The T2K experiment
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Introduction
Neutrinos are elementary particles with puzzling and not yet fully explored properties, playing a special role in the evolution of the Universe. They might reveal clues to explain its matter-antimatter asymmetry. Moreover, the existence of tiny neutrino masses, discovered in 1998-2002, could be a sign of phenomena beyond the Standard Model of Particle Physics.
T2K (Tokai-to-Kamioka) is an experiment operating in Japan since 2010. T2K studies neutrino oscillations (the transformation of the flavor of neutrinos during their propagation, for an introduction see https://en.wikipedia.org/wiki/Neutrino_oscillation) by producing a very intense neutrino beam in J-PARC (Tokai, Japan), measuring its properties close to the production point and then 295 km away at the Super-Kamiokande detector (Figure 1).
It has been the first experiment to provide evidence of a non-zero \(\theta_{13}\) angle of the neutrino mixing matrix, to directly observe the phenomenon of neutrino appearance (the appearance of neutrinos of a flavor different from the original flavor), and to provide indication of charge-parity (CP) violation in the neutrino sector.
T2K has been built and is operated by an international collaboration with more than 500 physicists and technical staff members from 59 institutions in 12 countries including Japan, several European countries, Russia, USA and Canada.
Scientific context and project history
Experiments measuring neutrinos coming from cosmic rays (so called atmospheric neutrinos), from the Sun, and from nuclear reactors produced a wealth of results in the period 1960-1990 providing evidence for neutrino oscillation. These evidences included a deficit in the flux of solar neutrinos observed by the Homestake, SAGE and GALLEX experiments, and a deficit of atmospheric neutrinos observed by Kamiokande and IMB. At the end of the 1980s, the concept of a long baseline neutrino experiment started to emerge, based on an intense neutrino beam produced by an accelerator, and a massive far detector located hundred of kilometers away. This kind of experiment could provide the definitive proof of neutrino oscillations, as the neutrino source is man-made and can be accurately controlled in terms of neutrino flux and energy. The relevant neutrino oscillation length was estimated to be of the order of 1000 km for neutrinos of 1 GeV. While neutrino oscillations were discovered in 1998-2002 with other methods by the SuperKamiokande, SNO and KamLAND experiments, long baseline neutrino experiments retained the interest of physicists because they are capable of very precise measurements, and because they are very sensitive to subleading effects.
K2K (KEK-to-Kamioka) was the first experiment of this kind running from 2000 to 2004 and provided important confirmations of neutrino oscillation, followed by the MINOS experiment in USA, taking data between 2005 and 2016. A second generation long-baseline neutrino experiment in Japan was proposed in 1999 by the two outstanding Japanese physicists Koichiro Nishikawa (Kyoto University and KEK) and Yoji Totsuka (University of Tokyo and KEK) and quickly attracted the interest of the neutrino community world-wide. After the submission of a Letter of Intent in 2001, the experiment was approved in 2003 and the construction started in 2004 to be completed in 2009.
Data taking started in 2010 and is scheduled to continue until 2026. During this period the beam power steadily increased, reaching 500 kW in 2018 and 800 kW in 2024, with record breaking number of protons per pulse. The Great East Japan Earthquake in 2011 provoked only minor damage to the experiment but the data taking was interrupted for one year.
Conceptual design
The main goal of the T2K experiment is to study neutrino oscillations. This is a quantum mechanical effect due to the existence of three neutrino flavor states \(\nu_e\), \(\nu_\mu\) and \(\nu_\tau\) – each associated to a charged lepton, respectively the electron, the muon and the tau - and three mass states \(\nu_1\), \(\nu_2\) and \(\nu_3\) with masses \(m_1\) , \(m_2\) and \(m_3\). A flavor state can be written as a linear combination of the mass states and the linear transformation between flavor states and mass states can be described by a matrix called the Pontecorvo-Maki-Nagawata-Sakata matrix. It can be parameterized with three mixing angles \(\theta_{12}\), \(\theta_{23}\) and \(\theta_{13}\), and one complex phase \(\delta_{CP}\) (additional parameters might be needed in specific extensions of the Standard Model of particle physics, for instance if the neutrinos are Majorana fermions). During their propagation, quantum interference effects induce the disappearance of the original flavor and the appearance of neutrinos of a new flavor, depending on the mixing angles, the phase and the squared mass differences between the mass states.
In T2K the beam at the production point is mainly composed of \(\nu_\mu\). The probability to observe a \(\nu_\mu\) in the far detector can be written as \(\tag{1} P ( \nu_\mu → \nu_\mu) \approx 1 – 4 \cos² \theta_{13} \sin² \theta_{23} (1 - \cos² \theta_{13} \sin² \theta_{23} ) \sin² (Δm²_{32} L / 4 E) \) where \(L \) is the propagation length, \(E\) the neutrino energy, and \(Δm²_{32} = m²_3 – m²_2\). The measurement of the \(\nu_\mu → \nu_\mu\) probability allows to precisely measure \(\theta_{23}\) and \(Δm²_{32}\) as \(\theta_{13}\) is precisely measured by reactor experiments. The appearance probability (the probability to observe a \(\nu_e\) in the far detector) is given by \(\tag{2} P ( \nu_\mu → \nu_e) \approx \sin² (2 \theta_{13} ) \sin² (\theta_{23}) \sin² (Δm²_{32}) L / 4 E) - (Δm²_{21} L / 4 E) 8 J_{CP} \sin² (Δm²_{32} L / 4 E), \) neglecting terms depending on the interaction of neutrinos with the Earth matter during their propagation. In Eq. 2, \(Δm²_{21} = m²_2 - m²_1 \) and the term \(J_{CP}\) , called the Jarlskog invariant, determining the size of CP violation effects, can be written \(\tag{3} J_{CP} = 1/8 \cos \theta_{13} \sin (2 \theta_{12} ) \sin (2 \theta_{23}) \sin (2 \theta_{13}) \sin \delta_{CP} \) As the \(\theta_{13}\) angle was still unknown in 2010 apart from upper limits, the first important goal of the T2K experiment was to provide information on it through the study of the \(\nu_\mu → \nu_e \) appearance probability (Eq. 2). The second term in Eq. 2 has a minus sign for neutrinos and a plus sign for antineutrinos and allows to extract \( \delta_{CP} \) from a measurement of the \( P ( \nu_\mu → \nu_e ) \) and \(P ( \overline{\nu}_\mu → \overline{\nu}_e )\) probabilities. This is today the main goal of the T2K-II phase of the experiment. The term describing the interaction of neutrinos with the Earth matter depends on the neutrino mass ordering : it is still not known whether \( m_3 > m_2 > m_1\) (called normal ordering) or \(m_2 > m_1 > m_3 \) (called inverted ordering).
The experiment is designed in a such a way that the quantity \( Δm²_{32} L/E \), appearing in Eq. 1 and 2, where \(L=295 \) km is the propagation length and \(E = 600\) MeV is the neutrino energy at the flux maximum, is close to \(\pi/2\) in order to maximize the appearance probability. This is achieved by deliberately aiming the beam a few degrees off the far detector. As the muons are produced in two-body decays of pions (\(\pi⁺ → \mu⁺ \nu_\mu \)), there is a strong correlation between the angle and the energy of the neutrinos. For a proton beam of 30 GeV, a 2.5 degrees off-axis angle generates a beam whose flux is very peaked at 600 MeV. This configuration is also quite effective in suppressing the neutrinos at high energy, that might induce background reactions in the far detector. A consequence of this experimental configuration is the nearly total suppression of the observed flux of \(\nu_\mu\), \(P (\nu_\mu → \nu_\mu ) \) being close to zero at the peak of the neutrino flux.
Neutrinos are electrically neutral and they interact with matter via the weak force, through the exchange of Z or W particles. In the latter case, the neutrino transforms into a charged lepton - an electron, muon or tau - that can be detected. Moreover the identification of this lepton is used to identify the flavour of the neutrino.
The T2K neutrino beam
A high intensity proton beam is produced by the Japanese Proton Accelerator Research Complex (J-PARC) in Tokai (Japan, Ibaraki Prefecture) through a chain of accelerators: a 180 MeV linear accelerator LINAC, a 3 GeV Rapid Cycling Synchrotron and the 30 GeV Main Ring (MR) synchrotron. The MR has achieved a record \( 3.3 \; 10^{14} \) per pulse at a repetition rate of 0.4 Hz.
The proton beam is extracted from the Main Ring and sent to a graphite target. The interaction of the protons with the carbon nuclei in the target copiously produces charged pions that are focused by a system of three magnetic horns. The horns are devices consisting of a metallic structure where a high pulsed current of 320 kA creates a strong toroidal magnetic field. The second horn of T2K is shown in Figure 2.
Depending on the polarity of the current, this field provides focusing for positively charged pions (Forward Horn Current, FHC), producing a neutrino beam, or negatively charged pions for a mostly antineutrino beam (Reverse Horn Current, RHC). After leaving the target, the pions decay through the weak decay \(\pi⁺ → \mu⁺ \nu_\mu \) in a 96 m long decay volume filled with helium (to reduce pion absorption) producing the neutrinos of the T2K beam. At the end of the volume, a beam dump stops most of the charged particles while the neutrinos continue their propagation towards the detectors.
The neutrino flux is directly proportional to the beam power, that steadily increased during the T2K data taking to reach 500 kW in 2018 and 800 kW in 2024. The time-integrated neutrino flux is proportional to the number of Protons On Target (POT). Up to 2020, T2K has registered \( 1.97 \; 10^{21}\) POT for FHC and \( 1.63 \; 10^{21}\) POT for RHC.
The near detectors
The flux and composition of the neutrino beam depends on the proton-nucleus cross-section for pion production of the primary protons, on the secondary interactions as well as on the exact geometry of materials in the target, in the horns etc. Any mismodelling of the cross-section or of the geometric and material model of the apparatus results in a systematic uncertainties on the neutrino beam. To minimize these systematic uncertainties a system of near detectors is located 280 m away from the target, in a pit inside the J-PARC laboratory.
INGRID (Interactive Neutrino GRID) is an array of detectors aimed at measuring precisely the neutrino direction and monitoring its stability. The INGRID modules are arranged in two arms, one horizontal and one vertical, covering a 10m x 10m section centered on the beam axis. Fourteen modules are disposed along these arms, each module is composed of iron planes and plastic scintillators. The beam center is measured daily to a precision better than 10 cm, corresponding to an uncertainty of 0.4 mrad on the beam direction.
ND280 (Figure 3) is a magnetized off-axis detector aimed at precisely measuring the neutrino interactions of the non-oscillated beam in order to characterize its properties (composition, flux) and to study neutrino-nucleus interactions. It reuses the UA1 dipole magnet (donated to J-PARC by the CERN laboratory) producing a 0.2 T field orthogonal to the neutrino beam direction.
ND280 consists of several sub-detectors, including two Fine Grained Detectors (FGD), three Time Projection Chambers (TPC), a \(\pi^0\) detector (P0D), an electromagnetic calorimeter and a Side Muon Detector. The ND280 TPCs are the first large size devices using Micro-Pattern detectors (in this case MicroMegas). All the other detectors are based on scintillators. The scintillation light for all these detectors is read out using “silicon photomultipliers” the solid state equivalent of the PhotoMultiplier Tubes. T2K uses a 667 pixel device developed by Hamamatsu and called Multi-Pixel Photon Counter, operated in the Geiger mode with a gain around \( 10^6 \) . T2K is the first experiment that has used in large numbers (64000) this innovative device.
For oscillation analyses, T2K uses the sample of neutrino interactions reconstructed in the tracking system comprised of FGD and TPC. Neutrinos interacting with an atomic nucleus (mainly carbon or oxygen) inside FGD will produce charged particles traversing the gas volume of the TPC. The electrons stripped off atoms in the TPC along the trajectory of these particles are subject to an electric field and made to drift towards the instrumented surfaces where they are detected. The charge and momentum of the charged particles can be measured from the curvature of the track induced by the magnetic field, using three-dimensional information provided by the TPC. The amount of charge deposited by these particles per unit length (also called dE/dx) is also measured and used to identify them.
The far detector
The Super-Kamiokande (SK) detector is used as the T2K far detector.
SK (Figure 4) is a water Cherenkov detector located deep inside Mt Ikeno in west Japan (Gifu prefecture) providing a shield of 1 km rock (equivalent to a water depth of 2700 m) against cosmic rays. It consists of a steel tank containing 50 kt of ultra pure water and is equipped with 13000 20-inches photomultipliers (PMT). SK has played a crucial role in the discovery of neutrino oscillation with its results on atmospheric and solar neutrinos. For the T2K period, SK was reequipped with PMT corresponding to a coverage of 40 % of the tank inner surface, after an accident that damaged many SK PMTs in 2001.
Neutrino interactions in Super-Kamiokande in a time window compatible with the passage of the beam (the time synchronization between J-PARC and the SK site is performed using GPS information) are used by T2K to study the neutrino oscillations.
With the T2K neutrino beam a neutrino interaction in the water tank produces often ultra-relativistic charged particles moving faster than the speed of light in water. They produce a flash of Cherenkov light on a cone centered on the particle momentum. This light is detected by the PMTs on the tank surface, producing a characteristic ring pattern (Figure 5). The pattern of photons detected by the PMTs can be used to identify the particle type: muons produce rings with sharp edges while electrons produce a fuzzy pattern because of brehmstrahlung. For particles stopping in the water tank, the energy can be estimated by the number of detected photons, while the reconstructed interaction point and the ring position allow to estimate the particle direction.
Analysis Method and Physics Results
The analysis of T2K data proceeds in three steps. First, the composition and flux of the neutrino beam are evaluated. A Monte Carlo simulation of the proton interactions in the target has been developed, including interactions of secondary particles in the material around the target, the effects of the focusing horns, particle decays etc. The pion production in proton nucleus interactions has been measured in NA61-SHINE, a dedicated experiment at CERN. In this experiment, a proton beam of known momentum interacts on a target (either a thin target or a target identical to the one used in T2K) and the particles produced are detected and measured.
In the second step, the data from the near detector are used. Neutrino-nucleus interactions at the T2K energies proceeding through charged current (the neutrino is transformed into a charged lepton, a muon or an electron, and interacts with the hadronic system through the exchange of a W boson) can be separated in three classes. The first class, quasi-elastic events, corresponds to the process \( \nu_\mu n → \mu p ) \) where n is a neutron in the nucleus that is considered as almost free, and p is a proton. Quasi-elastic interactions are important both because they have a large cross section for an incoming neutrino energy around 600 MeV and because the neutrino energy can be reconstructed on the basis of the measurement of the outgoing muon (or electron). The second class, called Charged Current Resonant (CCRes), corresponds to processes where the neutron is excited to a Delta resonance. The third class, called Charged Current Deep Inelastic Scattering (CCDIS), is dominant at higher energies and results in a breakup of the nucleon with the production of several hadronic particles in the final state.
The neutrino interactions with a muon in the final state reconstructed in ND280 are separated in three categories depending on the number of pions observed. The three categories are enriched respectively in quasi-elastic neutrino interactions, CCRes and CCDIS. The data from ND280 are very useful to reduce the systematic uncertainties because the neutrino-nucleus interaction cross-section are not known with sufficient precision for T2K purposes. Moreover the measurement of the muon charge allows to separate neutrinos from antineutrinos interactions.
At the end of the second step, the analyzers have a precise knowledge of the expected neutrino interaction rate at SK, as a function of the neutrino energy. For instance the number of expected \( \nu_\mu \) (\( \nu_e \)) events at SK is predicted with an uncertainty of 3 % (4.7%), to be compared with an uncertainty of 13% (14%) without using the near detector. This rate can be compared to the observed one, which is affected by the neutrino oscillation. The oscillation effect is quite dramatic for muon neutrinos (Figure 6) because, as explained previously, T2K is designed to have maximum muon neutrino disappearance, and because the \( \theta_{13} \) angle is close to π/4.
This comparison between expected and observed neutrino interaction rate is performed for muon and electron neutrinos, using both a neutrino and an anti-neutrino beam. These comparisons are used in a simultaneous fit for the relevant neutrino oscillation parameters, namely \( \Delta m²_{32} \) , \( \theta_{23} \) , \( \theta_{13} \) and \( \delta_{CP} \) and the mass ordering.
In 2011 T2K observed six electron neutrino events in SK, with a background of 1.5+-0.3 for \( \sin^2 (2 \theta_{13}) = 0 \). This was the first indication, at the level of 2.5 standard deviation, of a non-zero \( \theta_{13} \) angle and the first direct measurement of the appearance of neutrinos of a different flavour in a neutrino oscillation experiment. The reactor neutrino experiments, especially Daya Bay and RENO, made shortly after precision measurements of \( \theta_{13} \) that can be used as a constraint to interpret T2K data. In 2013 T2K reported the observation of electron neutrino appearance in a muon neutrino beam, the first direct observation of the appearance of neutrino of a new flavor. The observed number of electron neutrino events is sensitive to the phase \( \delta_{CP} \) with the maximum neutrino enhancement being for \( \delta_{CP} = - \pi/2\), giving at the same time the maximum antineutrino suppression. The observed numbers of electron neutrinos and antineutrinos are compatible with \( \delta_{CP} = - \pi/2\) . In 2020 T2K reported results excluding at 3 σ almost half of the allowed interval for \( \delta_{CP}\) (Figure 7). The confirmation of CP violation in the neutrino sector would be an important discovery in particle physics and might provide a clue to understand the matter-antimatter asymmetry in the Universe.
In this analysis of \( \nu_e\) appearance, two important backgrounds need to be well understood. The first is due to the \( \nu_e\) component in the beam (that is not due to \(\nu_\mu → \nu_\mu \) oscillation but coming from either muon or kaon decays), that is quite low and has been measured at the near detector. The second background is due to neutral current neutrino interaction where only a \( \pi^0\) is visible in the final state at SuperKamiokande. For asymmetric \( \pi^0\) decays, a \( \pi^0 → \gamma \gamma\) is not distinguishable from a single electron. This background has been strongly reduced thanks to improvements in the SK reconstruction.
T2K regularly updates its main analysis devoted to the precision measurement of the neutrino oscillation parameters that are currently limited by the number of events observed in the far detector.
The T2K data have enabled many studies of neutrinos, including several measurements of neutrino-nucleus cross-sections using ND280 and INGRID, searches for sterile neutrinos and heavy neutral leptons, searches for violation of Lorentz invariance etc.
T2K-II: the beam and ND280 upgrades for the second phase of the experiment
In 2015 the T2K collaboration decided to propose a new phase of the experiment, called T2K-II, to focus on an early measurement of CP violation in the neutrino sector, before the next generation experiments like HyperKamiokande and DUNE start operation. T2K-II has the sensitivity to discover CP violation at 3 σ for a sizeable range of \( \delta_{CP}\) values. To do this, the J-PARC accelerator chain is undergoing a major upgrade to reduce the repetition rate from 2.5 s to 1.3 s with an upgrade to the power supplies for the main magnets and the RF cavities. The beam power is expected to reach 1.3 MW after these upgrades. The beam upgrade is ongoing with very promising results.
To fully benefit from these improvements, the systematic uncertainties arising from the limited knowledge of the beam flux and the measured interaction rate in the near detector need also to be reduced accordingly. The T2K Collaboration has launched an upgrade of the ND280 detector, with two new TPCs, a scintillator detector SuperFGD and a Time-of-Flight system. The TPCs will be equipped with resistive Micromegas. In this device, a resistive foil is mounted over the anode, with the effect to naturally spread the charge of the electron avalanche over several neighboring pads. The space-point resolution is dramatically improved, going from 600 μm to about 150 μm.
SuperFGD is composed of 2 million scintillator cubes, each read-out by three orthogonal scintillating fibers. This high segmentation allows almost 3D track reconstruction. This detector has also been demonstrated to be capable of neutron detection, a very valuable tool to reconstruct antineutrino interactions. The new detectors for the ND280 Upgrade have been built and have been installed in J-PARC in 2023/2024.
In recent years the SK collaboration has decided to dissolve Gadolinium in the detector water. The Gadolinium nucleus has a high neutron capture cross-section, followed by the emission of a gamma ray. This helps to reconstruct neutrons in SK and is particularly useful to tag antineutrino interactions.
Prizes and distinctions
Koichiro Nishikawa (the founder and first spoke-person of the experiment) and the T2K collaboration were awarded the Breakthrough prize in 2016 together with other four experiments investigating neutrino oscillations. In 2020, Nature list of ten remarkable discoveries in 2020 included T2K results on the matter-antimatter asymmetry.
References
- K. Abe et al., Nucl.Instrum.Meth.A 659 (2011) 106-135 “The T2K Experiment”
- C. Giganti, S. Lavignac, M. Zito, Prog. in Part. and Nucl. Phys. 98 (2018) 1 "Neutrino oscillations : the rise of the PMNS paradigm"
- K. Abe et al., Phys.Rev.Lett. 107 (2011) 041801 Indication of Electron Neutrino Appearance from an Accelerator-produced Off-axis Muon Neutrino Beam
- K. Abe et al., Phys.Rev.Lett. 112 (2014) 061802 “Observation of Electron Neutrino Appearance in a Muon Neutrino Beam”
- K. Abe et al., Nature 580, 339–344 (2020) "Constraint on the matter–antimatter symmetry-violating phase in neutrino oscillations"
