quantity

decay constant

A number measuring the strength of a meson's binding, related to its probability of decaying into photons.
19 related articles · 2 formulas

Description

The decay constant of a meson quantifies the intrinsic strength of its coupling to the vacuum, which in turn determines how readily the meson can decay into lighter particles such as photons. It is a fundamental parameter in particle physics, appearing in the theoretical expressions for decay rates and branching ratios. For example, the decay constant of the pion is a key input in calculations of weak interactions and in tests of the Standard Model.

History

The concept was introduced in the 1950s and 1960s as part of the development of current algebra and the theory of strong interactions, with the pion decay constant being a central quantity in the work of Gell-Mann, Lévy, and others.

How it works

In quantum field theory, a meson is a bound state of a quark and an antiquark. The decay constant measures the amplitude for the meson to annihilate into the vacuum, effectively setting the scale of the meson's coupling to the weak or electromagnetic currents. A larger decay constant implies a stronger overlap between the meson's wavefunction and the point-like annihilation vertex, leading to a higher probability of decay into photons or other particles.

In practice

Decay constants are used to predict and interpret experimental results in particle accelerators, such as the measurement of rare meson decays to test the Standard Model and search for new physics.

Fun fact

The pion decay constant is approximately 130 MeV, a value that sets the scale for the strength of the strong force in low-energy processes.

Concept graph →

Formulas

$$F(x) = F_0 e^{-\alpha x}$$
Exponential decay describes decrease proportional to current value.
What is in the formula
Fvariablevalue of the decaying quantity at position x — amplitude varies
F_0variableinitial value at x = 0 — amplitude varies
xvariableindependent variable (position, time, etc.) — position metre
αvariabledecay constant (rate of decay per unit x) — decay constant per metre
$$t = \frac{1}{\lambda} \ln \left( \frac{N_0}{N} \right)$$
Time elapsed from initial to current isotope ratio.
What is in the formula
tvariableelapsed time — time second
λvariabledecay constant — decay constant per second
N_0variableinitial number of radioactive nuclei — number of nuclei
Nvariablecurrent number of radioactive nuclei — number of nuclei
lnoperatornatural logarithm of the ratio — natural logarithm

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