A new generation of accelerator and reactor experiments is opening an era of high-precision neutrino measurements to tackle questions such as leptonic CP violation, the mass hierarchy and the possibility of a fourth “sterile” neutrino, writes Mark Rayner.
In traditional Balinese music, instruments are made in pairs, with one tuned slightly higher in frequency than its twin. The notes are indistinguishable to the human ear when played together, but the sound recedes and swells a couple of times each second, encouraging meditation. This is a beating effect: fast oscillations at the mean frequency inside a slowly oscillating envelope. Similar physics is at play in neutrino oscillations. Rather than sound intensity, it’s the probability to observe a neutrino with its initial flavour that oscillates. The difference is how long it takes for the interference to make itself felt. When Balinese musicians strike a pair of metallophones, the notes take just a handful of periods to drift out of phase. By contrast, it takes more than 1020 de Broglie wavelengths and hundreds of kilometres for neutrinos to oscillate in experiments like the planned mega-projects Hyper-Kamiokande and DUNE.
The zeitgeist began to shift to artificially produced neutrinos
Neutrino oscillations revealed a rare chink in the armour of the Standard Model: neutrinos are not massless, but are evolving superpositions of at least three mass eigenstates with distinct energies. A neutrino is therefore like three notes played together: frequencies so close, given the as-yet immeasurably small masses involved, that they are not just indistinguishable to the ear, but inseparable according to the uncertainty principle. As neutrinos are always ultra-relativistic, the energies of the mass eigenstates differ only due to tiny mass contributions of m2/2E. As the mass eigenstates propagate, phase differences develop between them proportional to squared-mass splittings Δm2. The sought-after oscillations range from a few metres to the diameter of Earth.
The neutrino physics of the latter third of the 20th century was bookended by two anomalies that uncloaked these effects. In 1968 Ray Davis’s observation of a deficit of solar neutrinos prompted Bruno Pontecorvo to make public his conjecture that neutrinos might oscillate. Thirty years later, the Super-Kamiokande collaboration’s analysis of a deficit of atmospheric muon neutrinos from the other side of the planet posthumously vindicated the visionary Italian, and later Soviet, theorist’s speculation. Subsequent observations have revealed that electron, muon and tau neutrinos are orthogonal mixtures of mass eigenstates ν1 and ν2, separated by a small so-called solar splitting Δm221, and ν3, which is separated from that pair by a larger “atmospheric” splitting usually quantified by Δm232 (see “Little and large” figure). It is not yet known if ν3 is the lightest or the heaviest of the trio. This is called the mass-hierarchy problem.
“In the first two decades of the 21st century we have achieved a rather accurate picture of neutrino masses and mixings,” says theorist Pilar Hernández of the University of Valencia, “but the ordering of the neutrino states is unknown, the mass of the lightest state is unknown and we still do not know if the neutrino mixing matrix has imaginary entries, which could signal the breaking of CP symmetry,” she explains. “The very different mixing patterns in quarks and leptons could hint at a symmetry relating families, and a more accurate exploration of the lepton-mixing pattern and the neutrino ordering in future experiments will be essential to reveal any such symmetry pattern.”
Today, experiments designed to constrain neutrino mixing tend to dispense with astrophysical neutrinos in favour of more controllable accelerator and reactor sources. The experiments span more than four orders of magnitude in size and energy and fall into three groups (see “Not natural” figure). Much of the limelight is taken by experiments that are sensitive to the large mass splitting Δm232, which include both a cluster of current (such as T2K) and future (such as DUNE) accelerator-neutrino experiments with long baselines and high energies, and a high-performing trio of reactor-neutrino experiments (Daya Bay, RENO and Double Chooz) with a baseline of about a kilometre, operating just above the threshold for inverse beta decay. The second group is a beautiful pair of long-baseline reactor-neutrino experiments (KamLAND and the soon-to-be-commissioned JUNO), which join experiments with solar neutrinos in having sensitivity to the smaller squared-mass splitting Δm221. Finally, the third group is a host of short-baseline accelerator-neutrino experiments and very-short-baseline reactor neutrino experiments that are chasing tantalising hints of a fourth “sterile” neutrino (with no Standard-Model gauge interactions), which is split from the others by a squared-mass splitting of the order of 1 eV2.
Experiments with artificial sources of neutrinos have a storied history, dating from the 1950s, when physicists toyed with the idea of detecting neutrinos created in the explosion of a nuclear bomb, and eventually observed them streaming from nuclear reactors. The 1960s saw the invention of the accelerator neutrino. Here, proton beams smashed into fixed targets to create a decaying debris of charged pions and their concomitant muon neutrinos. The 1970s transformed these neutrinos into beams by focusing the charged pions with magnetic horns, leading to the discovery of weak neutral currents and insights into the structure of nucleons. It was not until the turn of the century, however, that the zeitgeist of neutrino-oscillation studies began to shift from naturally to artificially produced neutrinos. Just a year after the publication of the Super-Kamiokande collaboration’s seminal 1998 paper on atmospheric–neutrino oscillations, Japanese experimenters trained a new accelerator-neutrino beam on the detector.
Operating from 1999 to 2006, the KEK-to-Kamioka (K2K) experiment sent a beam of muon neutrinos from the KEK laboratory in Tsukuba to the Super-Kamiokande detector, 250 km away under Mount Ikeno on the other side of Honshu. K2K confirmed that muon neutrinos “disappear” as a function of propagation distance over energy. The experiments together supported the hypothesis of an oscillation to tau neutrinos, which could not be directly detected at that energy. By increasing the beam energy well above the tau-lepton mass, the CERN Neutrinos to Gran Sasso (CNGS) project, which ran from 2006 to 2012, confirmed the oscillation to tau neutrinos by directly observing tau leptons in the OPERA detector. Meanwhile, the Main Injector Neutrino Oscillation Search (MINOS), which sent muon neutrinos from Fermilab to northern Minnesota from 2005 to 2012, made world-leading measurements of the parameters describing the oscillation.
With νμ → ντ oscillations established, the next generation of experiments innovated in search of a subtler effect. T2K (K2K’s successor, with the beam now originating at J-PARC in Tokai) and NOvA (which analyses oscillations over the longer baseline of 810 km between Fermilab and Ash River, Minnesota) both have far detectors offset by a few degrees from the direction of the peak flux of the beams. This squeezes the phase space for the pion decays, resulting in an almost mono-energetic flux of neutrinos. Here, a quirk of the mixing conspires to make the musical analogy of a pair of metallophones particularly strong: to a good approximation, the muon neutrinos ring out with two frequencies of roughly equal amplitude, to yield an almost perfect disappearance of muon neutrinos – and maximum sensitivity to the appearance of electron neutrinos.
Testing CP symmetry
The three neutrino mass eigenstates mix to make electron, muon and tau neutrinos according to the Pontecorvo– Maki–Nakagawa–Sakata (PMNS) matrix, which describes three rotations and a complex phase δCP that can cause charge–parity (CP) violation – a question of paramount importance in the field due to its relevance to the unknown origin of the matter–antimatter asymmetry in the universe. Whatever the value of the complex phase, leptonic CP violation can only be observed if all three of the angles in the PMNS matrix are non-zero. Experiments with atmospheric and solar neutrinos demonstrated this for two of the angles. At the beginning of the last decade, short-baseline reactor-neutrino experiments in China (Daya Bay), Korea (RENO) and France (Double Chooz) were in a race with T2K to establish if the third angle, which leads to a coupling between ν3 and electrons, was also non-zero. In the reactor experiments this would be seen as a small deficit of electron antineutrinos a kilometre or so from the reactors; in T2K the smoking gun would be the appearance of a small number of electron neutrinos not present in the initial muon-neutrino-dominated beam.
After data taking was cut short by the great Sendai earthquake and tsunami of March 2011, T2K published evidence for the appearance of six electron-neutrino events, over the expected background of 1.5 ± 0.3 in the case of no coupling. Alongside a single tau-neutrino candidate in OPERA, these were the first neutrinos seen to appear in a detector with a new flavour, as previous signals had always registered a deficit of an expected flavour. In the closing days of the year, Double Chooz published evidence for 4121 electron–antineutrino events, under the expected tally for no coupling of 4344 ± 165, reinforcing T2K’s 2.5σ indication. Daya Bay and RENO put the matter to bed the following spring, with 5σ evidence apiece that the ν3-electron coupling was indeed non-zero. The key innovation for the reactor experiments was to minimise troublesome flux and interaction systematics by also placing detectors close to the reactors.
Since then, T2K and NOvA, which began taking data in 2014, have been chasing leptonic CP violation – an analysis that is out of the reach of reactor experiments, as δCP does not affect disappearance probabilities. By switching the polarity of the magnetic horn, the experiments can compare the probabilities for the CP-mirror oscillations νμ → νe and νμ → νe directly. NOvA data are inconclusive at present. T2K data currently err towards near maximal CP violation in the vicinity of δCP = –π/2. The latest analysis, published in April, disfavours leptonic CP conservation (δCP = 0, ±π) at 2σ significance for all possible mixing parameter values. Statistical uncertainty is the biggest limiting factor.
Major upgrades planned for T2K next year target statistical, interaction-model and detector uncertainties. A substantial increase in beam intensity will be accompanied by a new fine-grained scintillating target for the ND280 near-detector complex, which will lower the energy threshold to reconstruct tracks. New transverse TPCs will improve ND280’s acceptance at high angles, yielding a better cancellation of systematic errors with the far detector, Super-Kamiokande, which is being upgraded by loading 0.01% gadolinium salts into the otherwise ultrapure water. As in reactor-neutrino detectors, this will provide a tag for antineutrino events, to improve sample purities in the search for leptonic CP violation.
T2K and NOvA both plan to roughly double their current data sets, and are working together on a joint fit, in a bid to better understand correlations between systematic uncertainties, and break degeneracies between measurements of CP violation and the mass hierarchy. If the CP-violating phase is indeed maximal, as suggested by the recent T2K result, the experiments may be able to exclude CP conservation with more than 99% confidence. “At this point we will be in a transition from a statistics-dominated to a systematics-dominated result,” says T2K spokesperson Atsuko Ichikawa of the University of Kyoto. “It is difficult to say, but our sensitivity will likely be limited at this stage by a convolution of neutrino-interaction and flux systematics.”
The next generation
Two long-baseline accelerator-neutrino experiments roughly an order of magnitude larger in cost and detector mass than T2K and NOvA have received green lights from the Japanese and US governments: Hyper-Kamiokande and DUNE. One of their primary missions is to resolve the question of leptonic CP violation.
Hyper-Kamiokande will adopt the same approach as T2K, but will benefit from major upgrades to the beam and the near and far detectors in addition to those currently underway in the present T2K upgrade. To improve the treatment of systematic errors, the suite of near detectors will be complemented by an ingenious new gadolinated water-Cherenkov detector at an intermediate baseline: by spanning a range of off-axis angles, it will drive down interaction-model systematics by exploiting previously neglected information on the how the flux varies as a function of the angle relative to the centre of the beam. Hyper-Kamiokande’s increased statistical reach will also be impressive. The power of the Japan Proton Accelerator Research Complex (J-PARC) beam will be increased from its current value of 0.5 MW up to 1.3 MW, and the new far detector will be filled with 260,000 tonnes of ultrapure water, yielding a fiducial volume 8.4 times larger than that of Super-Kamiokande. Procurement of the photo-multiplier tubes will begin this year, and the five-year-long excavation of the cavern has already begun. Data taking is scheduled to commence in 2027. “The expected precision on δCP is 10–20 degrees, depending on its true value,” says Hyper-Kamiokande international co-spokesperson Francesca di Lodovico of King’s College, London.
In the US, the Deep Underground Neutrino Experiment (DUNE) will exploit the liquid-argon–TPC technology first deployed on a large scale by ICARUS – OPERA’s sister detector in the CNGS project. The idea for the technology dates back to 1977, when Carlo Rubbia proposed using liquid rather than gaseous argon as a drift medium for ionisation electrons. Given liquid-argon’s higher density, such detectors can serve as both target and tracker, providing high-resolution 3D images of the interactions – an invaluable tool for reducing systematics related to the murky world of neutrino–nucleus interactions.
The technology is currently being developed in two prototype detectors at CERN. The first hones ICARUS’s single-phase approach. “The performance of the prototype has been absolutely spectacular, exceeding everyone’s expectations,” says DUNE co-spokesperson Ed Blucher of the University of Chicago. “After almost two years of operation, we are confident that the liquid–argon technology is ready to be deployed at the huge scale of the DUNE detectors.” In parallel, the second prototype is testing a newer dual-phase concept. In this design, ionisation charges drift through an additional layer of gaseous argon before reaching the readout plane. The signal can be amplified here, potentially easing noise requirements for the readout electronics, and increasing the maximum size of the detector. The dual-phase prototype was filled with argon in summer 2019 and is now recording tracks.
The final detectors will have about twice the height and 10 to 20 times the footprint. Following the construction of an initial single-phase unit, the DUNE collaboration will likely pick a mix of liquid-argon technologies to complete their roster of four 10 kton far-detector modules, set to be installed a kilometre underground at the Sanford Underground Research Laboratory in Lead, South Dakota. Site preparation and pre-excavation activities began in 2017, and full excavation work is expected to begin soon, with the goal that data-taking begin during the second half of this decade. Work on the near-detector site and the “PIP-II” upgrade to Fermilab’s accelerator complex began last year.
Though similar to Hyper-Kamiokande at first glance, DUNE’s approach is distinct and complementary. With beam energy and baseline both four times greater, DUNE will have greater sensitivity to flavour-dependent coherent-forward-scattering with electrons in Earth’s crust – an effect that modifies oscillation probabilities differently depending on the mass hierarchy. With the Fermilab beam directed straight at the detector rather than off-axis, a broader range of neutrino energies will allow DUNE to observe the oscillation pattern from the first to the second oscillation maximum, and simultaneously fit all but the solar mixing parameters. And with detector, flux and interaction uncertainties all distinct, a joint analysis of both experiments’ data could break degeneracies and drive down systematics.
“If CP violation is maximal and the experiments collect data as anticipated, DUNE and Hyper-Kamiokande should both approach 5σ significance for the exclusion of leptonic CP conservation in about five years,” estimates DUNE co-spokesperson Stefan Söldner-Rembold of the University of Manchester, noting that the experiments will also be highly complementary for non-accelerator topics. The most striking example is supernova-burst neutrinos, he says, referring to a genre of neutrinos only observed once so far, during 15 seconds in 1987, when neutrinos from a supernova in the Large Magellanic Cloud passed through the Earth. “While DUNE is primarily sensitive to electron neutrinos, Hyper-Kamiokande will be sensitive to electron antineutrinos. The difference between the timing distributions of these samples encodes key information about the dynamics of the supernova explosion.” Hyper-Kamiokande spokesperson Masato Shiozawa of ICRR Tokyo also emphasises the broad scope of the physics programmes. “Our studies will also encompass proton decay, high-precision measurements of solar neutrinos, supernova-relic neutrinos, dark-matter searches, the possible detection of solar-flare neutrinos and neutrino geophysics.”
Half a century since Ray Davis and two co-authors published evidence for a 60% deficit in the flux of solar neutrinos compared to John Bahcall’s prediction, DUNE already boasts more than a thousand collaborators, and Hyper-Kamiokande’s detector mass is set to be 500 times greater than Davis’s tank of liquid tetrachloroethylene. If Ray Davis was the conductor who set the orchestra in motion, then these large experiments fill out the massed ranks of the violin section, poised to deliver what may well be the most stirring passage of the neutrino-oscillation symphony. But other sections of the orchestra also have important parts to play.
The question of the neutrino mass hierarchy will soon be addressed by the Jiangmen Underground Neutrino Observatory (JUNO) experiment, which is currently under construction in China. The project is an evolution of the Daya Bay experiment, and will seek to measure a deficit of electron antineutrinos 53 km from the Yangjiang and Taishan nuclear-power plants. As the reactor neutrinos travel, the small kilometre-scale oscillation observed by Daya Bay will continue to undulate with the same wavelength, revealed in JUNO as “fast” oscillations on a slower and deeper first oscillation maximum due to the smaller solar mass splitting Δm221 (see “An oscillation within an oscillation” figure).
“JUNO can determine the neutrino mass hierarchy in an unambiguous and definite way, independent from the CP phase and matter effects, unlike other experiments using accelerator or atmospheric neutrinos,” says spokesperson Yifang Wang of the Chinese Academy of Sciences in Beijing. “In six years of data taking, the statistical significance will be higher than 3σ.”
JUNO has completed most of the digging of the underground laboratory, and equipment for the production and purification of liquid scintillator is being fabricated. A total of 18,000 20-inch photomultiplier tubes and 26,000 3-inch photomultiplier tubes have been delivered, and most of them have been tested and accepted, explains Wang. The installation of the detector is scheduled to begin next year. JUNO will arguably be at the vanguard of a precision era for the physics of neutrino oscillations, equipped to measure the mass splittings and the solar mixing parameters to better than 1% precision – an improvement of about one order of magnitude over previous results, and even better than the quark sector, claims Wang, somewhat provocatively. “JUNO’s capabilities for supernova-burst neutrinos, diffused supernova neutrinos and geoneutrinos are unprecedented, and it can be upgraded to be a world-best double-beta-decay detector once the mass hierarchy is measured.”
With JUNO, Hyper-Kamiokande and DUNE now joining a growing ensemble of experiments, the unresolved leitmotifs of the three-neutrino paradigm may find resolution this decade, or soon after. But theory and experiment both hint, quite independently, that nature may have a scherzo twist in store before the grand finale.
A rich programme of short-baseline experiments promises to bolster or exclude experimental hints of a fourth sterile neutrino with a relatively large mixing with the electron neutrino that have dogged the field since the late 1990s. Four anomalies stack up as more or less consistent among themselves. The first, which emerged in the mid-1990s at Los Alamos’s Liquid Scintillator Neutrino Detector (LSND), is an excess of electron antineutrinos that is potentially consistent with oscillations involving a sterile neutrino at a mass splitting Δm2 ∼ 1 eV2. Two other quite disparate anomalies since then – a few-percent deficit in the expected flux from nuclear reactors, and a deficit in the number of electron neutrinos from radioactive decays in liquid-gallium solar-neutrino detectors – could be explained in the same way. The fourth anomaly, from Fermilab’s MiniBooNE experiment, which sought to replicate the LSND effect at a longer baseline and a higher energy, is the most recent: a sizeable excess of both electron neutrinos and antineutrinos, though at a lower energy than expected. It’s important to note, however, that experiments including KARMEN, MINOS+ and IceCube have reported null searches for sterile neutrinos that fit the required description. Such a particle would also stand in tension with cosmology, notes phenomenologist Silvia Pascoli of Durham University, as models predict it would make too large a contribution to hot dark matter in the universe today, unless non-standard scenarios are invoked.
Three different types of experiment covering three orders of magnitude in baseline are now seeking to settle the sterile-neutrino question in the next decade. A smattering of reactor-neutrino experiments a mere 10 metres or so from the source will directly probe the reactor anomaly at Δm2 ∼ 1 eV2. The data reported so far are intriguing. Korea’s NEOS experiment and Russia’s DANSS experiment report siren signals between 1 and 2 eV2, and NEUTRINO-4, also based in Russia, reports a seemingly outlandish signal, indicative of very large mixing, at 7 eV2. In parallel, J-PARC’s JSNS2 experiment is gearing up to try to reproduce the LSND effect using accelerator neutrinos at the same energy and baseline. Finally, Fermilab’s short-baseline programme will thoroughly address a notable weakness of both LSND and MiniBooNE: the lack of a near detector.
The Fermilab programme will combine three liquid-argon TPCs – a bespoke new short-baseline detector (SBND), the existing MicroBooNE detector, and the refurbished ICARUS detector – to resolve the LSND anomaly once and for all. SBND is currently under construction, MicroBooNE is operational, and ICARUS, removed from its berth at Gran Sasso and shipped to the US in 2017, has been installed at Fermilab, following work on the detector at CERN. “The short-baseline neutrino programme at Fermilab has made tremendous technical progress in the past year,” says ICARUS spokesperson and Nobel laureate Carlo Rubbia, noting that the detector will be commissioned as soon as circumstances allow, given the coronavirus pandemic. “Once both ICARUS and SBND are in operation, it will take less than three years with the nominal beam intensity to settle the question of whether neutrinos have an even more mysterious character than we thought.”
Muon neutrinos ring out with two frequencies of roughly equal amplitude, to yield almost perfect disappearance
Outside of the purview of oscillation experiments with artificially produced neutrinos, astrophysical observatories will scale a staggering energy range, from the PeV-scale neutrinos reported by IceCube at the South Pole, down, perhaps, to the few-hundred-μeV cosmic neutrino background sought by experiments such as PTOLEMY in the US. Meanwhile, the KATRIN experiment in Germany is zeroing in on the edges of beta-decay distributions to set an absolute scale for the mass of the peculiar mixture of mass eigenstates that make up an electron antineutrino (CERN Courier January/February 2020 p28). At the same time, a host of experiments are searching for neutrinoless double-beta decay – a process that can only occur if the neutrino is its own antiparticle. Discovering such a Majorana nature for the neutrino would turn the Standard Model on its head, and offer grist for the mill of theorists seeking to explain the tininess of neutrino masses, by balancing them against still-to-be-discovered heavy neutral leptons.
According to Mikhail Shaposhnikov of the Swiss Federal Institute of Technology in Lausanne, current and future reactor- and accelerator-neutrino experiments will provide an indispensable input for understanding neutrino physics. And not in isolation. “To reach a complete picture, we also need to know the mechanism for neutrino-mass generation and its energy scale, and the most important question here is the scale of masses of new neutrino states: if lighter than a few GeV, these particles can be searched for at new experiments at the intensity frontier, such as SHiP, and at precision experiments looking for rare decays of mesons, such as Belle II, LHCb and NA62, while the heavier states may be accessible at ATLAS and CMS, and at future circular colliders,” explains Shaposhnikov. “These new particles can be the key in solving all the observational problems of the Standard Model, and require a consolidated effort of neutrino experiments, accelerator-based experiments and cosmological observations. Of course, it remains to be seen if this dream scenario can indeed be realised in the coming 20 years.”
• This article was updated on 6 July, to reflect results presented at Neutrino 2020
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