Fermi constant

Fermi constant. The Fermi constant is a fundamental coupling constant that quantifies the strength of the weak interaction in particle physics. It is named for the pioneering physicist Enrico Fermi, who formulated an early theory of beta decay. This constant plays a central role in the Standard Model of particle physics, governing processes like muon decay and setting the scale for the electroweak interaction.

Definition and value

The Fermi constant, denoted G_F, is defined through the Fermi theory of weak decays. Its most precise determination comes from measurements of the lifetime of the muon, a fundamental lepton. The Particle Data Group provides the recommended value of approximately 1.166 × 10⁻⁵ GeV⁻². This value is extracted with high precision from experiments at facilities like the Brookhaven National Laboratory and CERN. The constant has dimensions of inverse energy squared, reflecting its origin in a four-fermion interaction within the historical Fermi theory.

Role in the Standard Model

Within the modern Standard Model, the Fermi constant is not an independent parameter but is derived from more fundamental quantities. It is intimately related to the mass of the W boson and the vacuum expectation value of the Higgs field. Specifically, it is connected to the coupling constant of the SU(2) gauge group and the electroweak mixing angle. This relationship is a key prediction of the Glashow–Weinberg–Salam model, unifying the electromagnetic interaction and the weak interaction. The constant sets the strength for charged-current interactions, governing processes like neutron decay and nuclear fusion in the Sun.

Relation to other constants

The Fermi constant is fundamentally linked to other pivotal constants in physics. Through the electroweak theory, it is related to the fine-structure constant and the masses of the W and Z bosons. The Cabibbo–Kobayashi–Maskawa matrix elements, which describe quark mixing, also appear in calculations involving this constant for processes like kaon decay. Furthermore, its value influences the predicted rate of neutrino scattering and is crucial in calculations for big bang nucleosynthesis. Comparisons with the gravitational constant highlight the vast difference in strength between the weak force and gravity.

Measurement and determination

The most accurate determinations of the Fermi constant come from studying the muon decay process. Precision experiments measure the muon lifetime with extraordinary accuracy using muon beams at laboratories like the Paul Scherrer Institute. These measurements are sensitive to QED radiative corrections, which must be calculated with high precision. Alternative determinations come from studies of beta decay in nuclei like tritium and from measurements of the parity-violating asymmetry in electron scattering. The consistency of values from different processes, such as those measured at SLAC National Accelerator Laboratory, provides a critical test of the Standard Model.

Historical context

The concept originated with Enrico Fermi's 1934 theory of beta decay, which modeled the process as a direct four-particle interaction at a single point in spacetime. This phenomenological theory was highly successful for decades. The development of the V−A theory by Richard Feynman, Murray Gell-Mann, Robert Marshak, and George Sudarshan refined its form. The true nature of the constant as an effective parameter emerging from the exchange of a massive W boson was revealed with the establishment of the electroweak theory by Sheldon Glashow, Abdus Salam, and Steven Weinberg. This theoretical advancement, later confirmed by experiments at the Super Proton Synchrotron, embedded the constant within the deeper framework of gauge theory.

Category:Physical constants Category:Particle physics Category:Enrico Fermi