It is generally believed that neutrino mass hierarchy can be determined at a long baseline experiment, often using accelerator neutrino beams. Reactor neutrino experiments at an intermediate baseline have the capability to distinguish normal or inverted hierarchy. Recently it has been demonstrated that the mass hierarchy could possibly be identified using Fourier transform to the L/E spectrum if the mixing angle $\sin^2(2θ_{13})>0.02$. In this study a more sensitive Fourier analysis is introduced. We found that an ideal detector at an intermediate baseline ($\sim 60$ km) could identify the mass hierarchy for a mixing angle $\sin^2(2θ_{13}) > 0.005$, without requirements on accurate information of reactor neutrino spectra and the value of $Δm^2_{32}$.
We study the advantages of a second identical detector at a medium baseline reactor neutrino experiment. A major obstruction to the determination of the neutrino mass hierarchy is the detector's unknown nonlinear energy response, which even under optimistic assumptions reduces the confidence in a hierarchy determination by about 1 sigma at a single detector experiment. Various energy response models are considered at one and two detector experiments with the same total target mass. A second detector at a sufficiently different baseline eliminates this 1 sigma reduction. Considering the unknown…
We examine the possibility of determining the neutrino mass hierarchy in the limit θ_{13} = 0 using atmospheric neutrinos as the source. In this limit, in which θ_{13} driven matter effects are absent, independent measurements of Δ_{31} and Δ_{32} can, in principle, lead to hierarchy determination. Since the difference between these two is Δ_{21}, one needs an experimental arrangement where Δ_{21} L/E \gtrsim 1 can be achieved. This condition can be satisfied by atmospheric neutrinos since they have a large range of energies and baselines. In spite of this, we find that hierarchy determination…
Crucial developments in neutrino physics would be the determination of the mass hierarchy (MH) and measurement of the CP phase in the leptonic sector. The patterns of the transition probabilities $P(ν_μ\rightarrow ν_τ)$ and $P(\barν_μ\rightarrow \barν_τ)$ are sensitive to these oscillation parameters. An asymmetry parameter can be defined as the difference of these two probabilities normalized to their sum. The profile of the asymmetry parameter gives a clear signal of the mass ordering as it is found to be positive for inverted hierarchy and negative for normal hierarchy. The asymmetry parame…
We point out a synergy between T-conjugated oscillation channels in the determination of the neutrino mass hierarchy with oscillation experiments with relatively short baselines (L < 700 km), where the matter effect is small. If information from all four oscillation channels $ν_μ\toν_e$, $\barν_μ\to\barν_e$, $ν_e\toν_μ$ and $\barν_e\to\barν_μ$ is available, a matter effect of few percent suffices to break the sign-degeneracy and allows to determine the neutrino mass hierarchy. The effect is discussed by analytical considerations of the relevant oscillation probabilities, and illustrated with n…
We study the problem of determination of the sign of Delta m^2_{31}, or the neutrino mass hierarchy, through observations of atmospheric neutrinos in future detectors. We consider two proposed detector types : (a) Megaton sized water Cerenkov detectors, which can measure the survival rates of nu_μ+ \barν_μand nu_e + \barν_e and (b) 100 kton sized magnetized iron detectors, which can measure the survival rates of ν_μand \barν_μ. For energies and path-lengths relevant to atmospheric neutrinos, these rates obtain significant matter contributions from P_{μe}, P_{μμ} and P_{ee}, leading to an appre…
The recent discovery by the Daya-Bay and RENO experiments, that θ_{13} is nonzero and relatively large, significantly impacts existing experiments and the planning of future facilities. In many scenarios, the nonzero value of θ_{13} implies that θ_{23} is likely to be different from π/4. Additionally, large detectors will be sensitive to matter effects on the oscillations of atmospheric neutrinos, making it possible to determine the neutrino mass hierarchy and the octant of θ_{23}. We show that a 50 kT magnetized liquid argon neutrino detector can ascertain the mass hierarchy with a significan…
We extend the Gunion Bertsch calculation of gluon radiation in single scattering to the case of finite mass quarks. This case applies to the radiative energy-loss of heavy quarks of intermediate energies propagating in a quark gluon plasma. We discuss more specifically the dead cone effect as well as the mass hierarchy of the collisional and radiative energy loss and provide some predictions for observables sensitive to the mass hierarchy of energy loss in ultrarelativistic heavy ion collisions.
After the neutrino mixing angle $θ_{13}$ has been precisely measured by the reactor antineutrino experiments, one of the most important open questions left in neutrino physics is the neutrino mass hierarchy. Jiangmen Underground Neutrino Observatory (JUNO) is designed to determine the neutrino mass hierarchy (MH) without exploring the matter effect. The JUNO site location is optimized to have the best sensitivity for the mass hierarchy determination. JUNO will employ a 20 kton liquid scintillator detector located in a laboratory 700 meters underground. The excellent energy resolution and PMT c…
Building on earlier studies, we investigate the possibility to determine the type of neutrino mass spectrum (i.e., "the neutrino mass hierarchy") in a high statistics reactor electron antineutrino experiment with a relatively large KamLAND-like detector and an optimal baseline of 60 Km. We analyze systematically the Fourier Sine and Cosine Transforms (FST and FCT) of simulated reactor antineutrino data with reference to their specific mass hierarchy-dependent features discussed earlier in the literature. We perform also a binned χ^2 analysis of the sensitivity of simulated reactor electron ant…
We report the results of Monte Carlo simulations of a medium baseline reactor neutrino experiment. The difference in baselines resulting from the 1 km separations of Daya Bay and Ling Ao reactors reduces the amplitudes of 1-3 oscillations at low energies, decreasing the sensitivity to the neutrino mass hierarchy. A perpendicular detector location eliminates this effect. We simulate experiments under several mountains perpendicular to the Daya Bay/Ling Ao reactors, considering in particular the background from the TaiShan and YangJiang reactor complexes. In general the hierarchy can be determin…
We describe a method for determining the hierarchy of the neutrino mass spectrum and theta_13 through remote detection of antineutrinos from a nuclear reactor. This method utilizing a single, 10-kt scintillating liquid detector at a distance of 50-64 kilometers from the reactor complex measures mass-squared differences involving nu_3 with a one (ten) year exposure provided sin2(2theta_13)>0.05 (0.02). Our technique applies the Fourier transform to the event rate as a function of neutrino flight distance over energy. Sweeping over a relevant range of delta-m2 resolves separate spectral peaks fo…
Determination of the neutrino mass hierarchy in a reactor neutrino experiment at medium baseline is discussed. Observation of the interference effects between the Δm^2_{31} and Δm^2_{32} oscillations enables a relative measurement independent of the knowledge of the absolute mass-squared difference. With a 20 kton liquid scintillator detector of 3%/\sqrt{E(MeV)} energy resolution, the Daya Bay II Experiment at a baseline of \sim 50 km from reactors of total thermal power 36 GW can determine the mass hierarchy at a confidence level of Δχ^2_{MH} \sim (10-12) (3-3.5 σ) in 6 years after taking int…
We discuss the neutrino mass hierarchy determination with atmospheric neutrinos in PINGU (Precision IceCube Next Generation Upgrade), based on a simulation with the GLoBES software including the full three flavor framework and parameter degeneracy, and we compare it to long-baseline experiment options. We demonstrate that the atmospheric mass hierarchy sensitivity depends on the achievable experiment properties and we identify the main targets for optimization, whereas the impact of a large number of tested systematical errors turns out to be small. Depending on the values of theta_23, delta, …
This article reports the optimized experimental requirements to determine neutrino mass hierarchy using electron antineutrinos ($\barν_e$) generated in a nuclear reactor. The features of the neutrino mass hierarchy can be extracted from the $|Δm^{2}_{31}|$ and $|Δm^{2}_{32}|$ oscillations by applying the Fourier sine and cosine transform to the $L/E$ spectrum. To determine the neutrino mass hierarchy above 90\% probability, the requirements on the energy resolution as a function of the baseline are studied at $\sin 2θ_{13}=0.1$. If the energy resolution of the neutrino detector is less than $0…
After the successful measurement of the mixing angle $θ_{13}$, the determination of the neutrino mass hierarchy has become a priority for future neutrino experiments. We propose a conventional $ν_μ$ beam with neutrino energies in the range 2-8 GeV aimed at a Mton underwater detector at the "magic" baseline of 2600 km. In this constellation it is sufficient to distinguish ($ν_μ$ induced) track-like interactions from cascade-like interactions with moderate purity to determine the mass hierarchy.
Neutrino oscillation experiments under neutrino pair beam from circulating excited heavy ions are studied. It is found that detection of double weak events has a good sensitivity to measure CP violating parameter and distinguish mass hierarchy patterns in short baseline experiments in which the earth-induced matter effect is minimized.
Ruling out the inverted neutrino hierarchy with neutrinoless double beta decay experiments is possible if a limit on the effective mass below the minimal theoretically possible value is reached. We stress that this lower limit depends strongly on the value of the solar neutrino mixing angle: it introduces an uncertainty of a factor of 2 within its current 3 sigma range. If an experiment is not background-free, a factor of two in effective mass corresponds to a combined factor of 16 improvement for the experimental parameters running time, detector mass, background level and energy resolution. …
Statistical methods of presenting experimental results in constraining the neutrino mass hierarchy (MH) are discussed. Two problems are considered and are related to each other: how to report the findings for observed experimental data, and how to evaluate the ability of a future experiment to determine the neutrino mass hierarchy, namely, sensitivity of the experiment. For the first problem where experimental data have already been observed, the classical statistical analysis involves constructing confidence intervals for the parameter Δm^2_{32}. These intervals are deduced from the parent di…
Medium-baseline reactor neutrino oscillation experiments (MBRO) have been proposed to determine the neutrino mass hierarchy (MH) and to make precise measurements of the neutrino oscillation parameters. With sufficient statistics, better than ~3%/\sqrt{E} energy resolution and well understood energy non-linearity, MH can be determined by analyzing oscillation signals driven by the atmospheric mass-squared difference in the survival spectrum of reactor antineutrinos. With such high performance MBRO detectors, oscillation parameters, such as \sin^22θ_{12}, Δm^2_{21}, and Δm^2_{32}, can be measure…
We demonstrate that the detection of shock modulations of the neutrino spectra from a galactic core-collapse supernova is sufficient to obtain a high significance determination of the neutrino mass hierarchy if the supernova event is observed in both a Mton-class water Cherenkov detector and a 100 kton-class liquid argon detector. Neither detailed supernova neutrino flux modelling nor observation of Earth matter effects is needed for this determination. As a corollary, a nonzero value of θ_x will be established.
Recent measurements of large theta_{13} by Daya Bay and RENO reactor experiments have opened up the possibility of determining the neutrino mass hierarchy, i.e. the sign of the mass squared splitting Delta m_{31}^2, the CP-violating phase delta_{CP} and the octant of theta_{23}. In the light of this result, we study the performance of a low energy neutrino factory (LENF) for determination of the mass hierarchy. In particular, we explore the potential of the nu_e$ and barν_e disappearance channels at LENF to determine the neutrino mass hierarchy, that is free from the uncertainties arising from…
The neutrino mass hierarchy, i.e., whether the $ν_3$ neutrino mass eigenstate is heavier or lighter than the $ν_1$ and $ν_2$ mass eigenstates, is one of the remaining undetermined fundamental features of the neutrino Standard Model. Its determination would represent an important step in the formulation of the generalized model, and would have a profound impact on the quest of the nature of neutrinos (Dirac or Majorana) and the search for a theory of flavor. In this review, we summarize the status of experimental and theoretical work in this field and explore the future opportunities that emerg…
The determination of the ordering of the neutrino masses (the hierarchy) is probably a crucial prerequisite to understand the origin of lepton masses and mixings and to establish their relationship to the analogous properties in the quark sector. Here, we follow an alternative strategy to the usual neutrino--antineutrino comparison in long baseline neutrino oscillation experiments: we exploit the combination of the neutrino-only data from the NOvA and the T2K experiments by performing these two off-axis experiments at different distances but at the same $<E >/L$, where $<E >$ is the mean neutr…
In the next 10 years medium baseline reactor neutrino experiments will attempt to determine the neutrino mass hierarchy and to precisely measure θ_12. Both of these determinations will be more reliable if data from identical detectors at distinct baselines are combined. While interference effects can be eliminated by choosing detector sites orthogonal to the reactor arrays, one of the greatest challenges facing a determination of the mass hierarchy is the detector's unknown energy response. By comparing peaks at similar energies at two identical detectors at distinct baselines, one eliminates …
In the next decade, a number of experiments will attempt to determine the neutrino mass hierarchy. Feasibility studies for such experiments generally determine the expected value of Delta chi^2. As the hierarchy is a discrete choice, Delta chi^2 does not obey a one degree of freedom chi^2 distribution and so the number of sigmas of confidence of the hierarchy determination is not the square root of the expected Delta chi^2. We present a simple formula for the sensitivity to the hierarchy that can be expected from the median experiment as a function of the expected Delta chi^2.
We explore the possibility of simultaneous determination of neutrino mass hierarchy and the CP violating phase by using two identical detectors placed at different baseline distances. We focus on a possible experimental setup using neutrino beam from J-PARC facility in Japan with beam power of 4MW and megaton (Mton)-class water Cherenkov detectors, one placed in Kamioka and the other at somewhere in Korea. We demonstrate, under reasonable assumptions of systematic uncertainties, that the two-detector complex with each fiducial volume of 0.27 Mton has potential of resolving neutrino mass hierar…
The possibility to determine the type of neutrino mass hierarchy by studying atmospheric neutrino oscillations with a detector capable to distinguish between neutrino and antineutrino events, such as magnetized iron calorimeters, is considered. We discuss how the ability to distinguish between the neutrino mass spectrum with normal and inverted hierarchy depends on detector characteristics like neutrino energy and direction resolutions or charge miss-identification, and on the systematical uncertainties related to the atmospheric neutrino fluxes. We show also how the neutrino mass hierarchy de…
The relatively large measured value of $θ_{13}$ has opened up the possibility of determining the neutrino mass hierarchy through earth matter effects. Amongst the current accelerator-based experiments only NOvA has a long enough baseline to observe earth matter effects. However, NOvA is plagued with uncertainty on the knowledge of the true value of $δ_{CP}$, and this could drastically reduce its sensitivity to the neutrino mass hierarchy. The earth matter effect on atmospheric neutrinos on the other hand is almost independent of $δ_{CP}$. The 50 kton magnetized Iron CALorimeter at the India-ba…
The determination of the neutrino mass hierarchy, whether the $ν_3$ neutrino mass eigenstate is heavier or lighter than the $ν_1$ and $ν_2$ mass eigenstates, is one of the remaining undetermined fundamental aspects of the Standard Model in the lepton sector. Furthermore the mass hierarchy determination will have an impact in the quest of the neutrino nature (Dirac or Majorana mass terms) towards the formulation of a theory of flavour. The Jiangmen Underground Neutrino Observatory (JUNO) is a reactor neutrino experiment under construction at Kaiping, Jiangmen in Southern China composed by a lar…
Multi-megaton scale under ice and underwater detectors of atmospheric neutrinos with few GeV's energy threshold (PINGU, ORCA) open up new possibilities in the determination of neutrino properties, and in particular the neutrino mass hierarchy. With a dense array of optical modules it will be possible to determine the inelasticity, $y$, of the charged current $ν_μ$ events in addition to the neutrino energy $E_ν$ and the muon zenith angle $θ_μ$. The discovery potential of the detectors will substantially increase with the measurement of $y$. It will enable (i) a partial separation of the neutrin…
We investigate the possibilities offered by the long baseline experiments T2K, No$ν$a, LBNE and LAGUNA for the evaluation of the neutrino mass hierarchy and CP violating phase $δ_{CP}$. We consider a neutrino and antineutrino energy in the interval [0.5,12] GeV. It is found that the clearest possible distinction between the two hierarchy signatures is provided by LAGUNA for an (anti)neutrino energy $E_{(\barν)ν}\simeq 0.5$ GeV in the $(\barν_μ \rightarrow \barν_μ) ν_μ\rightarrow ν_μ$ disappearance channel. For LBNE at $E_{\barν}\simeq 1$ GeV the $\barν_μ\rightarrow \barν_μ$ channel may also pr…
Preliminary results of MINOS experiment indicate that theta23 is not maximal. Global fits to world neutrino data suggest two nearly degenerate solutions for theta23: one in the lower octant (LO: theta23 < 45 degree) and the other in the higher octant (HO: theta23 > 45 degree). numu to nue oscillations in superbeam experiments are sensitive to the octant and are capable of resolving this degeneracy. We study the prospects of this resolution by the current T2K and upcoming NOvA experiments. Because of the hierarchy-deltacp degeneracy and the octant-deltacp degeneracy, the impact of hierarchy on …
Determination of the neutrino mass hierarchy using a reactor neutrino experiment at $\sim$60 km is analyzed. Such a measurement is challenging due to the finite detector resolution, the absolute energy scale calibration, as well as the degeneracies caused by current experimental uncertainty of $|Δm^2_{32}|$. The standard $χ^2$ method is compared with a proposed Fourier transformation method. In addition, we show that for such a measurement to succeed, one must understand the non-linearity of the detector energy scale at the level of a few tenths of percent.
The Coulomb enhancement of low energy electrons in nuclear beta decay generates sharp cutoffs in the accompanying antineutrino spectrum at the beta decay endpoint energies. It has been conjectured that these features will interfere with measuring the effect of a neutrino mass hierarchy on an oscillated nuclear reactor antineutrino spectrum. These sawtooth-like features will appear in detailed reactor antineutrino spectra, with characteristic energy scales similar to the oscillation period critical to neutrino mass hierarchy determination near a 53 km baseline. However, these sawtooth-like dist…
We discuss the physics potential of intermediate $L \sim 20 ÷30$ km baseline experiments at reactor facilities, assuming that the solar neutrino oscillation parameters $Δm^2_{\odot}$ and $θ_{\odot}$ lie in the high-LMA solution region. We show that such an intermediate baseline reactor experiment can determine both $Δm^2_{\odot}$ and $θ_{\odot}$ with a remarkably high precision. We perform also a detailed study of the sensitivity of the indicated experiment to $Δm^2_{\rm atm}$, which drives the dominant atmospheric $ν_μ$ ($\barν_μ$) oscillations, and to $θ$ - the neutrino mixing angle limited …
Enhancing the sensitivity to neutrino oscillation parameters using synergy between T2K, NO$ν$A and JUNO
Theoretical Physics Division, Physical Research Laboratory（物理研究实验室理论物理部）；Institute of High Energy Physics, Chinese Academy of Sciences（中国科学院高能物理研究所）；Spallation Neutron Source Science Center（散裂中子源科学中心）；Theory Division, Saha Institute of Nuclear Physics（萨哈核物理研究所理论部）；School of Physical Sciences, Indian Association for the Cultivation of Science（印度科学促进协会物理科学学院）；Department of Physics, University of Toronto（多伦多大学物理系）；Tata Institute of Fundamental Research（塔塔基础研究所）；Division of Sciences, Krea University（克里亚大学科学学部）
Proposed medium-baseline reactor neutrino experiments offer unprecedented opportunities to probe, at the same time, the mass-mixing parameters which govern $ν_e$ oscillations both at short wavelength (delta m^2 and theta_{12}) and at long wavelength (Delta m^2 and theta_{13}), as well as their tiny interference effects related to the mass hierarchy (i.e., the relative sign of Delta m^2 and delta m^2). In order to take full advantage of these opportunities, precision calculations and refined statistical analyses of event spectra are required. In such a context, we revisit several input ingredie…
A next-generation neutrino telescope infrastructure, the Kilometer Cube Neutrino Telescope KM3NeT, is currently under construction in the Mediterranean Sea. Its low energy configuration ORCA is optimised for the detection of atmospheric neutrinos with energies above ~1 GeV. The main goal of the ORCA detector is the precise measurement of atmospheric neutrino oscillation parameters and the determination of the neutrino mass ordering. The detector is also sensitive to a variety of other physics topics, such as dark matter, non-standard interactions and sterile neutrinos. An overview is presented…
In the past decade, the precise measurement of the lastly known neutrino mixing angle $θ_{13}$ has enabled the resolution of neutrino mass hierarchy (MH) at medium-baseline reactor neutrino oscillation (MBRO) experiments. On the other hand, recent calculations of the reactor neutrino flux predict percent-level sub-structures in the $\barν_e$ spectrum due to Coulomb effects in beta decay. Such fine structure in the reactor spectrum could be an important issue for the determination of neutrino MH for the MBRO approach since they could affect the sub-dominant oscillation pattern used to discrimin…
