixing matrix. The angles governing this matrix are large, the smallest being the θ 13 angle, approximately 9 degrees. The situation is therefore considerably different than for the CKM mixing matrix relevant for the quark sector. We can further notice that neutrinos, the most abundant fermions in the Universe according to our current theoretical framework, play a fundamental role in the evolution of the Universe and in particular in structure formation. It is a fundamental question to ascertain whether they also play a role in the matter-antimatter asymmetry, as proposed by the leptogenesis model. This question is related to the search for CP violating phenomena in the lepton sector. These considerations call for a deeper understanding of these particles, as a possible window on new phenomena.
Today, neutrino oscillations have been firmly established using solar, atmospheric, reactor, and accelerator neutrinos in a variety of experimental configurations, baselines and energies. A recent measurement [1] by the Daya Bay experiment (Fig. 1) gives a very clean graphical representation of this phenomenon, with a clear oscillatory pattern emerging.
These results have established the three neutrino Standard Model paradigm. In this paradigm, a central role is played by the Pontecorvo-Maki-Nakagawa-Sakata neutrino mixing matrix. This matrix U relates the mass eigenstates ν 1 , ν 2 and ν 3 (with masses m 1 , m 2 and m 3 ) to the flavour f eigenstates ν e , ν µ and ν τ via with c i j = cos θ i j and s i j = sin θ i j . In the case of Majorana neutrinos, additional CP violation parameters are present. The other relevant oscillation parameters are the squared mass splittings ∆m 2 i j = m 2 i − m 2 j . The precision on the parameters governing this matrix prior to this conference is shown in Table 1 [2]: the few percent precision level has been reached or will be soon reached, with the notable exception of the θ 23 angle. Another unknown is the ordering of the mass states, that could either be m 1 < m 2 < m 3 (normal hierarchy) or m 3 < m 1 < m 2 (inverted hierarchy).   In this review, we will show how all the more easily accessible transitions have been probed, namely ν µ → ν µ (as well as its CP conjugate), ν µ → ν τ and ν µ → ν e with neutrino beams, andν e →ν e with reactor antineutrinos. Moreover recent results are presented, mainly obtained with reactor and accelerator experiments, providing further improvements in the determination of several parameters and opening new experimental avenues.
The next steps in the study of neutrino oscillations are related to the following crucial questions and tasks: • Is θ 23 precisely equal to 45 • ? Otherwise, in which octant does this angle lie?
• Is the neutrino mass hierarchy normal or inverted ?
• What is the value of the CP violation parameter δ CP ?
• Perform precision tests of the PMNS paradigm (ideally at the % level, as for the CKM matrix) • Are there any new neutrino states ?
Answering these questions will provide new information for model builders, help determine a possible symmetry between ν µ and ν τ , and provide new input and plausibility for the theories of leptogenesis.
Several short baseline experiments (LSND, Mini-BooNE, reactors, Ga source) have revealed anomalies that could be interpreted as due to oscillations with a ∆m 2 eV 2 , that does not fit with the other mass splitting observed. No global satisfactory interpretation can be found because of tensions within the data [3], especially between appearance data and disappearance results. Most notably the goodness of fit of these global fits is very poor. An intense experimental effort, at accelerators (MicroBooNE), reactors and using intense sources (SOX) is ongoing to probe these anomalies, with first results expected in the next years.

Tau neutrino appearance
The disappearance of atmospheric neutrinos has been the first signal where the existence of neutrino oscillation has been established. In the standard PMNS paradigm this disappearance is related to the appearance of tau neutrinos, however indications of this process have so far not been conclusive.
The OPERA experiment has performed a search for ν µ → ν τ appearance with a baseline of 732 km (CERN to Gran Sasso) using the Emulsion Cloud Chamber technique. It has recently observed a fourth ν τ candidate [4] in the τ → h decay channel (Fig. 2). In this search the total background has been evaluated to be 0.233 ± 0.041. The null hypothesis (no ν τ appearance) is excluded with a significance of 4.2 σ.   [4]. The ν τ interaction vertex is v1, the τ track is labelled "parent" ending in the decay vertex v2 and the hadron track is labelled "daughter". Notice that a segment of the τ track has been detected. The τ decay length is 1090 ± 30 µm.
Super-Kamiokande [5] has searched for ν τ -like events in atmospheric neutrinos (2806 days, corresponding to the SK-I SK-II and SK-III phases of the experiment). To do this, they have defined a neural network based on event features (like the total visible energy, the number of decay electrons, the sphericity) capable of discriminating between the signal and other atmospheric neutrino interactions. They have found an excess with 3.8 σ significance for upgoing events (Fig. 3). The fitted value of the tau normalization is 1.42 ± 0.35(stat) +0.14 −0.12 (syst) to be compared to the expectation of one, while a value of zero would indicate no ν τ in the sample. The observed number of fitted events is calculated to be 180.1 ± 44.3(stat) +17.8 −15.2 (syst) events. These results provide evidence that the muon neutrino disappearance first observed in atmospheric neutrinos and later in long baseline experiments is mainly due to the ν µ → ν τ transition.

Reactor neutrino experiments
Reactor neutrino experiments take advantage of the large number of antineutrinos (of the order of 10 20 /s) produced in the β decays of the fission products. At short baselines L, the oscillation probability for an antineutrino of energy E can be written as P(ν e →ν e ) 1 − sin 2 2θ 13 sin 2 ∆m 2 31 L 4E (2) allowing a clean determination of θ 13 .
The detection technique is based on the inverse beta decay processν e p → e + n. The signal is given by   [5] for selected events in the SK-I to SK-III data set, including distributions for taulike (NN>0.5), upward-going [cos(θ) < -0.2], nontaulike (NN<0.5), and downward-going [cos(θ) > 0.2] events. NN is the output of a neural network designed to select tau neutrino events. The histogram shows the best fit including ν τ (gray) and the background (white) from other atmospheric neutrinos. the positron annihilation signal followed by the neutron capture on a Gadolinium nucleus, providing a delayed coincidence. The detectors are based on liquid scintillators.
To control the flux, all the projects use (or envisage to use) near detectors built with the same technology as the far detectors. The control of the backgrounds and of the systematic uncertainties is crucial. For instance Daya Bay has shown that they can control the relative energy scale uncertainty within 0.2% (was 0.35%) for the 8 detectors. Double Chooz has shown a very good control (within 0.36 %) of the energy reconstruction as a function of the event position inside the detector. To achieve this they have used muon-produced neutrons which provide a good calibration source illuminating all the detector. In Table 2 we present the main parameters of the running reactor experiments devoted to the measurement of the θ 13 mixing angle.
The Daya Bay experiment has presented at this conference [6] the most precise determination of the θ 13 mixing angle (Fig. 4) sin 2 2θ 13 = 0.084 ± 0.005. ( as well as |∆m 2 ee | = 2.44 +0.10 −0.11 10 −3 eV 2 , where ∆m 2 ee is defined by sin 2 ∆m 2 ee L 4E = cos 2 θ 12 sin 2 ∆m 2 31 L 4E + . This result is based on a data set four times larger (621 livedays) than the previously published result and provides an impressive precision of 6 % on sin 2 2θ 13 . Over 1 million antineutrinos were detected, of which 150k are in the far detectors. The results from RENO (sin 2 2θ 13 = 0.101 ± 0.013) [7] and Double Chooz (sin 2 2θ 13 = 0.090 +0.032 +0.029 ) [8] are in good agreement with the Daya Bay result, although with a significantly larger total uncertainty. The shape of the deficit induced by the neutrino oscillations agrees with the prediction from the near detectors extrapolated to the far detectors.  However, comparing both the measured positron spectrum and the derived antineutrino spectrum to the theoretical predictions, a distortion ("bump"), with an integral corresponding to a few percent of the total spectrum, was observed by Double Chooz [8], RENO [7] and Daya Bay [9] at an energy of around 5 MeV (Fig. 5). It is significant that all three experiments observe the same effect in the same energy range. The theoretical prediction is derived for 235 U, 239 Pu and 241 Pu from a measurement of their β spectrum at the ILL research reactor in the 1980. There, the positron spectrum was the primary measurement. The conversion from the positron to the antineutrino spectrum is done globally, since each of these spectra is composed of several thousands β decays branches: this conversion might introduce systematic uncertainties at the few % level.
Preliminary studies disfavour background and energy-scale as a explanation of this discrepancy. According to preliminary studies the θ 13 measurement would not be affected thanks to the near detectors. A discussion on possible causes underlying this effect can be found for instance in [10] where discrepancies between the conversion method and ab initio calculations of the antineutrino spectrum are pointed out.   [8], after subtraction of the background, to the non-oscillation prediction as a function of the visible energy of the prompt signal. The overlaid red line is the rate of the best-fit to the non-oscillation prediction with the reactor flux uncertainty (green) and the total systematic uncertainty (orange).
Clearly new studies in the coming years will be required to understand the origin of this distortion, studies which are necessary in order to reach the ultimate precision from reactor experiments both for the θ 13 measurements but also for possible investigations of new neutrino states.

Accelerator neutrino experiments
Long-baseline experiments using muon neutrino beams are sensitive to ν µ disappearance, which has the following approximate expression P(ν µ → ν µ ) 1 − 4 cos 2 θ 13 sin 2 θ 23 (1 − cos 2 θ 13 × sin 2 θ 23 ) sin 2 ∆m 2 32 L 4E (4) for normal hierarchy, while for inverted hierarchy the relevant mass splitting is ∆m 2 13 , and to the ν e appearance, governed by P(ν µ → ν e ) sin 2 2θ 13 sin 2 θ 23 sin 2 ∆m 2 31 L 4E − sin 2θ 12 sin 2θ 23 2 sin θ 13 sin 2 ∆m 2 21 L 4E sin 2 2θ 13 sin 2 ∆m 2 31 L 4E sin δ CP (5) The disappearance channel provides sensitivity to the mixing angle θ 23 and to the ∆m 2 32 (∆m 2 13 ) mass splitting for the normal (inverted) hierarchy. Notice that there is no ν e appearance for θ 13 = 0 (at least at this order, a much smaller appearance term exists related to the solar mass splitting ∆m 2 21 and therefore with a much longer oscillation length). The appearance channel provides sensitivity to the mixing angle θ 13 and its subleading terms to the CP violating phase δ CP . In the current phase of these experiments, the sensitivity is such that the results can start constraining the subleading terms as we will show.

MINOS
MINOS is a long-baseline experiment (735 km) from Fermilab to the Soudan mine, using a 5.4 kt magnetized iron/scintillator, on the NuMI beamline. MINOS has recently released a combined three flavour fit [11] to neutrino beam data (10.71 10 20 Protons-On-Target (POT)) antineutrino beam data (3.36 10 20 POT), MINOS+ and atmospheric neutrinos (Fig. 6). MINOS+ corresponds to a new phase of the project, with data being collected at a higher neutrino energy, on the same beam line at the same time as the NOvA experiment.

T2K
T2K is a long-baseline (295 km) neutrino experiment in Japan between J-PARC (Tokai) and Super-Kamiokande (SK). The primary proton beam with an energy of 30 GeV, a beam power of 235 kW, has provided 6.57 10 20 POT. This represents 8% of the final design exposure. The far detector is Super-Kamiokande with 22.5 kt fiducial mass and nearly 100% livetime.
The main features of the T2K experiment are: • The use for the first time of an off-axis beam. This ensures that the flux has a narrow peak tuned to the first oscillation maximum. This feature minimizes the rate of high energy neutrinos whose interactions can produce background for the electron neutrino appearance search.
• The pion and kaon production by the interaction of 30 GeV protons on carbon has been measured by the NA61 experiment at CERN. This provides a good constraint for the determination of the beam flux.
• The excellent particle identification capabilities in Super-Kamiokande. The µ → e misidentification is at the 1% level. This allows to cleanly distinguish ν e from ν µ interactions.
T2K has a sophisticated set of near detectors measuring neutrino interactions at 280 m from the target [12]. These measurements allow to significantly reduce the flux and cross-section systematic uncertainty down to 7% (Fig. 7). The selection used for the far detector in the ν µ disappearance analysis is based on one-ring µ-like events. The sample selected in this way is shown in Fig. 8: it consists of 120 events while 446±23 (syst.) events are expected in the case of no oscillation, showing muon neutrino disappearance in a dramatic way. The best fit [13] is close to the point of maximum mixing θ 23 = π/4 and the allowed region provides the best constraint on the θ 23 value (Fig. 9). The 1D 68% confidence intervals are sin 2 (θ 23 ) = 0.514 +0.055 −0.056 (0.511 ± 0.055) and ∆m 2 32 = 2.51 ± 0.10 (∆m 2 13 = 2.48 ± 0.10) × 10 −3 eV 2 /c 4 for the normal hierarchy (inverted hierarchy). The T2K neutrino interaction generator, NEUT, includes an effective model (pionless ∆ decay) that models some but not all of the expected multinucleon cross section. The impact of possible multinucleon effects in neutrino interactions has been studied in more detail. The mean biases in the determined oscillation parameters are less than 1% for the ensemble, though the sin 2 (θ 23 ) biases showed a 3.5% rms spread.
The search for a signal of ν e appearance yields a sample of 28 events (Fig.10) in the far detector while the background, in the case of no appearance, is evaluated to be 4.9±0.6 (syst.) events. The dominant contribution to the background is given by the intrinsic ν e in the beam. Their flux has been measured in the near detector to be 1.01 ± 0.10 with respect the prediction [12]. This gives 7.3 σ evidence of a non-zero θ 13 angle [15] and constitutes the first direct observation of the appearance  [13]. Top: The observed spectrum and expected spectrum with interaction modes for the T2K best fit. Bottom: The ratio of the observed spectrum (points) to the no-oscillation hypothesis, and the best oscillation fit (solid).   Figure 9: Allowed regions at 68 % and 90 % CL in the ∆m 2 32 versus sin 2 θ 23 plane for T2K [13], Super-Kamiokande [14] and MI-NOS [11].  Figure 10: The reconstructed energy distribution for T2K ν e candidate events [15] in the far detector with the MC prediction at the best fit of sin 2 2θ 13 = 0.144. Figure 11 shows for each value of δ CP the one dimensional allowed interval for sin 2 2θ 13 . By comparing these intervals to the value measured by the reactors experiments, it is possible to derive allowed regions for δ CP . For instance, especially for the case of inverted hierarchy, the values around δ CP π/2 are disfavoured.
In T2K, a combined fit [16] using the ν µ disappearance and ν e appearance samples has been conducted. This study takes advantage of the fact that the appearance and disapperance probabilities shown in Eq. 6 and Eq. 9 depend on the same parameters set, if the subleading terms are taken into account. Moreover, from an experimental point of view, there are some correlated systematic uncertainties that are best taken into account in this kind of combined fit rather than in an external fit, where only an approximate (or none at all) treatment of these effects is possible. The results of this fit are shown in Fig. 12. Using the measurement of θ 13 done by reactor experiments, the excluded regions for δ CP at the 90% CL are [0.146,0.825]π ([-0.080,1.091]π) for normal (inverted) mass hierarchy.
The best fit point is obtained for a value very close to δ CP = −1/2π. Of course this is only a very preliminary hint that will need much more data to become a firmly established experimental result. However, a few points can be made already now. First, if nature has chosen the value δ CP = 3/2π CP violation effects are maximal and therefore relatively easier to detect. We can also notice that this solution satisfies the leptogenesis bound [17] | sin θ 13 sin δ CP | ≥ 0.11 with no additional source of CP violation .
T2K has recently resumed data-taking in the antineutrino mode and more results in this field are expected.  Figure 11: The T2K 68% and 90% CL allowed regions for sin 2 2θ 13 , as a function of δ CP assuming normal hierarchy (top) and inverted hierarchy (bottom) [15]. The solid line represents the best fit sin 2 2θ 13 value for given δ CP values. The shaded region shows the average θ 13 value from the PDG2012. Figure 12: ∆χ 2 as a function of δ CP obtained by a global analysis of T2K data [16], combining appearance and disappearance samples and the measurement of θ 13 by the reactor experiments. The horizontal lines show the critical value ∆χ 2 corresponding to a confidence level of 90%. The blue and gray bands indicate the 90% CL excluded regions.

NOvA
NOvA is an off-axis experiment from Fermilab to Ash River (810 km) on the NuMI beam line. Its far detector is a 14 kt totally active structure filled with liquid scintillator. The first neutrino events have been observed this year. The physics goals of NOvA are similar to those of T2K, that is a study of ν e appearance with a long baseline, in order to study CP violation effect. Given the much longer baseline, NOvA will also have some sensitivity to the neutrino mass hierarchy through matter effects. NOvA has recently started data-taking and first results are expected in 2015.

Conclusions
The study of neutrino oscillations has provided many surprising discoveries in the last 15 years, establishing the three neutrino mixing paradigm, implying physics beyond the SM. The field is approaching the few % precision era due to dedicated experimental efforts. The experiments begin to be sensitive to CP violation via the interplay of accelerator and reactor observables. Major efforts are ongoing towards answering the remaining open questions and providing precision tests.
For the long-baseline accelerator experiments, recent studies are focussed on the LBNO project in Europe, LBNF in USA and Hyper-Kamiokande in Japan with different baselines and technologies. The full exploration of the PMNS matrix and in particular of the CPviolating parameter δ CP will require the construction of at least one of this experiments in the next decade.