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Chien-Shiung Wu and collaborators tested parity conservation by measuring the beta decay of oriented cobalt-60 nuclei at very low temperature. Their apparatus placed a beta counter inside a demagnetization cryostat and used the accompanying gamma ray anisotropy to monitor nuclear orientation. The emitted electrons favored one direction relative to the nuclear spin. Because parity reverses momentum while leaving angular momentum unchanged, that directional asymmetry distinguishes a process from its mirror image and demonstrated parity violation in the weak interaction.^[ref]

A physicist.^[ref]

In 1956, Tsung-Dao Lee and Chen Ning Yang examined the evidence for parity conservation in the weak interaction. Their paper, Question of Parity Conservation in Weak Interactions, distinguished an untested assumption from an established experimental result and proposed comparing electron emission along opposite directions relative to oriented nuclear spins, explicitly considering cobalt-60. It proposed a test; it did not report the later Wu experiment.^[ref]

The conceptual improvement is the choice of observable. An angle between two polar vectors is preserved by spatial reflection; its distribution can conceal parity violation. An angle between an axial vector and a polar vector changes to its supplement. Thus a spin-resolved directional measurement asks a different question from an unpolarized total decay rate.

Parity violation means that a physical law fails to be invariant under the spatial reflection represented by the parity operator. A process and its fully inverted counterpart can then have different probabilities. For beta-minus decay with polarized parent atomic nuclei, a nonzero correlation between nuclear spin and emitted electron momentum is such a test. Rotational symmetry alone allows this correlation: a pseudoscalar is unchanged by proper rotations but changes sign under spatial reflection.

Chirality distinguishes the two inequivalent Weyl spinor representations of the proper Lorentz group. For a Dirac spinor, define ${\gamma }^5=i{\gamma }^0{\gamma }^1{\gamma }^2{\gamma }^3$ and the chiral projectorsThey satisfy $P_L{P}_R=0$ and $P_L+P_R=I$. Proper Lorentz transformations preserve each chiral representation, whereas parity exchanges them. Helicity instead measures the projection of spin angular momentum along momentum. For a massive particle it can change under a boost that overtakes the particle, so it must not be identified with chirality. For massless positive-energy particles the left-chiral field annihilates negative-helicity particles and creates positive-helicity antiparticles.

The Standard Model is a chiral gauge theory: left- and right-chiral fields have different gauge group representations. In the convention $Q=T_3+Y$, one generation containsThe minimal field content has no right-handed neutrino. A sterile right-handed field is a possible extension, not a required member of that minimal list. The table displays weak isospin, hypercharge and color charge assignments, not assignments of massive-particle helicity.

The weak charged current contains $\bar{\nu }{\gamma }^{\mu }{P}_{L}e{W}_{\mu }^{+}$ and its Hermitian conjugate, with coupling $g/\sqrt{2}$. Only the left-chiral lepton doublet participates, giving parity violation. Both chiralities can couple to the Z boson, but their coefficients differ:Here $T_3$ is that of the left-chiral component. For the electron, it is $-1/2$. The photon and gluon couplings of a charged massive fermion are vectorlike; this does not make the full electroweak interaction vectorlike.

A bare Dirac mass term $m\bar{\psi }\psi =m({\bar{\psi }}_L{\psi }_R+{\bar{\psi }}_R{\psi }_L)$ joins the two chiral representations. Their different electroweak quantum numbers forbid that term before electroweak symmetry breaking. A Yukawa interaction, such as $-y_e{\bar{L}}_{L}H{e}_R+h.c.$, is gauge invariant; the Higgs doublet expectation value then gives $m_e=y_{e}v/\sqrt{2}$. Up-type quarks use the conjugate doublet. Thus chirality explains the weak charge assignments, their parity violation, and why masses arise through the Higgs mechanism. The consistency of these chiral assignments also requires Standard Model anomaly cancellation.

parity reverses spatial coordinates and polar vectors such as momentum, while leaving axial vectors such as angular momentum unchanged. The correlation $\mathbf{J}\cdot {\mathbf{p}}_e$ is therefore parity odd. For polarized beta-emitting nuclei one can measurewhere $\theta$ is measured from nuclear polarization, $\mathcal{P}$ its magnitude and $A$ a decay-dependent coefficient. A nonzero spin–momentum asymmetry is incompatible with parity invariance.

The cobalt-60 experiment polarized nuclei at low temperature and compared beta emission along and opposite the polarization axis. Preferential emission on one side established weak-interaction parity violation. Reversing polarization tests whether the asymmetry follows nuclear orientation; warming the sample removes polarization, while gamma anisotropy monitors its loss. Detector acceptance, backgrounds and magnetic deflection of charged particles must be separated from a true emission asymmetry.^[ref]

In the modern weak charged current, the V-A interaction couples to left-chiral fermion fields. In the massless limit this selects left-helicity neutrinos and right-helicity antineutrinos. Massive charged leptons need not be pure-helicity states, consistent with the factor $v/c$. Strong and electromagnetic interactions conserve parity to the usual experimental approximation; parity violation alone should not be confused with CP violation or a failure of CPT.

Parity is full spatial reflection, $\mathbf{x}\mapsto -\mathbf{x}$, represented by a parity operator $\mathcal{P}$. A polar vector, such as momentum, reverses, whereas an axial vector, such as spin, does not. A state of definite parity has $\mathcal{P}|\psi ⟩={\eta }_P|\psi ⟩$, with ${\eta }_P=\pm 1$ in the usual convention. A multiparticle state's parity includes both the product of its intrinsic parities and its orbital spatial factor, for example $(-1{)}^L$ for relative orbital angular momentum $L$.

An interaction conserves parity when its dynamics are invariant under this transformation, equivalently $[H,\mathcal{P}]=0$ for a time-independent Hamiltonian. Parity violation means that a process and its fully reflected counterpart need not have the same probability. It is more than a left-right asymmetry in an unreflected laboratory apparatus.

The electromagnetic and strong sectors of the Standard Model conserve parity to the accuracy relevant here, taking the strong-sector Yang-Mills theta term to vanish. The weak charged current selects left-chiral fermions and right-chiral antifermions, as defined by fermion chirality; the reflected right-chiral charged current is not equally present. The neutral weak current also generally has different left- and right-chiral couplings. Consequently the weak sector violates parity; this does not mean that every individual weak decay must have opposite initial and final parity. For a massive particle, helicity and fermion chirality should be distinguished.

For both modes, a leading weak quark transition in $K^{+}=u\bar{s}$ is $\bar{s}\to \bar{u}+W^{+}$, followed by $W^{+}\to u\bar{d}$, with the original $u$ acting as a spectator quark. This produces the four quarks needed for ${\pi }^{+}{\pi }^0$, using the $u\bar{u}$ component of ${\pi }^0$. Producing three pions additionally requires a $d\bar{d}$ pair from strong hadronization. A representative quark-line diagram draws it as gluon emission and splitting.

The three-pion assignment is $u\bar{d}$, $u\bar{d}$, and $d\bar{u}$, matching ${\pi }^{+}{\pi }^{+}{\pi }^{-}$. The extra soft pair creation is a schematic representation of hadronization, not a controlled perturbative prediction of the relative decay rates. Both processes are first order in the effective weak interaction.

There is an explicit error or hypothetical assumption to address: the original PDF assigns $0^{+}$ to all these mesons. Taken literally, the two-pion final state has $L=0$, because all particles have zero spin and the initial $J$ is zero. Its parity is $(+1{)}^2(-1{)}^0=+1$. For three spinless particles, use two Jacobi orbital angular momentum quantum numbers $l,L$. Coupling to total zero requires $l=L$, so the orbital parity $(-1{)}^{l+L}$ is $+1$ and the three-particle parity is also $+1$. Thus under the printed $0^{+}$ assignment, both channels conserve parity.

The named physical pions and kaons are instead pseudoscalar mesons with $J^P=0^{-}$. With those physical assignments,ThereforeThese two opposite-parity final states from the same physical kaon are a classic illustration of parity violation in a weak decay. The physical conclusion requires correcting the printed parity assignment explicitly.

An observable that reverses sign under parity but has a nonzero expectation in a suitably prepared experiment tests parity violation. A polar momentum reverses, whereas an axial spin angular momentum does not. Thus $\mathbf{J}\cdot \mathbf{p}$ and helicity are parity-odd; an apparatus asymmetry must be separated from a physical asymmetry by reversing the preparation or analyser.

In the Wu experiment, polarized cobalt-60 nuclei preferentially emit beta decay electrons in one direction relative to the nuclear spin angular momentum. The distribution contains $A\mathbf{P}\cdot {\mathbf{p}}_e/E_e$; its sign changes under spatial inversion. Reversing the nuclear polarization reverses the observed asymmetry.^[ref]

In the Goldhaber experiment, the sign of the circular polarization of selected gamma rays determines the sign of the neutrino helicity. A preference for negative helicity is parity-odd because spatial inversion would produce the positive-helicity state. This provides a different experimental observable from the electron angular distribution.

The charged two-pion and three-pion channels can be assigned to the same spin-zero kaon by their parent mass and lifetime. For two spinless pions, total angular momentum zero forces their relative orbital angular momentum to zero, so the product of their intrinsic parities givesFor three spinless pions, use Jacobi orbital angular momenta $l,L$. Coupling them to total zero requires $l=L$, and henceThus both channels cannot conserve parity in decays of one parent with a definite parity. The weak decay interaction permits the observed coexistence.

Dalitz plots identify the three-body events, determine their internal kinematics, and allow amplitude and angular-momentum analyses through their populations and resonance structures. Together with the spin and parent-identity evidence, they support the parity assignment. They are not a standalone parity-odd observable: reversing all three momenta leaves every $s_{ij}$, and therefore every point on the plot, unchanged. A flat distribution by itself cannot establish parity violation without the channel and spin information.

For the Pole forward-backward asymmetry for charged leptons, integrating the normalized distribution over the two hemispheres cancels the even term in the numerator. Since ${\int }_{-1}^1(1+z^2)dz=8/3$ and ${\int }_0^{1}zdz-{\int }_{-1}^{0}zdz=1$,Within this single-$Z$, tree-level model, a nonzero asymmetry requires unequal left/right coupling magnitudes, demonstrating parity violation in the vertices. For $g_L=g_R$ the odd angular term vanishes and $A_{FB}=0$; equal magnitudes with opposite signs also give zero. This inference is process-specific: a forward-backward asymmetry is not universally a parity-odd observable, since reversing both beam and outgoing momenta leaves their relative Angle unchanged. Purely electromagnetic Bhabha scattering is a concrete parity-conserving process with a forward-peaked, asymmetric distribution.

For the supplied ${\sin }^2{\theta }_W=0.23153$,The measurement differs by $0.0188-0.01620=0.00260$, or $0.79$ times its quoted uncertainty of $0.0033$, so it is consistent with the prediction. Statistical fluctuations alone preclude exact equality; photon exchange, initial-state radiation and electroweak radiative corrections also modify the idealized pure-resonance prediction and provide physical reasons for small differences.

For a negative muon with rest-frame spin vector $\mathbf{s}$, the leading massless-electron distribution is $d\Gamma /(dxd\Omega )=G_F^2{m}_{\mu }^5{x}^2[(3-2x)+(1-2x)\hat{\mathbf{k}}\cdot \mathbf{s}]/(384{\pi }^4)$, where $x=2E_e/m_{\mu }\in [0,1]$. Its final-spin sum is $64G_F^2(k\cdot q^{\prime })(q\cdot (p-m_{\mu }s))$. The spin vector is axial whereas the electron direction is polar, so their scalar product reverses under parity. Its occurrence demonstrates parity violation by the left-chiral weak charged current.

For a pure resonant Z boson with negligible fermion masses, ${\mathcal{A}}_f=(|g_L^f{|}^2-|g_R^f{|}^2)/(|g_L^f{|}^2+|g_R^f{|}^2)$ and $A_{FB}=3{\mathcal{A}}_e{\mathcal{A}}_f/4$. Lepton universality makes this $3{\mathcal{A}}_{\ell }^2/4$ for charged leptons. A nonzero value diagnoses parity violation within this single-resonance approximation; a general angular forward-backward asymmetry need not be parity odd.

The Wu experiment was performed by Chien-Shiung Wu, Ernest Ambler, Raymond Webster Hayward, Dale D. Hoppes, and Ralph Percy Hudson; its 1957 report was Experimental Test of Parity Conservation in Beta Decay. Their experiment supplied the evidence that the Lee-Yang proposal for a parity test had called for.^[ref]

A cobalt-60 surface layer on a cerium magnesium nitrate crystal was cooled by adiabatic demagnetization; a solenoid's magnetic field polarized its atomic nuclei. An internal anthracene counter detected electrons by particle scintillation; a light pipe carried flashes to a photomultiplier. Polar and equatorial gamma ray counters monitored nuclear polarization and effective temperature; bulk thermometry could miss surface heating.^[ref]

Reversing nuclear polarization reversed the electron excess; warming erased it with gamma ray anisotropy. Warm rates were field-independent. Cooling-field reversal checked remanence; poorly polarized sources checked magnetic deflection. Electrons favored the direction opposite spin.^[ref]

The gamma ray anisotropy diagnoses the preparation; the electron asymmetry diagnoses parity violation. These are different jobs. A directionally uneven gamma ray signal alone need not violate parity conservation: a distribution even in the cosine of the angle can distinguish an axis from its perpendicular without distinguishing its two ends. The spin-momentum correlation instead distinguishes those ends.

The inference requires control of changes in detection efficiency, electron transport and nuclear polarization. A fixed detector under spin reversal avoids physically exchanging detector positions, but still requires checks for magnetic field effects. The result establishes parity violation in this weak interaction process. A precise microscopic coupling requires more information than the existence or sign of a counting asymmetry; the following model makes that distinction explicit.