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59-632: If neutrinos have mass, they may oscillate into flavors that an experiment may not detect, leading to a further dimming, or "disappearance," of the electron antineutrinos. KamLAND is located at an average flux-weighted distance of approximately 180 kilometers from the reactors, which makes it sensitive to the mixing of neutrinos associated with large mixing angle (LMA) solutions to the solar neutrino problem . The KamLAND detector's outer layer consists of an 18 meter-diameter stainless steel containment vessel with an inner lining of 1,879 photo-multiplier tubes (1325 17" and 554 20" PMTs). Photocathode coverage

118-433: A "charged-lepton-centric" superposition such as  | ν e ⟩ , which is an eigenstate for a "flavor" that is fixed by the electron's mass eigenstate, and not in one of the neutrino's own mass eigenstates. Because the neutrino is in a coherent superposition that is not a mass eigenstate, the mixture that makes up that superposition oscillates significantly as it travels. No analogous mechanism exists in

177-493: A 1,000-metric-ton detection mass, which is over twice the size of similar detectors, such as Borexino . However, the increased volume of the detector also demands more shielding from cosmic rays, requiring the detector be placed underground. As part of the Kamland-Zen double beta decay search, a balloon of scintillator with 320 kg of dissolved xenon was suspended in the center of the detector in 2011. A cleaner rebuilt balloon

236-620: A 1.8 MeV ν ¯ e {\displaystyle {\bar {\nu }}_{e}} energy threshold . The prompt scintillation light from the positron ( e + {\displaystyle e^{+}} ) gives an estimate of the incident antineutrino energy, E ν = E p r o m p t + < E n > + 0.9 M e V {\displaystyle E_{\nu }=E_{prompt}+<E_{n}>+0.9MeV} , where E p r o m p t {\displaystyle E_{prompt}}

295-444: A 515-day data sample, 365.2 events were predicted in the absence of oscillation, and 258 events were observed. These results established antineutrino disappearance at high significance. The KamLAND detector not only counts the antineutrino rate, but also measures their energy. The shape of this energy spectrum carries additional information that can be used to investigate neutrino oscillation hypotheses. Statistical analyses in 2005 show

354-404: A changing superposition mixture of mass eigenstates as the neutrino travels; but a different mixture of mass eigenstates corresponds to a different mixture of flavor states. For example, a neutrino born as an electron neutrino will be some mixture of electron, mu , and tau neutrino after traveling some distance. Since the quantum mechanical phase advances in a periodic fashion, after some distance

413-471: A characteristic 2.2 MeV γ ray . This delayed-coincidence signature is a very powerful tool for distinguishing antineutrinos from backgrounds produced by other particles. To compensate for the loss in ν ¯ e {\displaystyle {\bar {\nu }}_{e}} flux due to the long baseline, KamLAND has a much larger detection volume compared to earlier devices. The KamLAND detector uses

472-468: A combined fit gives Δ m 2 = 7.9 − 0.5 + 0.6 ⋅ 10 − 5 eV 2 {\displaystyle \Delta {m^{2}}=7.9_{-0.5}^{+0.6}\cdot 10^{-5}{\text{eV}}^{2}} and tan 2 ⁡ θ = 0.40 − 0.07 + 0.10 {\displaystyle \tan ^{2}\theta =0.40_{-0.07}^{+0.10}} ,

531-434: A different superposition of the three (propagating) neutrino states of definite mass. Neutrinos are emitted and absorbed in weak processes in flavor eigenstates but travel as mass eigenstates . As a neutrino superposition propagates through space, the quantum mechanical phases of the three neutrino mass states advance at slightly different rates, due to the slight differences in their respective masses. This results in

590-452: A different lepton family number. The probability of measuring a particular flavor for a neutrino varies between three known states, as it propagates through space. First predicted by Bruno Pontecorvo in 1957, neutrino oscillation has since been observed by a multitude of experiments in several different contexts. Most notably, the existence of neutrino oscillation resolved the long-standing solar neutrino problem . Neutrino oscillation

649-544: A few percent, it is satisfactory to know the distance to within 1%. The first experiment that detected the effects of neutrino oscillation was Ray Davis' Homestake experiment in the late 1960s, in which he observed a deficit in the flux of solar neutrinos with respect to the prediction of the Standard Solar Model , using a chlorine -based detector. This gave rise to the solar neutrino problem . Many subsequent radiochemical and water Cherenkov detectors confirmed

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708-556: A matrix product: The 2×2 matrix is real symmetric and so (by the spectral theorem ) it is orthogonally diagonalizable . That is, there is an angle θ such that if we define then where λ 1 and λ 2 are the eigenvalues of the matrix. The variables x 1 and x 2 describe normal modes which oscillate with frequencies of λ 1 {\displaystyle {\sqrt {\lambda _{1}\,}}} and λ 2 {\displaystyle {\sqrt {\lambda _{2}\,}}} . When

767-450: A neutrino changing its flavor is Or, using SI units and the convention introduced above This formula is often appropriate for discussing the transition ν μ ↔ ν τ in atmospheric mixing, since the electron neutrino plays almost no role in this case. It is also appropriate for the solar case of ν e ↔ ν x , where ν x is a mix (superposition) of ν μ and ν τ . These approximations are possible because

826-449: A very precise measurement of neutrino oscillation in an energy range of hundreds of MeV to a few TeV, and with a baseline of the diameter of the Earth ; the first experimental evidence for atmospheric neutrino oscillations was announced in 1998. Many experiments have searched for oscillation of electron anti -neutrinos produced in nuclear reactors . No oscillations were found until a detector

885-476: Is 34%. Its second, inner layer consists of a 13 m -diameter nylon balloon filled with a liquid scintillator composed of 1,000 metric tons of mineral oil , benzene , and fluorescent chemicals. Non-scintillating, highly purified oil provides buoyancy for the balloon and acts as a buffer to keep the balloon away from the photo-multiplier tubes; the oil also shields against external radiation. A 3.2 kiloton cylindrical water Cherenkov detector surrounds

944-403: Is a combination of both normal modes. Over time, these normal modes drift out of phase, and this is seen as a transfer of motion from the first pendulum to the second. The description of the system in terms of the two pendulums is analogous to the flavor basis of neutrinos. These are the parameters that are most easily produced and detected (in the case of neutrinos, by weak interactions involving

1003-498: Is a function of the ratio ⁠ L  / E ⁠   , where L is the distance traveled and E is the neutrino's energy. (Details in § Propagation and interference below.) All available neutrino sources produce a range of energies, and oscillation is measured at a fixed distance for neutrinos of varying energy. The limiting factor in measurements is the accuracy with which the energy of each observed neutrino can be measured. Because current detectors have energy uncertainties of

1062-413: Is expressed as The above formula is correct for any number of neutrino generations. Writing it explicitly in terms of mixing angles is extremely cumbersome if there are more than two neutrinos that participate in mixing. Fortunately, there are several meaningful cases in which only two neutrinos participate significantly. In this case, it is sufficient to consider the mixing matrix Then the probability of

1121-620: Is expressed as a unitary transformation relating the flavor and mass eigenbasis and can be written as where The symbol U α i {\displaystyle U_{\alpha i}} represents the Pontecorvo–Maki–Nakagawa–Sakata matrix (also called the PMNS matrix , lepton mixing matrix , or sometimes simply the MNS matrix ). It is the analogue of the CKM matrix describing

1180-401: Is infeasible on multiple levels. The idea of neutrino oscillation was first put forward in 1957 by Bruno Pontecorvo , who proposed that neutrino–antineutrino transitions may occur in analogy with neutral kaon mixing . Although such matter–antimatter oscillation had not been observed, this idea formed the conceptual foundation for the quantitative theory of neutrino flavor oscillation, which

1239-449: Is non-zero only if neutrino oscillation violates CP symmetry ; this has not yet been observed experimentally. If experiment shows this 3×3 matrix to be not unitary , a sterile neutrino or some other new physics is required. Since | ν j ⟩ {\displaystyle \left|\,\nu _{j}\,\right\rangle } are mass eigenstates, their propagation can be described by plane wave solutions of

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1298-459: Is not in a mass eigenstate; however, the charged lepton would lose coherence, if it had any, over interatomic distances (0.1  nm ) and would thus quickly cease any meaningful oscillation. More importantly, no mechanism in the Standard Model is capable of pinning down a charged lepton into a coherent state that is not a mass eigenstate, in the first place; instead, while the charged lepton from

1357-524: Is of great theoretical and experimental interest, as the precise properties of the process can shed light on several properties of the neutrino. In particular, it implies that the neutrino has a non-zero mass outside the Einstein-Cartan torsion , which requires a modification to the Standard Model of particle physics . The experimental discovery of neutrino oscillation, and thus neutrino mass, by

1416-705: Is planned with additional xenon. KamLAND-PICO is a planned project that will install the PICO-LON detector in KamLand to search for dark matter. PICO-LON is a radiopure NaI(Tl) crystal that observes inelastic WIMP-nucleus scattering. Improvements to the detector are planned, adding light collecting mirrors and PMTs with higher quantum efficiency. KamLAND started to collect data on January 17, 2002. First results were reported using only 145 days of data. Without neutrino oscillation , 86.8 ± 5.6 events were expected, however, only 54 events were observed. KamLAND confirmed this result with

1475-457: Is responsible for oscillation is often written as (with c and ℏ {\displaystyle \hbar } restored) where 1.27 is unitless . In this form, it is convenient to plug in the oscillation parameters since: If there is no CP-violation ( δ is zero), then the second sum is zero. Otherwise, the CP asymmetry can be given as In terms of Jarlskog invariant the CP asymmetry

1534-461: Is the prompt event energy including the positron kinetic energy and the e + e − {\displaystyle e^{+}e^{-}} annihilation energy. The quantity < E n {\displaystyle E_{n}} > is the average neutron recoil energy , which is only a few tens of kiloelectronvolts (keV). The neutron is captured on hydrogen approximately 200 microseconds (μs) later, emitting

1593-470: Is the standard gravity , L is the length of the pendulum, m is the mass of the pendulum, and x is the horizontal displacement of the pendulum. As an isolated system the pendulum is a harmonic oscillator with a frequency of g / L {\displaystyle {\sqrt {g/L\;}}\,} . The potential energy of a spring is 1 2 k x 2 {\displaystyle {\tfrac {1}{2}}kx^{2}} where k

1652-421: Is the spring constant and x is the displacement. With a mass attached it oscillates with a period of k / m {\displaystyle {\sqrt {k/m\;}}\,} . With two pendulums (labeled a and b ) of equal mass but possibly unequal lengths and connected by a spring, the total potential energy is This is a quadratic form in x a and x b , which can also be written as

1711-494: The Lorentz factor , γ , is greater than 10 in all cases. Using also t ≈ L , where L is the distance traveled and also dropping the phase factors, the wavefunction becomes Eigenstates with different masses propagate with different frequencies. The heavier ones oscillate faster compared to the lighter ones. Since the mass eigenstates are combinations of flavor eigenstates, this difference in frequencies causes interference between

1770-698: The MiniBooNE appeared in Spring ;2007 and contradicted the results from LSND, although they could support the existence of a fourth neutrino type, the sterile neutrino . In 2010, the INFN and CERN announced the observation of a tauon particle in a muon neutrino beam in the OPERA detector located at Gran Sasso , 730 km away from the source in Geneva . T2K , using a neutrino beam directed through 295 km of earth and

1829-677: The Super-Kamiokande Observatory and the Sudbury Neutrino Observatories was recognized with the 2015 Nobel Prize for Physics . A great deal of evidence for neutrino oscillation has been collected from many sources, over a wide range of neutrino energies and with many different detector technologies. The 2015 Nobel Prize in Physics was shared by Takaaki Kajita and Arthur B. McDonald for their early pioneering observations of these oscillations. Neutrino oscillation

Kamioka Liquid Scintillator Antineutrino Detector - Misplaced Pages Continue

1888-518: The W boson ). The description in terms of normal modes is analogous to the mass basis of neutrinos. These modes do not interact with each other when the system is free of outside influence. When the pendulums are not identical the analysis is slightly more complicated. In the small-angle approximation, the potential energy of a single pendulum system is 1 2 m g L x 2 {\displaystyle {\tfrac {1}{2}}{\tfrac {mg}{L}}x^{2}} , where g

1947-459: The 3×3 form, it is given by where c ij ≡ cos θ ij , and s ij ≡ sin θ ij . The phase factors α 1 and α 2 are physically meaningful only if neutrinos are Majorana particles —i.e. if the neutrino is identical to its antineutrino (whether or not they are is unknown)—and do not enter into oscillation phenomena regardless. If neutrinoless double beta decay occurs, these factors influence its rate. The phase factor δ

2006-592: The KamLAND-Zen Collaboration using the KamLAND-Zen 800 published results about neutrinoless double-beta decay in Xe-136 using data collected between February 5, 2019 and May 8, 2021. No neutrinoless double-beta decay was observed, and the established lower bound for half-life was T > 2.3 × 10 26 {\displaystyle 2.3\times 10^{26}} yr corresponding to upper limits on

2065-407: The Standard Model that would make charged leptons detectably oscillate. In the four decays mentioned above, where the charged lepton is emitted in a unique mass eigenstate, the charged lepton will not oscillate, as single mass eigenstates propagate without oscillation. The case of (real) W boson decay is more complicated: W boson decay is sufficiently energetic to generate a charged lepton that

2124-463: The Super-Kamiokande detector, measured a non-zero value for the parameter θ 13 in a neutrino beam. NOνA , using the same beam as MINOS with a baseline of 810 km, is sensitive to the same. Neutrino oscillation arises from mixing between the flavor and mass eigenstates of neutrinos. That is, the three neutrino states that interact with the charged leptons in weak interactions are each

2183-606: The U/Th radiopower to under 60TW. Combination results with Borexino were published in 2011, measuring the U/Th heat flux. New results in 2013, benefiting from the reduced backgrounds due to Japanese reactor shutdowns, were able to constrain U/Th radiogenic heat production to 11.2 − 5.1 + 7.9 {\displaystyle 11.2_{-5.1}^{+7.9}} TW using 116 ν ¯ e {\displaystyle {\bar {\nu }}_{e}} events. This constrains composition models of

2242-499: The W ;boson decay is not initially in a mass eigenstate, neither is it in any "neutrino-centric" eigenstate, nor in any other coherent state. It cannot meaningfully be said that such a featureless charged lepton oscillates or that it does not oscillate, as any "oscillation" transformation would just leave it the same generic state that it was before the oscillation. Therefore, detection of a charged lepton oscillation from W boson decay

2301-407: The analogous mixing of quarks . If this matrix were the identity matrix , then the flavor eigenstates would be the same as the mass eigenstates. However, experiment shows that it is not. When the standard three-neutrino theory is considered, the matrix is 3×3. If only two neutrinos are considered, a 2×2 matrix is used. If one or more sterile neutrinos are added (see later), it is 4×4 or larger. In

2360-524: The best neutrino oscillation parameter determination to that date. Since then a 3 neutrino model has been used. Precision combined measurements were reported in 2008 and 2011: KamLAND also published an investigation of geologically-produced antineutrinos (so-called geoneutrinos ) in 2005. These neutrinos are produced in the decay of thorium and uranium in the Earth's crust and mantle . A few geoneutrinos were detected and these limited data were used to limit

2419-754: The bulk silicate Earth and agrees with the reference Earth model. KamLAND-Zen uses the detector to study beta decay of Xe from a balloon placed in the scintillator in summer 2011. Observations set a limit for neutrinoless double-beta decay half-life of 1.9 × 10 yr . A double beta decay lifetime was also measured: 2.38 ± 0.02 ( s t a t ) ± 0.14 ( s y s t ) ∗ 10 21 {\displaystyle 2.38\pm {0.02(\mathrm {stat} )}\pm {0.14(\mathrm {syst} )}*10^{21}}  yr, consistent with other xenon studies. KamLAND-Zen plans continued observations with more enriched Xe and improved detector components. An improved search

Kamioka Liquid Scintillator Antineutrino Detector - Misplaced Pages Continue

2478-414: The charged leptons (electrons, muons, and tau leptons) have never been observed to oscillate. In nuclear beta decay, muon decay, pion decay, and kaon decay, when a neutrino and a charged lepton are emitted, the charged lepton is emitted in incoherent mass eigenstates such as  | e ⟩ , because of its large mass. Weak-force couplings compel the simultaneously emitted neutrino to be in

2537-490: The containment vessel, acting as a muon veto counter and providing shielding from cosmic rays and radioactivity from the surrounding rock. Electron antineutrinos ( ν e ) are detected through the Inverse beta decay reaction ν ¯ e + p → e + + n {\displaystyle {\bar {\nu }}_{e}+p\to e^{+}+n} , which has

2596-618: The corresponding flavor components of each mass eigenstate. Constructive interference causes it to be possible to observe a neutrino created with a given flavor to change its flavor during its propagation. The probability that a neutrino originally of flavor α will later be observed as having flavor β is This is more conveniently written as where Δ j k m 2   ≡ m j 2 − m k 2   . {\displaystyle \Delta _{jk}m^{2}\ \equiv m_{j}^{2}-m_{k}^{2}~.} The phase that

2655-574: The deficit, but neutrino oscillation was not conclusively identified as the source of the deficit until the Sudbury Neutrino Observatory provided clear evidence of neutrino flavor change in 2001. Solar neutrinos have energies below 20  MeV . At energies above 5 MeV, solar neutrino oscillation actually takes place in the Sun through a resonance known as the MSW effect , a different process from

2714-409: The effective Majorana neutrino mass of 36 – 156 meV. The KamLAND-Zen collaboration is planning to construct another apparatus, KamLAND2-Zen in the long term. Neutrino oscillation Neutrino oscillation is a quantum mechanical phenomenon in which a neutrino created with a specific lepton family number ("lepton flavor": electron , muon , or tau ) can later be measured to have

2773-526: The form where In the ultrarelativistic limit , | p → j | = p j ≫ m j   , {\displaystyle \left|{\vec {p}}_{j}\right|=p_{j}\gg m_{j}~,} we can approximate the energy as where E is the energy of the wavepacket (particle) to be detected. This limit applies to all practical (currently observed) neutrinos, since their masses are less than 1 eV and their energies are at least 1 MeV, so

2832-411: The mixing angle θ 13 is very small and because two of the mass states are very close in mass compared to the third. The basic physics behind neutrino oscillation can be found in any system of coupled harmonic oscillators . A simple example is a system of two pendulums connected by a weak spring (a spring with a small spring constant ). The first pendulum is set in motion by the experimenter while

2891-631: The neutrinoless double beta decay half-life. The KamLAND-Zen 400 operated from 2011 October to 2015 October and was then replaced by KamLAND-Zen 800. The second KamLAND-Zen experiment apparatus, KamLAND-Zen 800 , with bigger balloon of about 750 kg of Xenon was installed in the KamLAND detector 10 May 2018. The operation was expected to start winter 2018-2019 with 5 years of expected operation. The KamLAND-Zen 800 experiment started data taking in January 2019 and first results were published in 2020. In March 2022

2950-530: The parameter θ 13 . In December 2011, the Double Chooz experiment found that θ 13 ≠ 0 . Then, in 2012, the Daya Bay experiment found that θ 13 ≠ 0  with a significance of 5.2 σ  ; These results have since been confirmed by RENO . Neutrino beams produced at a particle accelerator offer the greatest control over the neutrinos being studied. Many experiments have taken place that study

3009-449: The same oscillations as in atmospheric neutrino oscillation using neutrinos with a few GeV of energy and several-hundred-km baselines. The MINOS , K2K , and Super-K experiments have all independently observed muon neutrino disappearance over such long baselines. Data from the LSND experiment appear to be in conflict with the oscillation parameters measured in other experiments. Results from

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3068-509: The second begins at rest. Over time, the second pendulum begins to swing under the influence of the spring, while the first pendulum's amplitude decreases as it loses energy to the second. Eventually all of the system's energy is transferred to the second pendulum and the first is at rest. The process then reverses. The energy oscillates between the two pendulums repeatedly until it is lost to friction . The behavior of this system can be understood by looking at its normal modes of oscillation. If

3127-474: The spectrum distortion is inconsistent with the no-oscillation hypothesis and two alternative disappearance mechanisms, namely the neutrino decay and de-coherence models. It is consistent with 2-neutrino oscillation and a fit provides the values for the Δm and θ parameters. Since KamLAND measures Δm most precisely and the solar experiments exceed KamLAND's ability to measure θ, the most precise oscillation parameters are obtained in combination with solar results. Such

3186-502: The state will nearly return to the original mixture, and the neutrino will be again mostly electron neutrino. The electron flavor content of the neutrino will then continue to oscillate – as long as the quantum mechanical state maintains coherence . Since mass differences between neutrino flavors are small in comparison with long coherence lengths for neutrino oscillations, this microscopic quantum effect becomes observable over macroscopic distances. In contrast, due to their larger masses,

3245-413: The two pendulums are identical then one normal mode consists of both pendulums swinging in the same direction with a constant distance between them, while the other consists of the pendulums swinging in opposite (mirror image) directions. These normal modes have (slightly) different frequencies because the second involves the (weak) spring while the first does not. The initial state of the two-pendulum system

3304-461: The vacuum oscillation described later in this article. Following the theories that were proposed in the 1970s suggesting unification of electromagnetic, weak, and strong forces, a few experiments on proton decay followed in the 1980s. Large detectors such as IMB , MACRO , and Kamiokande II have observed a deficit in the ratio of the flux of muon to electron flavor atmospheric neutrinos (see muon decay ). The Super-Kamiokande experiment provided

3363-475: Was first developed by Maki, Nakagawa, and Sakata in 1962 and further elaborated by Pontecorvo in 1967. One year later the solar neutrino deficit was first observed, and that was followed by the famous article by Gribov and Pontecorvo published in 1969 titled "Neutrino astronomy and lepton charge". The concept of neutrino mixing is a natural outcome of gauge theories with massive neutrinos, and its structure can be characterized in general. In its simplest form it

3422-445: Was installed at a distance 1–2 km. Such oscillations give the value of the parameter θ 13 . Neutrinos produced in nuclear reactors have energies similar to solar neutrinos, of around a few MeV. The baselines of these experiments have ranged from tens of meters to over 100 km (parameter θ 12 ). Mikaelyan and Sinev proposed to use two identical detectors to cancel systematic uncertainties in reactor experiment to measure

3481-506: Was published in August 2016, increasing the half-life limit to 1.07 × 10 yr , with a neutrino mass bound of 61–165 meV. The first KamLAND-Zen apparatus, KamLAND-Zen 400 , completed two research programs, Phase I (2011 Oct. - 2012 Jun.) and Phase II (2013 Dec. - 2015 Oct.). The combined data of Phase I and II implied the lower bound 1.07 × 10 26 {\displaystyle 1.07\times 10^{26}} years for

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