Parity violation in weak interactions flipped our understanding of nature's symmetry. It revealed that the universe distinguishes left from right, challenging long-held beliefs about fundamental forces. This discovery reshaped particle physics and our view of the cosmos.

Helicity, the alignment of a particle's spin with its motion, became crucial in weak interactions. The Standard Model shows weak forces only interact with left-handed particles and right-handed antiparticles, highlighting the unique nature of this fundamental force.

Parity Conservation

Fundamentals of Parity

• Parity inverts spatial coordinates of a system creating its mirror image
• Quantum mechanics represents parity with operator P having eigenvalues +1 (even parity) or -1 (odd parity)
• Strong and electromagnetic interactions conserve parity laws remain unchanged under parity transformations
• Parity conservation leads to selection rules in particle decays and transitions (beta decay)
• Intrinsic parity of particles determines wavefunction transformation under parity operations
• Total parity of isolated system remains constant over time in strong and electromagnetic interactions

Applications of Parity Conservation

• Particle physics uses parity conservation to predict allowed and forbidden decay modes
• Nuclear physics employs parity conservation in understanding nuclear structure and transitions
• Atomic physics utilizes parity conservation in spectroscopic selection rules
• Molecular physics applies parity conservation to rotational and vibrational spectra analysis
• Condensed matter physics leverages parity conservation in crystal structure studies
• Astrophysics considers parity conservation in stellar evolution models and nucleosynthesis

Parity Violation in Weak Interactions

Discovery of Parity Violation

• τ-θ puzzle in 1950s two particles with identical properties decayed into states with different parities
• T.D. Lee and C.N. Yang proposed parity violation in weak interactions in 1956 resolving τ-θ puzzle
• C.S. Wu and colleagues experimentally verified parity violation in 1957 using beta decay of polarized cobalt-60 nuclei
• Wu experiment showed preferential direction for electron emission in beta decay contradicting expected symmetry
• Discovery fundamentally shifted understanding of weak interactions and universal symmetries
• Parity violation observation contributed to V-A (Vector minus Axial vector) theory of weak interactions development

Implications of Parity Violation

• Weak interactions violate mirror symmetry distinguishing between left and right
• Neutrinos produced in weak interactions always left-handed antineutrinos always right-handed
• Parity violation requires reassessment of fundamental symmetries in particle physics
• Discovery led to exploration of other symmetry violations (charge conjugation, time reversal)
• Parity violation crucial in understanding matter-antimatter asymmetry in the universe
• Weak interaction structure fundamentally different from other fundamental forces due to parity violation

Helicity in Weak Interactions

Helicity Fundamentals

• Helicity defined as projection of particle's spin along motion direction
• Right-handed particles have positive helicity left-handed particles have negative helicity
• Standard Model weak interactions couple exclusively to left-handed particles and right-handed antiparticles
• Massive particles' helicity frame-dependent can be reversed by changing reference frame
• Massless particles (photons) have frame-independent helicity equivalent to chirality
• Neutrino oscillations imply neutrino mass complicating helicity picture in weak interactions

Helicity in Particle Physics

• Weak interactions demonstrate maximal parity violation coupling only to specific helicity states
• Helicity crucial in understanding neutrino properties and interactions
• Particle accelerator experiments use helicity to study weak interaction processes
• Helicity considerations important in designing detectors for neutrino experiments
• Helicity plays role in theories beyond Standard Model (supersymmetry, extra dimensions)
• Cosmology uses helicity in studying early universe processes and particle interactions

Implications of Parity Violation

Theoretical Developments

• V-A theory developed describing weak interactions as combination of vector (V) and axial vector (A) currents
• V-A structure explains observed maximal parity violation and coupling to left-handed particles
• Parity violation requires charge conjugation (C) symmetry violation leading to combined CP symmetry
• Parity violation contributed to electroweak theory formulation unifying electromagnetic and weak interactions
• Weak interaction structure necessitates W and Z bosons as weak force mediators
• Parity violation influences development of grand unified theories and quantum gravity models

Experimental Consequences

• Beta decay rates affected by parity violation leading to new experimental techniques
• Atomic parity violation experiments probe weak nuclear force at low energies
• Neutrino physics experiments designed to account for helicity and parity violation effects
• Particle collider experiments use parity violation to study electroweak processes
• Nuclear physics experiments investigate parity-violating effects in nuclei
• Precision measurements of parity violation test Standard Model predictions and search for new physics