⚛️Particle Physics Unit 5 – Weak Interactions & Electroweak Theory

Key Concepts

• Weak force one of the four fundamental forces of nature alongside strong force, electromagnetic force, and gravity
• Responsible for radioactive decay and plays a crucial role in nuclear processes (nuclear fusion in the Sun)
• Mediated by the exchange of W and Z bosons, which are massive gauge bosons
• Weak interactions involve the change of flavor of quarks and leptons, allowing for processes like beta decay
• Electroweak theory unifies the electromagnetic and weak interactions into a single framework
  • Developed by Sheldon Glashow, Abdus Salam, and Steven Weinberg in the 1960s
• Parity violation weak interactions do not conserve parity, unlike other fundamental forces
• Charge-parity (CP) violation weak interactions are the only known source of CP violation in the Standard Model

Historical Background

• In the 1930s, Enrico Fermi developed a theory of beta decay, which laid the foundation for understanding weak interactions
• The parity violation in weak interactions was discovered in 1956 by Chien-Shiung Wu and collaborators
• In the 1960s, Glashow, Salam, and Weinberg independently developed the electroweak theory, unifying the electromagnetic and weak forces
  • They were awarded the Nobel Prize in Physics in 1979 for their contributions
• The W and Z bosons, predicted by the electroweak theory, were discovered in 1983 at CERN
• The discovery of the Higgs boson in 2012 at the Large Hadron Collider (LHC) provided further confirmation of the electroweak theory

Weak Force Carriers

• W bosons ($W^+$ and $W^-$) mediate charged-current weak interactions, which change the flavor of quarks and leptons
  • $W^+$ boson has a positive electric charge, while $W^-$ boson has a negative electric charge
  • Mass of W bosons approximately 80.4 GeV/c², about 80 times the mass of a proton
• Z boson ($Z^0$) mediates neutral-current weak interactions, which do not change the flavor of particles
  • $Z^0$ boson has no electric charge
  • Mass of Z boson approximately 91.2 GeV/c², slightly heavier than the W bosons
• The large masses of the W and Z bosons are a consequence of the Higgs mechanism, which breaks the electroweak symmetry and gives rise to their masses

Weak Interactions

• Weak interactions can change the flavor of quarks and leptons, allowing for processes like beta decay and neutrino interactions
• Beta decay involves the emission of an electron (or positron) and an antineutrino (or neutrino) due to the conversion of a neutron into a proton (or vice versa)
  • Mediated by the $W^-$ boson ($n \rightarrow p + e^- + \bar{\nu}_e$)
• Neutrino interactions can be either charged-current (mediated by W bosons) or neutral-current (mediated by Z bosons)
  • Example of a charged-current neutrino interaction: $\nu_e + n \rightarrow p + e^-$
• Weak interactions also play a role in the decay of heavy quarks (charm, bottom, top) and leptons (muon, tau)
• The strength of weak interactions is much weaker than the strong and electromagnetic interactions, leading to longer lifetimes for particles that decay via the weak force

Electroweak Unification

• The electroweak theory unifies the electromagnetic and weak interactions into a single framework
• At high energies (above $\sim$ 100 GeV), the electromagnetic and weak forces have equal strength and are described by a single gauge symmetry ($SU(2)_L \times U(1)_Y$)
  • $SU(2)_L$ represents the weak isospin symmetry, and $U(1)_Y$ represents the weak hypercharge symmetry
• The Higgs mechanism breaks the electroweak symmetry at lower energies, giving rise to the distinct electromagnetic and weak forces observed at everyday scales
  • The Higgs field acquires a non-zero vacuum expectation value, which breaks the $SU(2)_L \times U(1)_Y$ symmetry to the $U(1)_{EM}$ symmetry of electromagnetism
• The electroweak theory predicts the existence of the W and Z bosons, as well as the Higgs boson
• The mixing of the $SU(2)_L$ and $U(1)_Y$ gauge fields gives rise to the photon ($\gamma$) and the Z boson, while the W bosons are the gauge bosons of the $SU(2)_L$ symmetry

Experimental Evidence

• The discovery of parity violation in weak interactions (1956) provided early evidence for the unique nature of the weak force
• The observation of neutral currents in neutrino interactions (1973) at CERN supported the existence of the Z boson
• The discovery of the W and Z bosons (1983) at CERN was a major triumph for the electroweak theory
  • Masses and decay properties of the W and Z bosons were found to be consistent with theoretical predictions
• Precision measurements of the Z boson resonance at the Large Electron-Positron Collider (LEP) at CERN (1989-2000) provided stringent tests of the electroweak theory
• The discovery of the Higgs boson (2012) at the LHC confirmed the Higgs mechanism and the role of electroweak symmetry breaking in the Standard Model
• Ongoing experiments continue to test the predictions of the electroweak theory and search for possible deviations that could hint at new physics beyond the Standard Model

Mathematical Framework

• The electroweak theory is a non-Abelian gauge theory based on the $SU(2)_L \times U(1)_Y$ symmetry group
  • $SU(2)_L$ represents the weak isospin symmetry, and $U(1)_Y$ represents the weak hypercharge symmetry
• The Lagrangian of the electroweak theory includes kinetic terms for the gauge fields, the Higgs field, and the fermion fields, as well as interaction terms between these fields
• The Higgs mechanism is incorporated through the Higgs potential, which leads to the spontaneous breaking of the electroweak symmetry
  • The Higgs field acquires a non-zero vacuum expectation value, $v \approx 246$ GeV
• The mixing of the $SU(2)_L$ and $U(1)_Y$ gauge fields is described by the weak mixing angle, $\theta_W$, which relates the masses of the W and Z bosons: $\cos\theta_W = M_W / M_Z$
• The coupling constants of the electromagnetic and weak interactions are related by: $e = g \sin\theta_W = g' \cos\theta_W$, where $g$ and $g'$ are the coupling constants of the $SU(2)_L$ and $U(1)_Y$ gauge groups, respectively
• Feynman diagrams are used to calculate the probabilities of various electroweak processes, taking into account the propagators of the gauge bosons and the vertices describing the interactions between particles

Applications and Implications

• Understanding weak interactions is crucial for describing various nuclear processes, such as nuclear beta decay and nuclear fusion in the Sun
• The electroweak theory is a key component of the Standard Model of particle physics, which describes the properties and interactions of elementary particles
• The discovery of the Higgs boson has opened up new avenues for studying the properties of the Higgs field and its role in the universe
  • The Higgs mechanism not only gives mass to the W and Z bosons but also to fermions through Yukawa interactions
• CP violation in weak interactions is thought to play a role in the observed matter-antimatter asymmetry in the universe
  • The amount of CP violation in the Standard Model is insufficient to explain the observed asymmetry, suggesting the need for new sources of CP violation beyond the Standard Model
• The electroweak theory has been successfully tested to high precision, but there are still open questions and potential hints of new physics
  • The nature of neutrino masses and mixing, which are not explained by the Standard Model
  • The possible existence of additional Higgs bosons or new gauge bosons at higher energies
• Ongoing and future experiments at the LHC and other facilities aim to further test the electroweak theory, search for new physics, and shed light on these open questions