NationMaster - Encyclopedia: Neutrino oscillation

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Encyclopedia > Neutrino oscillation

Neutrino oscillation is a quantum mechanical phenomenon predicted by Bruno Pontecorvo whereby a neutrino created with a specific lepton flavor (electron, muon or tau) can later be measured to have a different flavor. The probability of measuring a particular flavor for a neutrino varies periodically as it propagates. Neutrino oscillation is of theoretical and experimental interest as observation of the phenomenon implies that the neutrino has a non-zero mass, which is not part of the original Standard Model of particle physics. Fig. ... Bruno Pontecorvo Bruno Pontecorvo (Pisa, Italy 1913 - Dubna, Russia 1993) was an Italian atomic physicist, early assistant of Enrico Fermi then author of numerous studies in high energy physics, especially on neutrinos. ... The neutrino is an elementary particle. ... In physics, a particle is a lepton if it has a spin of 1/2 and does not experience the strong nuclear force. ... In particle physics, flavor is a property of a fermion that identifies it, a label that specifies the name of the particle. ... The Electron is a fundamental subatomic particle that carries an electric charge. ... The moons shadow, as seen in muons 700m below ground at the Soudan 2 detector. ... Tau (upper case Î¤, lower case Ï„) is the 19th letter of the Greek alphabet. ... The framework of quantum mechanics requires a careful definition of measurement, and a thorough discussion of its practical and philosophical implications. ... Theoretical physics employs mathematical models and abstractions of physics, as opposed to experimental processes, in an attempt to understand Nature. ... Experimental physics is the part of physics that deals with experiments and observations pertaining to natural/physical phenomena, as opposed to theoretical physics. ... The Standard Model of Fundamental Particles and Interactions For the Standard Model in Cryptography, see Standard Model (cryptography). ... Particles explode from the collision point of two relativistic (100 GeV per nucleon) gold ions in the STAR detector of the Relativistic Heavy Ion Collider. ...

Observations

A great deal of evidence for neutrino oscillations has been collected from many sources, over a wide range of neutrino energies and with many different detector technologies.

Solar neutrino oscillation

The first experiment to detect the effects of neutrino oscillations was Ray Davis's Homestake Experiment, in which he observed a deficit in the flux of solar neutrinos using a chlorine-based detector. This gave rise to the Solar neutrino problem. Many subsequent radiochemical and water Cerenkov detectors confirmed the deficit, but neutrino oscillations weren't conclusively identified as the source of the deficit until the Sudbury Neutrino Observatory provided clear evidence of neutrino flavor change. Raymond Davis Jr. ... The Homestake Experiment (sometimes referred to as the Davis Experiment) was an experiment headed by astrophysicists Raymond Davis, Jr. ... The Sun is the star of our solar system. ... General Name, Symbol, Number chlorine, Cl, 17 Chemical series halogens Group, Period, Block 17, 3, p Appearance yellowish green Atomic mass 35. ... The solar neutrino problem was a major discrepancy between measurements of the neutrinos flowing through the Earth and theoretical models of the solar interior, lasting from the mid-1960s to about 2002. ... Cherenkov radiation glowing in the core of a TRIGA reactor Cherenkov radiation (also spelled Cerenkov or sometimes ÄŒerenkov) is electromagnetic radiation emitted when a charged particle passes through an insulator at a speed greater than the speed of light in that medium. ... Artists concept of SNOs detector. ...

Solar neutrinos have energies below 20 MeV and travel an astronomical unit between the source and detector. 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 the vacuum oscillations described later in this article. An electronvolt (symbol: eV) is the amount of energy gained by a single unbound electron when it falls through an electrostatic potential difference of one volt. ... The astronomical unit (AU or au or a. ... The Mikheyev-Smirnov-Wolfenstein effect is a particle physics process which acts to enhance neutrino oscillations in matter. ...

Atmospheric neutrino oscillation

Large detectors such as IMB, MACRO, and Kamiokande II observed a deficit in the ratio of the flux of muon to electron flavor atmospheric neutrinos. The Super Kamiokande experiment provided a very high precision measurement of neutrino oscillations in an energy range of hundreds of MeV to a few TeV, and with a baseline of the radius of the Earth. IMB, the Irvine-Michigan-Brookhaven detector, was a nucleon decay experiment and neutrino observatory located in a salt mine on the shore of Lake Erie in the United States. ... MACRO, or the Monopole, Astrophysics and Cosmic Ray Observatory, is a particle physics experiment located at the Laboratori Nazionali del Gran Sasso in Abruzzo, Italy. ... The interior of Super-K Super-Kamiokande, or Super-K for short, is a neutrino observatory in Japan. ... Super-Kamiokande, or Super-K for short, is a neutrino observatory in Japan. ... Earth (IPA: , often referred to as the Earth, Terra, the World or Planet Earth) is the third planet in the solar system in terms of distance from the Sun, and the fifth largest. ...

Reactor neutrino oscillations

Many experiments have searched for oscillations of electron anti-neutrinos produced at nuclear reactors. A high precision observation of reactor neutrino oscillation has been made by the KamLAND experiment. Neutrinos produced in nuclear reactors have energies similar to solar neutrinos, a few MeV. The baselines of these experiments have ranged from tens of meters to over 100km. In particle physics, antimatter extends the concept of the antiparticle to matter, wherein if a particle and its antiparticle come into contact with each other, the two annihilate â€”that is, they may both be converted into other particles with equal energy in accordance with Einsteins equation E = mc2. ... Nuclear power station at Leibstadt, Switzerland. ... Image:Kamland detector. ...

Beam neutrino oscillations

Neutrinos beams produced at a particle accelerator offer the greatest control over the neutrinos being studied. Many experiments have taken place which study the same neutrino oscillations which take place in atmospheric neutrino oscillation, using neutrinos with a few GeV of energy and several hundred km baselines. The MINOS experiment recently announced that it observes consistency with the results of the K2K and Super-K experiments. The MINOS result has not yet been published in a peer reviewed journal but it is expected that their results will be published soon. A 1960s single stage 2 MeV linear Van de Graaff accelerator, here opened for maintenance A particle accelerator is a device that uses electric fields to propel electrically charged particles to high speeds and magnetic fields to contain them. ... In Greek mythology, Minos was a semi-legendary king of Crete, son of Zeus and Europa. ...

The controversial observation of beam neutrino oscillation at the LSND experiment is currently being tested by MiniBooNE. Results from MiniBooNE are expected in the fall of 2006. The Liquid Scintillator Neutrino Detector (LSND) was a scintillation counter at Los Alamos National Laboratory that measured the number of neutrinos being produced by a reactor. ... MiniBooNE is the first phase of the Booster Neutrino Experiment (BooNE) at Fermilab which is designed to check the results of the LSND experiment. ...

Theory, formally

The idea of neutrino oscillations was put forward in 1957 by Bruno Pontecorvo, in analogy with a similar phenomenon observed in the neutral kaon system. The quantitative theory described below was developed by him in 1967. One year later the solar neutrino deficit was first observed, that was followed by the famous paper of Gribov and Pontecorvo published in 1969 titled "Neutrino astronomy and lepton charge". Bruno Pontecorvo Bruno Pontecorvo (Pisa, Italy 1913 - Dubna, Russia 1993) was an Italian atomic physicist, early assistant of Enrico Fermi then author of numerous studies in high energy physics, especially on neutrinos. ...

Maki-Nakagawa-Sakata matrix

Solar and atmospheric neutrino experiments have shown that neutrino oscillations are due to a mismatch between the flavor and mass eigenstates of neutrinos. The relationship between these eigenstates is given by Categories: Physics stubs | Neutrino observatories | Ontario ... Super-Kamiokande, or Super-K for short, is a neutrino observatory in Japan. ... In linear algebra, the eigenvectors (from the German eigen meaning inherent, characteristic) of a linear operator are non-zero vectors which, when operated on by the operator, result in a scalar multiple of themselves. ...

$left| nu_{alpha} rightrangle = sum_{i} U_{alpha i}^{*} left| nu_{i} rightrangle,$

$left| nu_{i} rightrangle = sum_{alpha} U_{alpha i} left| nu_{alpha} rightrangle$ ,

where

$left| nu_{alpha} rightrangle$ is a neutrino with definite flavor. α = e (electron), $μ$ (muon) or $τ$ (tau).
$left| nu_{i} rightrangle$ is a neutrino with definite mass. i = 1, 2, 3.
$*$ represents a complex conjugate (for antineutrinos, the complex conjugate should be dropped from the first equation, and added to the second).

$U α i$ represents the Maki-Nakagawa-Sakata matrix (also called the "MNS matrix", "neutrino mixing matrix", or sometimes "PMNS matrix" to include Pontecorvo). It is the equivalent of the CKM matrix for 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. In mathematics, the complex conjugate of a complex number is given by changing the sign of the imaginary part. ... Antineutrinos, the antiparticles of neutrinos, are neutral particles produced in nuclear beta decay. ... Bruno Pontecorvo Bruno Pontecorvo (Pisa, Italy 1913 - Dubna, Russia 1993) was an Italian atomic physicist, early assistant of Enrico Fermi then author of numerous studies in high energy physics, especially on neutrinos. ... In the standard model of particle physics the Cabibbo Kobayashi Maskawa matrix (CKM matrix, sometimes earlier called KM matrix) is a unitary matrix which contains information on the strength of flavour changing weak decays. ... These are the 6 quarks and their most likely decay modes. ... In linear algebra, the identity matrix of size n is the n-by-n square matrix with ones on the main diagonal and zeros elsewhere. ...

When the standard three neutrino theory is considered, the matrix is 3×3. If only two neutrinos are considered, a 2×2 used. If one or more sterile neutrinos are added (see later) it is 4×4 or larger. In the 3×3 form, it is given by: ^[1]

$U = begin{bmatrix} U_{e 1} & U_{e 2} & U_{e 3} U_{mu 1} & U_{mu 2} & U_{mu 3} U_{tau 1} & U_{tau 2} & U_{tau 3} end{bmatrix} = begin{bmatrix} c_{12} c_{13} & s_{12} c_{13} & s_{13} e^{-idelta} - s_{12} c_{23} - c_{12} s_{23} s_{13} e^{i delta} & c_{12} c_{23} - s_{12} s_{23} s_{13} e^{i delta} & s_{23} c_{13} s_{12} s_{23} - c_{12} c_{23} s_{13} e^{i delta} & - c_{12} s_{23} - s_{12} c_{23} s_{13} e^{i delta} & c_{23} s_{13} end{bmatrix} begin{bmatrix} e^{ialpha_1 / 2} & 0 & 0 0 & e^{ialpha_2 / 2} & 0 0 & 0 & 1 end{bmatrix},$

where $s 12 = sinθ 12$ , $c 12 = cosθ 12$ , etc. The phase factors α₁ and α₂ are non-zero only if neutrinos are Majorana particles (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 is non-zero only if neutrino oscillation violates CP symmetry. This is expected, but not yet observed experimentally. If experiment shows this 3x3 matrix to be not unitary, a sterile neutrino or some other new physics is required. In mathematics and physics, in particular in the theory of the orthogonal groups, spinors are certain kinds of mathematical objects (group representations of Spin(N), roughly speaking) similar to vectors, but which change sign under a rotation of radians. ... In the process of beta decay unstable nuclei decay by converting a neutron in the nucleus to a proton and emitting an electron and anti-neutrino. ... CP is the product of two symmetries: C for charge conjugation, which transforms a particle into its antiparticle, and P for parity, which creates the mirror image of a physical system. ...

Propagation and interference

Since $left| nu_{i} rightrangle$ are mass eigenstates, their propagation can be described by plane wave solutions of the form In the physics of wave propagation (especially electromagnetic waves), a plane wave (also spelled planewave) is a constant-frequency wave whose wavefronts (surfaces of constant amplitude and phase) are infinite parallel planes normal to the propagation direction. ...

$|nu_{i}(t)rangle = e^{ -i ( E_{i} t - vec{p}_{i} cdot vec{x}) }|nu_{i}(0)rangle$ ,

where

quantities are expressed in natural units $(c = hbar = 1)$
$E i$ is the energy of the mass-eigenstate $i$ ,
$t$ is the time from the start of the propagation,
$vec{p}_{i}$ is the 3-dimensional momentum,
$vec{x}$ is the current position of the particle relative to its starting position

In the ultrarelativistic limit, $|vec{p}_i| = p_i gg m_i$ , we can approximate the energy as In physics, Planck units are physical units of measurement originally proposed by Max Planck. ... In classical mechanics, momentum (pl. ... In physics, ultrarelativistic is said of a particle when its speed is very close to the speed of light , such that its total energy is almost completely due to its momentum (), and thus can be approximated by . ...

$E_{i} = sqrt{p_{i}^2 + m_{i}^2 }simeq p_{i} + frac{m_{i}^2}{2 p_{i}} approx E + frac{m_{i}^2}{2 E}$ ,

This limit applies to all practical neutrinos which their mass is less than 1eV and their energies are at least 1MeV, so the Lorentz factor γ is greater than 10⁶ in all cases. Using also t ≈ L, where L is the distance traveled and also dropping the phase factors, the wavefunction becomes: It has been suggested that Lorentz term be merged into this article or section. ...

$|nu_{i}(L)rangle = e^{ -i m_{i}^2 L/2E }|nu_{i}(0)rangle$ ,

Eigenstates with different masses propagate at different speeds. The heavier ones lag behind while the lighter ones pull ahead. Since the mass eigenstates are combinations of flavor eigenstates, this difference in speed causes interference between 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 Interference of two circular waves - Wavelength (decreasing bottom to top) and Wave centers distance (increasing to the right). ...

$P_{alpharightarrowbeta}=left|leftlangle nu_{beta}|nu_{alpha}(t)rightrangle right|^{2}=left|sum_{i}U_{alpha i}^{*}U_{beta i}e^{ -i m_{i}^2 L/2E }right|^{2}.$

This is more conveniently written as

$begin{matrix}P_{alpharightarrowbeta}=delta_{alphabeta} & - & 4{displaystyle sum_{i>j}Re(U_{alpha i}^{*}U_{beta i}U_{alpha j}U_{beta j}^{*}})sin^{2}(frac{Delta m_{ij}^{2}L}{4E}) & + & {displaystyle 2sum_{i>j}Im(U_{alpha i}^{*}U_{beta i}U_{alpha j}U_{beta j}^{*})sin(}frac{Delta m_{ij}^{2}L}{2E})end{matrix}$ ,

where $Delta m_{ij}^{2} equiv m_{i}^2 - m_{j}^2$ . The phase that is responsible for oscillation is often written as (with c and $hbar$ restored)^[2]

$frac{Delta m^2, c^3, L}{4 hbar E} = frac{{rm GeV}, {rm fm}}{4 hbar c} times frac{Delta m^2}{{rm eV}^2} frac{L}{rm km} frac{rm GeV}{E} approx 1.267 times frac{Delta m^2}{{rm eV}^2} frac{L}{rm km} frac{rm GeV}{E}$ ,

where 1.267 is unitless. In this form, it is convenient to plug in the oscillation parameters since:

The mass differences, Δm², are known to be on the order of 1eV²
Oscillation distances, L, in modern experiments are on the order of kilometers
Neutrino energies, E, in modern experiments are typically on order of GeV.

If there is no CP-violation (δ is zero), then the second sum is zero. A kilometre (American spelling: kilometer) (symbol: km) is a unit of length equal to 1000 metres (from the Greek words khilia = thousand and metro = count/measure). ... CP-symmetry is a symmetry obtained by a combination of the C-symmetry and the P-symmetry. ...

Two neutrino case

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 cases in which only two neutrinos participate significantly. In this case, it is sufficient to consider the mixing matrix

$U = begin{pmatrix} costheta & sintheta -sintheta & costheta end{pmatrix}$

Then the probability of a neutrino changing its flavor is

$P_{alpharightarrowbeta, alphaneqbeta} = sin^{2}2theta sin^{2} left(frac{Delta m^2 L}{4E}right), mathrm{(natural,units)}$

Or, using SI units and the convention introduced above The International System of Units (symbol: SI) (for the French phrase Système International dUnités) is the most widely used system of units. ...

$P_{alpharightarrowbeta, alphaneqbeta} = sin^{2}2theta sin^{2}left( 1.267 frac{Delta m^2 L}{E} frac{rm GeV}{rm eV^{2},rm km}right)$

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 superposition of ν_μ and ν_τ. These approximations are possible because the mixing angle θ₁₃ is very small and because two of the mass states are very close in mass compared to the third.

Theory, graphically

It may be easier to understand the process of neutrino oscillation if it is presented with pictures instead of equations. This is easiest to do if only two types of neutrinos are considered. Here is the initial state of the neutrino, a plane wave of a single pure flavor (called "flavor 1" for generality, but it could be, for instance, a muon neutrino):

Image File history File links Neutrino_flavor_1_initial. ...

This flavor state is a combination of mass states:

Image File history File links Neutrino_masses_1_and_2_initial. ...

However, each mass state is also made up of flavor states. The second flavor state could represent the tau neutrino:

Image File history File links Neutrino_flavors_and_masses_initial. ...

Notice that if the two flavor 1 curves are added together, the original full wave is reproduced. On the other hand, if the flavor 2 curves are added, they cancel each other completely. Now, each of the mass 1 components travel slower than each of the mass 2 components, so over time they lag behind:

Image File history File links Neutrino_flavors_and_masses_later. ...

If, at this later time, the corresponding flavor states are added together, it is no longer the case that only flavor 1 is non-zero. Now there is less flavor 1 and a non-zero amount of flavor 2:

Image File history File links Neutrino_flavors_later. ...

The probability of observing a flavor is equal to the square of the amplitude of its wave. As time goes on, the heights of the resulting flavor waves will change periodically. This is the oscillation. The mixing angle controls how big this oscillation is. If the angle is maximal ( $sin 2 2θ = 1$ ), then the probability oscillates from 100% for the first flavor to 100% for the second. If the angle is smaller, then the first flavor's probability never goes to zero, but rather oscillates between 100% and some intermediate value. Amplitude is a nonnegative scalar measure of a waves magnitude of oscillation, that is, magnitude of the maximum disturbance in the medium during one wave cycle. ...

The oscillation of three or more neutrino flavors can also be visualized this way. However, if there is CP-violation, not all waves will start in phase as is always the case when there are only two neutrinos. CP-symmetry is a symmetry obtained by a combination of the C-symmetry and the P-symmetry. ...

Two neutrino probabilities in vacuum

In the approximation where only two neutrinos participate in the oscillation, the probability of oscillation follows a simple pattern:

The blue curve shows the probability of the original neutrino retaining its identity. The red curve shows the probability of conversion to the other neutrino. The maximum probability of conversion is equal to $sin 2 2θ$ . The frequency of the oscillation is controlled by $Δ m 2$ . Image File history File links Download high-resolution version (1000x618, 7 KB) I made this image myself and am releasing it to the public domain. ...

Two neutrino probabilities through the Sun

The figure below shows an example of osicllation probabilites of electron and muon neutrinos as they propagate from core of the sun to the edge of the sun.

Image File history File links Two_neutrino_probabilities_through_the_solar_matter. ...

Three neutrino probabilities

If three neutrinos are considered, the probability for each neutrino to appear is somewhat complex. Here are shown the probabilties for each initial flavor, with one plot showing a long range to display the slow "solar" oscillation and the other zoomed in to display the fast "atmospheric" oscillation. The oscillation parameters used here are consistent with current measurements, but since some parameters are still quite uncertain, these graphs are only qualitatively correct in some aspects. These values were used:

$sin 2 θ 13 = 0.08$ . (If it turns out to be much smaller or zero, the small wiggles shown here will be much smaller or non-existent, respectively.)
$sin 2 θ 23 = 0.95$ . (It may turn out to be exactly one.)
$sin 2 θ 12 = 0.86$ .
$δ = 0$ . (If it is actually large, these probabilities will be somewhat distorted and different for neutrinos and antineutrinos.)
$Delta m^2_{12} = 8 times 10^{-5} {rm eV}^2$ .
$Delta m^2_{23} approx Delta m^2_{13} = 2.4 times 10^{-3} {rm eV}^2$ .

Electron neutrino oscillations, long range. Here and in the following diagrams black means electron neutrino, blue means muon neutrino and red means tau neutrino.	Electron neutrino oscillations, short range
Muon neutrino oscillations, long range	Muon neutrino oscillations, short range
Tau neutrino oscillations, long range	Tau neutrino oscillations, short range

Image File history File links Download high-resolution version (1000x618, 9 KB) I made this myself and am releasing it to the public domain. ... Image File history File links Download high-resolution version (1000x618, 9 KB) I made this myself and am releasing it to the public domain. ... Image File history File links Download high-resolution version (1000x618, 4 KB) I made this myself and am releasing it to the public domain. ... Image File history File links Download high-resolution version (1000x618, 4 KB) I made this myself and am releasing it to the public domain. ... Image File history File links Download high-resolution version (1000x618, 8 KB) I made this myself and am releasing it to the public domain. ... Image File history File links Download high-resolution version (1000x618, 8 KB) I made this myself and am releasing it to the public domain. ... Image File history File links Download high-resolution version (1000x618, 8 KB) I made this myself and am releasing it to the public domain. ... Image File history File links Download high-resolution version (1000x618, 8 KB) I made this myself and am releasing it to the public domain. ... Image File history File links Download high-resolution version (1000x618, 8 KB) I made this myself and am releasing it to the public domain. ... Image File history File links Download high-resolution version (1000x618, 8 KB) I made this myself and am releasing it to the public domain. ... Image File history File links Download high-resolution version (1000x618, 8 KB) I made this myself and am releasing it to the public domain. ... Image File history File links Download high-resolution version (1000x618, 8 KB) I made this myself and am releasing it to the public domain. ...

Observed values of oscillation parameters

$sin^2(2theta_{13}) < 0.19^{}_{}$ at 90% confidence level ( $theta_{13} < 13^circ$ ) ^[3]

$tan^2(theta_{12}) = 0.45^{+0.09}_{-0.07}$ . This corresponds to $theta_{12}=theta_{rm sol}={33.9^circ}^{+2.4^circ}_{-2.2^circ}$ ("sol" stands for solar) ^[4]

$sin^2(2theta_{23}) = 1^{+0}_{-0.1}$ , corresponding to $theta_{23}=theta_{rm atm}=45pm 7^circ$ ("atm" for atmospheric)^[5]

$Delta m^2_{21}=Delta m^2_{rm sol}= 8.0^{+0.6}_{-0.4}cdot 10^{-5} {rm eV}^2$ ^[4]

$Delta m^2_{31} approx Delta m^2_{32} = Delta m^2_{rm atm}= 2.4^{+0.6}_{-0.5}cdot 10^{-3} {rm eV}^2$ ^[5]

δ is unknown

Solar neutrino experiments combined with KamLAND have measured the so-called solar parameters $Delta m^2_{rm sol}$ and $sin 2 θ sol$ . Atmospheric neutrino experiments such as Super-Kamiokande together with the K2K first long baseline accelerator neutrino experiment have determined the so-called atmospheric parameters $Delta m^2_{rm atm}$ and $sin 2 2θ atm$ . An additional experiment MINOS is expected to reduce the experimental errors significantly thereby increasing precision.^[6] Schematic of the KamLAND detector The Kamioka Liquid Scintillator Antineutrino Detector (KamLAND) is an experiment at the Kamioka Observatory, an underground neutrino observatory near Toyama, Japan. ... Super-Kamiokande, or Super-K for short, is a neutrino observatory in Japan. ... In Greek mythology, Minos was a semi-legendary king of Crete, son of Zeus and Europa. ...

For atmospheric neutrinos (where the relevant difference of masses is about $Delta m^2 =2.5times 10^{-3}mbox{ eV}^2$ and the typical energies are $Eapprox 1,mbox{ GeV}$ ), oscillations become visible for neutrinos travelling several hundred km, which means neutrinos that reach the detector from below the horizon.

From atmospheric and solar neutrino oscillation experiments, it is known that two mixing angles of the MNS matrix are large and the third is smaller. This is in sharp contrast to the CKM matrix in which all three angles are small and hierarchically decreasing. Nothing is known about the CP-violating phase of the MNS matrix. Electron neutrinos are produced in the sun as a product of nuclear fusion. ...

If the neutrino mass proves to be of Majorana type (making the neutrino its own antiparticle), it is possible that the MNS matrix has more than one phase. In mathematics and physics, in particular in the theory of the orthogonal groups, spinors are certain kinds of mathematical objects (group representations of Spin(N), roughly speaking) similar to vectors, but which change sign under a rotation of radians. ...

Origins of neutrino mass

The question of how neutrino masses arise has not been answered conclusively. In the Standard Model of particle physics, fermions only have mass because of interactions with the Higgs field (see Higgs boson). These interactions involve both left- and right-handed versions of the fermion (see chirality). However, only left-handed neutrinos have been observed so far. In particle physics, fermions are particles with half-integer spin. ... The Higgs boson is a hypothetical massive scalar elementary particle predicted to exist by the Standard Model of particle physics. ... A phenomenon is said to be chiral if it is not identical to its mirror image (see Chirality (mathematics)). The spin of a particle may be used to define a handedness for that particle. ...

Neutrinos may have another source of mass through the Majorana mass term. This type of mass applies for electrically-neutral particles since otherwise it would allow particles to turn into anti-particles, which would violate conservation of electric charge. In mathematics and physics, in particular in the theory of the orthogonal groups, spinors are certain kinds of mathematical objects (group representations of Spin(N), roughly speaking) similar to vectors, but which change sign under a rotation of radians. ...

The smallest modification to the Standard Model, which only has left-handed neutrinos, is to allow these left-handed neutrinos to have Majorana masses. The problem with this is that the neutrino masses are implausibly smaller than the rest of the known particles (at least 500,000 times smaller than the mass of an electron), which, while it does not invalidate the theory, is not very satisfactory.

The next simplest addition would be to add right-handed neutrinos into the Standard Model, which interact with the left-handed neutrinos and the Higgs field in an analogous way to the rest of the fermions. These new neutrinos would interact with the other fermions solely in this way, so are not phenomenologically excluded. The problem of the disparity of the mass scales remains.

See-saw mechanism

Main article: Seesaw mechanism

The most popular solution currently is the seesaw mechanism, where right-handed neutrinos with very large Majorana masses are added. If the right-handed neutrinos are very heavy, they induce a very small mass for the left-handed neutrinos, which is proportional to the inverse of the heavy mass. In theoretical physics, the seesaw mechanism is a mechanism to generate very small numbers from reasonable numbers and very large numbers. ...

If it is assumed that the neutrinos interact with the Higgs field with approximately the same strengths as the charged fermions do, the heavy mass should be close to the GUT scale. Note that, in the Standard Model there is just one fundamental mass scale (which can be taken as the scale of $SU(2)_Ltimes U(1)_Y$ breaking) and all masses (such as the electron or the mass of the Z boson) have to originate from this one. Grand unification, grand unified theory, or GUT is a theory in physics that unifies the strong interaction and electroweak interaction. ...

The apparently innocent addition of right handed neutrinos has the effect of adding new mass scales, completely unrelated to the mass scale of the Standard Model. Thus, heavy right handed neutrinos look to be the first real glimpse of physics beyond the Standard Model. It is interesting to note that right handed neutrinos can help to explain the origin of matter through a mechanism known as leptogenesis. In physics, leptogenesis is a process which creates leptons. ...

Other sources

There are alternative ways to modify the standard model that are similar to the addition of heavy right-handed neutrinos (e.g., the addition of new scalars or fermions in triplet states) and other modifications that are less similar (e.g., neutrino masses from loop effects and/or from suppressed couplings). One example of the last type of models is provided by certain versions supersymmetric extensions of the standard model of fundamental interactions, where R parity is not a symmetry. There, the exchange of supersymmetric particles such as squarks and sleptons can break the lepton number and lead to neutrino masses. These interactions are normally excluded from theories as they come from a class of interactions that lead to unacceptably rapid proton decay if they are all included. These models have little predictive power and are not able to provide a cold dark matter candidate but they are considered interesting since they would be compatible with new observable signals in particle colliders. In particle physics, a squark is a hypothetical boson partner of a quark whose existence is implied by supersymmetry. ... In particle physics, a slepton is a hypothetical bosonic partner of a lepton whose existence is implied by supersymmetry. ...

References

^ S. Eidelman et al. (2004). "Particle Data Group - The Review of Particle Physics". Physics Letters B 592 (1). Chapter 15: Neutrino mass, mixing, and flavor change. Revised September 2005.
^ "A Simple Parameterization of Matter Effects on Neutrino Oscillations", M. Honda, Y. Kao, N. Okamura and T. Takeuchi, 2006.
^ C. Bemporad [Chooz Collaboration], Nucl. Phys. Proc. Suppl. 77 (1999) 159.
^ ^a ^b Limit from the Solar and KamLAND Experiments, Phys. Rev. C 72, 055502 (2005)
^ ^a ^b Evidence for an oscillatory signature in atmospheric neutrino oscillation. Apr 2004. Published in Phys. Rev. Lett. 93, 101801
^ Double Chooz Letter of Intent

M.C. Gonzalez-Garcia, Y. Nir, "A review of evidence of neutrino masses and the implications", Reviews of Modern Physics 75 (2003) p.345-402.

External links

All neutrino data in one plot

Maury Goodman, "The Neutrino Oscillation Industry" (2005). (Provides links to many other neutrino oscillation websites.)

Categories: Leptons | Standard Model | Electroweak theory

Results from FactBites:

Neutrino oscillation - Wikipedia, the free encyclopedia (2520 words)
	Neutrino oscillation is of theoretical and experimental interest as observation of the phenomenon implies that the neutrino has a non-zero mass, which is not part of the original Standard Model of particle physics.
	Solar and atmospheric neutrino experiments have shown that neutrino oscillations are due to a mismatch between the flavor and mass eigenstates of neutrinos.
	From atmospheric and solar neutrino oscillation experiments, it is known that two mixing angles of the MNS matrix are large and the third is smaller.

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