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1 Proc. 14th Int. Symp. on Nuclei in the Cosmos (NIC2016) Neutrino Oscillation Experiments Kate Scholberg 1 1 Department of Physics, Duke University, Durham, NC, 27708, USA schol@phy.duke.edu (Received September 12, 2016) The discovery of neutrino oscillations was recognized by the 2015 Nobel Prize. Tremendous progress has been made in the past two decades on understanding of neutrino mass and mixing properties, yet there are remaining unknowns. This talk presented an overview of neutrino oscillation experiments, with emphasis on recent results from beam and reactor experiments, as well as exciting prospects for the next decades. KEYWORDS: neutrinos, neutrino oscillations, neutrino mass 1. Introduction: Neutrino Mass and Oscillations In the standard three-flavor neutrino picture, the neutrinos are the neutral partners to the charged leptons. The flavor states are related to the mass states by a unitary mixing matrix, the Pontecorvo- Maki-Nakagawa-Sakata (PMNS) matrix U. This matrix is now conventionally parameterized as three Euler-like rotations: U = c 23 s 23 0 s 23 c 23 c 13 0 s 13 e iδ s 13 e iδ 0 c 13 c 12 s 12 0 s 12 c , (1) where s i j represents sine of the mixing angle θ i j and c i j represents cosine. The parameters associated with this picture are four independent parameters associated with the matrix: the three mixing angles θ 23, θ 12 and θ 13 and a complex phase δ associated with CP-violating observables. (Two Majorana phases will be ignored here, as they are unobservable in oscillation experiments.) In addition there are three masses, m 1, m 2 and m 3, or alternatively, two mass differences and an absolute mass scale. The signs of the mass differences matter: if there are two light states and one heavy state, we have a normal ordering (NO) and if there are two heavy states and one light one the ordering is said to be inverted (IO). (Note that the mass ordering, MO, is commonly referred to in the literature as the mass hierarchy. However that terminology has recently become less popular in the literature, because the three mass states may be degenerate and not hierarchical, i.e., the differences may be much less than the absolute scale.) The main observable consequence of this picture is that neutrino flavors oscillate as neutrinos propagate. In a three-flavor context, the probability for a neutrino born in flavor state f to be observed in flavor state g is P(ν f ν g ) = δ f g 4 i> j Re(U f i U giu f j U g j ) sin2 (1.27 m 2 i j L/E) ±2 i> j Im(U f i U giu f j Ug j ) sin(2.54 m2 i jl/e), (2) for baseline L in km, neutrino energy E in GeV, and m 2 i j = m 2 i m 2 j in ev 2. The positive sign in front of the last term holds for neutrinos and the negative sign holds for antineutrinos. This expression shows that the oscillation has two length scales driven by different m 2 i j values. For m2 23 >> m The Author(s) This article is available under the terms of the Creative Commons Attribution 4.0 License. Any further distribution of this work must maintain attribution to the author(s) and the title of the article, journal citation, and DOI.

2 and appropriate L/E (the case for many real situations), the decoupled oscillation can be well described by the two-flavor probability equation P(ν f ν g ) = sin 2 2θ sin 2 (1.27 m 2 L/E), (3) where the appropriate effective mass-squared difference and mixing angle depend on L/E. Oscillation observables can be either an energy- and baseline-dependent disappearance of neutrinos born in some flavor state (i.e., after propagation, a neutrino ends up in a flavor state for which it is below charged-current interaction threshold at the given neutrino energy), or else an energy-and baseline-dependent appearance of leptons with flavor indicating a different neutrino flavor state. 2. Current Status There has been enormous progress over the past two decades in understanding of neutrino oscillations. Two decades ago, there were two neutrino disappearance anomalies: solar ν e neutrino rates were observed to be suppressed, in an energy-threshold-dependent way, in several experiments (chlorine and gallium radiochemical experiments, as well as the Kamiokande II water-cherenkov experiment) [1]. Furthermore IMB [2] and Kamiokande II [3] had observed an energy-dependent deficit of upward-going atmospheric ν µ. Now, in both cases, these anomalies have been resolved and shown definitively to be due to neutrino oscillations. The observation of neutrino oscillations in the solar and atmospheric sectors was awarded the Nobel Prize in The Solar Sector The solar neutrino anomaly can now be considered solved, thanks to the SNO experiment, which by observation of flavor-blind neutral-current interactions has demonstrated ν e ν µ,τ [4]. These measurements were in conjunction with precise ν e disappearance measurements from Super- Kamiokande [5], and more recently, Borexino [6], a low-threshold liquid scintillator experiment. The oscillations seen in wild neutrinos from the Sun were later confirmed, and the relevant parameters strongly restricted to the large-mixing angle solution, by the KamLAND reactor ν e experiment [7]. The KamLAND experiment has observed the oscillation wiggle in L/E for reactor neutrinos with baselines of hundreds of kilometers from the sum of reactors in Japan and Korea. 2.2 The Atmospheric Sector The narrative in the atmospheric sector took a similar satisfying turn: tame neutrinos ended up telling the same story as the wild ones. For the atmospheric neutrino case, Super-K has made very high-significance measurements consistent with the two-flavor ν µ ν τ hypothesis [8]. Subsequently, multiple long-baseline accelerator experiments sending GeV neutrinos over hundreds of kilometers have confirmed disappearance of beam ν µ and are now in a precision measurement phase. The first of these was K2K (beam from KEK to Super-K) [9]. K2K was followed by MINOS (Fermilab to Soudan) [10] and CNGS (CERN to Gran Sasso). Current-generation experiments are T2K (J-PARC to Super-K) [11] and NOνA (Fermilab to Ash River) [12]. Tau neutrino appearance has now been explicitly measured in the CNGS beam [13] (and in atmospheric neutrinos [14]). The long-baseline neutrino beams have been steadily increasing in intensity, and future-generation experiments including an upgraded J-PARC beam to Super-K (T2K-II) [15] and then Hyper-Kamiokande [16], and LBNF/DUNE (Fermilab to Homestake) [17] will eventually reach the MW range. 2.3 The Little Twist in the Middle : θ 13 A decade ago, the third mixing angle θ 13 was unknown, having only limits from the CHOOZ reactor experiment [18]. There are two main experimental approaches for measuring θ 13 : reactors, which emit few-mev ν e, should see disappearance modulated by sin 2 2θ 13 on a few-km timescale. For 2

3 sin 2 θ θ 12 / sin 2 θ θ 23 / sin 2 θ θ 13 / δ CP / m ev [ m 2 3l ev Table I. Three-flavor oscillation allowed ranges at 3σ, taken from a recent fit to global data [25], for any mass ordering. In this reference s convention, m 2 3l m2 31 > 0 for NO and m2 3l m2 32 < 0 for IO. ] non-zero θ 13, long-baseline beams of GeV ν µ ( ν µ ) should observe a small component of ν e ( ν e ) after several hundred kilometers. Until 2011 several reactor experiments (Double Chooz in France [19], RENO in Korea [20], and Daya Bay in China [21]) were in competition with the T2K [22] and NOνA [23] beam experiments. Now, all have been spectacularly successful, with all of these experiments measuring, consistently, a relatively large value of θ 13 (about as large as previously allowed by the CHOOZ experiment). The Daya Bay experiment has the highest precision [24]. All experiments are continuing to take more data. The current overall status is that we now have a three-flavor picture that fits all of these data very well [25] (see Tab. I), with 3σ knowledge of the parameters at the few tens of percent level or better. 3. Unknowns in the Three-Flavor Picture However, there are still unknowns. A significant unknown, not addressed here, is whether the nature of the neutrino is Majorana or Dirac, i.e., whether the neutrino is its own antiparticle. The only real way of going after this question is via searches for neutrinoless double beta decay, and a worldwide effort is underway [26,27]. A second significant unknown is the absolute mass scale of the neutrino; there are kinematic and cosmological approaches to this question [27]. Neutrino oscillation experiments are sensitive only to mass differences and so cannot address these questions. Turning to oscillation-related parameters: among these, there are basically three unknowns at the current time. The value of CP δ is unknown at the 3σ level (although see below; there are now some hints). We also do not know the sign of mass-squared difference for the larger mass splitting; this is the mass ordering unknown. Although we know that the value of θ 23 is close to π/4, we do not know how close it is; and if it is not exactly π/4, we do not know whether it is greater or smaller, i.e., what octant it is in. Of these, the CP δ has been the most tantalizing, due to its potential (although perhaps tenuous) connection to leptogenesis [28]. But it is worth noting that knowledge of all of the mixing parameters is valuable, not only because one can test the relations between parameters predicted by mass models, but because testing the three-flavor paradigm is a way to look for beyond-the-sm physics [27]. 3

4 Future Prospects for Neutrino Oscillation Experiments 4.1 Determining the Mass Ordering There are several possible ways to get at the question of the neutrino mass ordering, using both wild and tame neutrinos. They are all challenging. The long-baseline beam method is the most reliable one, in the sense that it will certainly yield the answer given sufficient exposure. The idea is that in the three-flavor picture neutrinos and antineutrinos have different oscillation probabilities for ν µ ν e and ν µ ν e in matter, depending on the ordering (and baseline). The probabilities also depend on CP δ. The difference for different MO is stronger at > 1000-km baseline, where it will be easier to disentangle MO and CP effects. Currentgeneration experiments, such as T2K and NOvA, will have a chance at determining the ordering, if parameters are favorable. Although T2K s baseline (295 km) is relatively short, NOvA s is longer and so leads to better MO sensitivity. NOvA makes use of the NuMI beam from Fermilab with a 14-kton scintillator detector at an off-axis location 810 km away. There are two long-baseline-beam next-generation experiments for which work is underway. The main project in the U.S. is LBNF/DUNE (Long-Baseline Neutrino Experiment), a planned 40-kton liquid argon time-projection chamber to be located in South Dakota and combined with a 1.2 MW beam from Fermilab. The 1300-km baseline gives LBNF/DUNE excellent MO reach (see Fig. 1). The other next-generation long-baseline oscillation experiment is Hyper-Kamiokande, which will employ an upgraded beam from J-PARC [29] in conjunction with water-cherenkov detector near the Super-K site (so similar baseline as T2K). Wild neutrinos may yet provide information on the MO. They have the advantage that the atmospheric neutrino source is free, and comes with a range of baselines and energies (but of course cannot be controlled). The MO information is in the form of the matter-oscillation-induced distortion of the observed angular and energy distributions: one expects an angular-dependent ν µ ν e resonance for neutrinos in the NO and for antineutrinos in the IO at around 5-10 GeV for upward-going neutrinos. Both large statistics and good detector ability to reconstruct neutrino energy and direction are required to distinguish the ordering. Both Hyper-K and DUNE will have sensitivity (Hyper-K is stronger in statistics, DUNE in precision reconstruction), as well as potentially PINGU [30], a proposed infill of the IceCube detector to lower the energy threshold and improve reconstruction. The INO (India-based Neutrino Observatory) [31] will host a proposed iron calorimeter with a magnetic field, enabling atmospheric neutrino observations with lepton sign selection and hence ability to distinguish ν from ν, enhancing MO sensitivity. Systematic uncertainties are the dominant issue for determining the MO with atmospheric neutrinos. A complementary method for determining the ordering, which does not depend on matter effects, is to use reactor neutrinos. The idea is to look for the very slight MO-dependent vacuum-oscillation suppression difference of the reactor ν e energy spectrum at a distance of about 60 km (e.g., [32]). Extremely good energy resolution and knowledge of the energy scale are required. The JUNO [33] and RENO-50 [34] experiments, both involving 20-kton-scale scintillator experiments, aim to tackle this challenging measurement. Finally, the neutrino burst observed from a core-collapse supernova may bring information on the MO via a number of different observables [35 38] although of course, one must wait for a nearby supernova before one can exploit this possibility. 4.2 Measuring CP Delta The main observable for measuring CP-violating δ is, as for MO, a ν µ ν e oscillation pattern at long baseline in neutrinos and antineutrinos, assuming that the MO-dependent matter effects are either negligible, or known. The proposed long-baseline experiments described above also have good reach for CP violation. As an example, the sensitivity of LBNF/DUNE is shown in Fig. 1. Hyper-K 4

5 also has good sensitivity to CP (although less good sensitivity to MO, due to shorter baseline). Fig. 1. As an example, sensitivities to MO and CP δ for DUNE, in combination with other experiments. Figures and caption from [17]. Left: minimum significance with which the mass hierarchy can be determined for all values of δ (100%), 50% and in the most optimistic scenario (0%) as a function of exposure. This plot assumes normal mass ordering. (The inverted hierarchy case is very similar.) Right: significance with which the CP violation can be determined as a function of the value of δ for an exposure of 300 kton MW year, assuming normal MO (left) or inverted MO (right). The shaded region represents the range in sensitivity due to potential variations in the beam design. 4.3 Recent CP Hints A joint fit of T2K ν µ disappearance and ν e appearance, combined with reactor ν e disappearance, constrains possible CP values and shows a mild preference for δ = π/2 [39]. The new NOνA results are consistent [23]. A new T2K data set including antineutrino data now excludes δ = 0 and π at 90% C.L.. The allowed region for δ in radians is [ 3.02, 0.49] (NO assumed), [ 1.87, 0.98] (IO assumed) [40]. Normal ordering is now also slightly favored by the beam and atmospheric [41] data. However, these hints still have weak statistical significance. While there are prospects for improvement in the next 5-10 years [42], we will very likely need the next-generation experiments LBNF/DUNE and Hyper-K to know the answers to 5σ. 5. Summary We now have a robust and simple three-flavor neutrino paradigm, which is very successful in describing diverse experimental data. There are still some entirely unknown parameters notably, the MO and CP δ towards which there are clear experimental approaches to take. The approaches are challenging but promising. In general, we will need to push the measurement uncertainties further to find new physics beyond the three-flavor paradigm. Not discussed here are some anomalies, which could point to sterile neutrinos (i.e, new neutrino states without standard-model weak interactions) or other new physics. These are being addressed experimentally by multiple experiments [43]. We await more data to learn what surprises lie in store for us. References 5

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