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A neutrino participating in the weak interactions of the Standard Model, in contrast to a sterile state. Its thermal cosmological abundance and momentum distribution depend on weak decoupling and subsequent cosmic history.

Arthur B. McDonald led work at the Sudbury Neutrino Observatory, which distinguished a change of neutrino flavor from a low total solar neutrino flux. Reactions on deuterium provided different flavor sensitivities: the charged-current channel selected electron neutrinos, while the neutral-current channel measured all active neutrino flavors. Their comparison revealed a non-electron component while the total flux agreed with solar expectations. The detector thereby tested the solar neutrino problem without requiring all missing electron-flavor events to mean missing solar production.^[ref]

A physicist working in experimental particle astrophysics.^[ref]

For ground-to-ground beta-minus decay of bare nuclei, the nuclear mass difference supplies the electron rest energy as well as the kinetic energy shared among products. Neglecting recoil and neutrino mass, $T_{\max }=Q_{{\beta }^{-}}$. For neutral atomic masses the additional final atomic electron cancels the emitted electron rest-mass subtraction, giving $Q\simeq [M_{\mathrm{atom}}(i)-M_{\mathrm{atom}}(f)]c^2$ up to electron-binding corrections. A daughter excitation reduces the endpoint by its excitation energy.

A. W. Sunyar helped measure neutrino helicity with Maurice Goldhaber and L. Grodzins in 1958. Nuclear-recoil selection, magnetic polarization analysis and resonance-scattered gamma-ray counting linked a measurable photon signal to the emitted neutrino's handedness.^[ref]

The experiment inferred the neutrino property through angular-momentum correlations rather than requiring a direct track of the escaping neutrino.

Beta decay is a weak interaction process changing the proton-to-neutron composition of an atomic nucleus while preserving its mass number. In beta-minus decay, a neutron converts to a proton with an emitted electron and electron antineutrino; in beta-plus decay, a proton converts to a neutron with an emitted Positron and electron neutrino, when the complete energy balance permits it.^[ref]

The emitted beta particle is created in the transition rather than being an ordinary orbital electron expelled from the atom. Its kinetic energy varies because the available Q value is shared with the neutrino and daughter recoil. A magnetic electron spectrometer can separate different emitted momenta; a detector then records a continuous distribution rather than one universal electron energy.

Conservation of electric charge, energy and angular momentum constrains the final state. Nuclear binding matters: a free proton cannot undergo ordinary beta-plus decay, although an energetically allowed proton-to-neutron transition can occur within an appropriate atomic nucleus.

Beta equilibrium is a condition in which weak reactions interconverting neutrons and protons produce no net change of composition. For matter where neutrinos are thermally trapped, the reaction $n+{\nu }_e\rightleftharpoons p+e^{-}$ gives the chemical equilibrium conditionwhere each $\mu$ is the corresponding chemical potential. In cold neutrino-transparent neutron star matter, one usually takes ${\mu }_{{\nu }_e}=0$, giving ${\mu }_n={\mu }_p+{\mu }_e$. The escaping neutrinos do not form an equilibrated thermal bath in that approximation.^[ref]

Charge neutrality in matter containing only neutrons, protons and electrons additionally requires $n_p=n_e$. Given a total baryon density, these relations and an equation of state determine the composition. As an illustrative chemical-potential check, ${\mu }_n=1000$ MeV and ${\mu }_p=900$ MeV require ${\mu }_e=100$ MeV in the transparent approximation. At finite temperature, balancing emission and capture rates is the more general kinetic condition; nuclear statistical equilibrium under strong reactions alone does not impose beta equilibrium.

A beta particle is an electron or Positron emitted in beta decay. It has the same intrinsic properties as an electron or Positron produced by another process; the name identifies its origin rather than a new particle species.

Unlike a specified two-body alpha transition, ordinary beta emission shares available energy with a neutrino and daughter recoil. The emitted beta particles therefore have a continuous range of kinetic energies. In an applied magnetic field, electrons and positrons curve in opposite senses for the same incident direction. Detector response, energy loss in the sample and collection geometry modify the measured distribution.

An energetically allowed weak nuclear transition converts a proton into a neutron, emitting a positron and electron neutrino. Positron annihilation deposits additional electromagnetic energy, while the neutrino can escape. These transitions are steps of the CNO cycle and the pp III branch; an isolated free proton cannot undergo this decay.

Why can a star shine for so long, and why do hotter stellar cores favor different nuclear reactions? A useful theory must supply both an adequate energy reservoir and the right stellar energy-generation rate. Nuclear binding energy supplies the reservoir; the thermonuclear reaction rate, stellar composition and stellar structure determine how quickly it is spent. The proton–proton chain and CNO cycle are two routes for hydrogen burning with very different temperature sensitivities.

In his 1967 lecture, Hans Albrecht Bethe contrasted the short Kelvin-Helmholtz cooling time with long ages inferred from terrestrial and stellar evidence.^[ref]

For an original solar-scale estimate, choose mass $M=1.99\times 10^{30}\mathrm{kg}$, radius $R=6.96\times 10^8\mathrm{m}$ and luminosity $L=3.83\times 10^{26}\mathrm{W}$. The characteristic Kelvin-Helmholtz cooling time $G{M}^2/(RL)$ is about $31\mathrm{Myr}$; the precise gravitational reservoir has a structure-dependent coefficient. If a fraction $f=0.10$ of the mass can burn its initial hydrogen mass fraction $X=0.70$, with a chosen rest-energy conversion fraction $\eta =0.007$, the fuel estimate isThis assumes fixed luminosity and neglects neutrino losses. It demonstrates the reservoir advantage, rather than predicting the Sun's age or its full stellar evolution. Having enough fuel still does not identify a reaction: the fuel must release energy at a rate compatible with hydrostatic equilibrium and radiative transfer.

Hans Albrecht Bethe and Charles Louis Critchfield calculated deuterium formation from two protons in 1938, combining quantum tunnelling with a weak conversion of a proton into a neutron. Their calculated nuclear reaction cross-section was a theoretical input to hydrogen burning.^[ref] In 1939, Hans Albrecht Bethe analysed the catalytic carbon–nitrogen route and compared required stellar core temperatures with stellar structure estimates in Table VIII. His reported solar agreement used historical abundance and structure assumptions; it should not be read as a modern demonstration that the CNO cycle dominates the Sun.^[ref]

Hans Albrecht Bethe's 1967 lecture credits Carl Friedrich von Weizsäcker's independent 1938 carbon–nitrogen cycle discovery, distinguishing it from calculation of rates and temperature dependence.^[ref] The 1967 Nobel Prize in Physics recognized Hans Albrecht Bethe's contributions to nuclear reaction theory, especially stellar energy production.^[ref]

Laboratory nuclear reaction cross-sections were inputs, not measurements of an artificial star. The 1939 paper converted thick-target yields to nuclear reaction cross-sections using a range–energy relation and tabulated capture data.^[ref] A concrete apparatus example is the Cockcroft-Walton lithium disintegration experiment, with an accelerated proton beam, lithium target, zinc sulfide screen and beam-blocking control. Its nuclear reaction differs from both stellar burning routes. The 1967 lecture stresses extrapolation below laboratory access and tests for nearby nuclear levels.^[ref]

A blazar is an active galactic nucleus whose relativistic jet is viewed close to its direction of motion. Relativistic beaming enhances the apparent radiation from approaching material and changes observed variability timescales. Its extreme brightness is therefore affected by orientation as well as by the power supplied by black-hole accretion.

A source's brightness and spectrum do not directly identify the particles responsible for every emission component. Radio through gamma-ray observations and their timing help distinguish candidate mechanisms, while TXS 0506+056 illustrates the additional information supplied by a possible association with high-energy neutrinos.

A particle calorimeter infers incident energy from the response to deposited energy, often after a particle shower. Segmentation supplies directional information relative to the collision position. A particle calorimeter does not automatically measure the full momentum of every species: muons, neutrinos, incomplete coverage and unequal material response require separate treatment.

Carlo Rubbia helped establish the experimental existence of the massive carriers of the weak interaction, the W boson and Z boson. His lecture explains how proton–antiproton collisions produced candidate events whose energetic leptons and reconstructed kinematics distinguished them from abundant hadronic backgrounds. For decays involving a neutrino, missing transverse momentum supplied information about an unseen particle. The discovery connected electroweak theory with identifiable short-lived particles in a collider detector.^[ref]

A physicist.^[ref]

For a massless incident neutrino and a stationary target electron, the invariant squared center-of-mass energy is $s=m_e^2+2m_e{E}_{\nu }$ in natural units. Production of a charged lepton of mass $m_{\ell }$ and a massless neutrino requires $s\ge m_{\ell }^2$, giving the displayed threshold. For the electron flavour the threshold is zero; for heavier charged leptons it is enhanced by the small stationary-target mass.

A lepton with nonzero electric charge, such as an electron or muon; neutrinos are electrically neutral.

A singular value decomposition of the charged-lepton Yukawa matrix uses independent unitary rotations of left- and right-handed leptons. Their gauge-covariant kinetic terms are unchanged because each rotation mixes identical Standard Model representations. After electroweak symmetry breaking, the nonnegative singular values give Dirac masses $m_i=y_{i}v/\sqrt{2}$ and diagonal Higgs boson couplings $m_i/v$. When the neutrinos are massless, rotating their left-handed fields with the charged partners preserves the diagonal weak charged current.

At leading order, for final fermions much lighter than the Z boson, the partial decay width is proportional to $N_c(|g_L{|}^2+|g_R{|}^2)$. Here $N_c$ is the final-state color multiplicity in a decay width, and $g_L=T_{3L}-Q{\sin }^2{\theta }_W$, $g_R=T_{3R}-Q{\sin }^2{\theta }_W$ are the dimensionless left- and right-chirality couplings. The common normalization cancels in ratios.

For an electron, $g_L=-1/2+{\sin }^2{\theta }_W$, $g_R={\sin }^2{\theta }_W$. For one active neutrino flavour, $g_L=1/2$, $g_R=0$. ThereforeThere is no extra flavour factor for a single specified neutrino species. Summing the three active species produces three times that invisible partial width, within the same massless approximation.

A branch of the CNO cycle proceeds through proton captures on nitrogen-15 and oxygen-16, beta-plus decay of fluorine-17, and ${}^{17}\mathrm{O}(p,\alpha ){}^{14}\mathrm{N}$. Returning through oxygen-15 and nitrogen-15 closes the cycle. It also catalyzes the conversion of four protons into helium-4, with branch-dependent neutrino loss.

The process by which a stalled outgoing shock in a collapsing stellar core regains sufficient energy to expel outer material. Neutrino heating and multidimensional flow can contribute, while dissociation and radiation drain energy. Collapse does not guarantee a successful ordinary supernova.

The Cosmic neutrino background is the relic population of neutrinos left after thermal decoupling in cosmology. As the universe expands, their momenta redshift; the decoupled distribution retains a temperature parameter proportional to the inverse scale factor, even after massive neutrinos become nonrelativistic.

The standard ideal temperature ratio follows from cosmological entropy conservation. Assume instantaneous neutrino decoupling before electron-positron annihilation and negligible chemical potentials. The coupled photon–electron–Positron sector initially has entropy degrees of freedom $2+(7/8)4=11/2$, dropping to two after annihilation. Conserving its comoving entropy heats the photons relative to the freely redshifting neutrinos, givingFor example, a photon temperature of $2.725\mathrm{K}$ corresponds to a relic-neutrino temperature parameter near $1.95\mathrm{K}$ in this idealization. Residual interactions during non-instantaneous neutrino decoupling slightly modify the distribution, so the simple ratio is an approximation.^[ref]

The cosmic neutrino background last-scattering surface is the locus from which relic neutrinos that reach an observer underwent their final appreciable scattering. Although neutrino decoupling occurs before photon decoupling, a massive neutrino travels slower than light after becoming nonrelativistic, so its last-scattering surface need not be farther away than the cosmic microwave background last-scattering surface.