A quantity is subject to exponential decay if it decreases at a rate proportional to its current value. Symbolically, this process can be expressed by the following differential equation, where N is the quantity and λ (lambda) is a positive rate called the exponential decay constant, disintegration constant, rate constant, or transformation constant:
The solution to this equation (see derivation below) is:
In particle physics, a pion (/ˈpaɪ.ɒn/, PIE-on) or pi meson, denoted with the Greek letter pi (π), is any of three subatomic particles: π
, π
, and π
. Each pion consists of a quark and an antiquark and is therefore a meson. Pions are the lightest mesons and, more generally, the lightest hadrons. They are unstable, with the charged pions π
and π
decaying after a mean lifetime of 26.033 nanoseconds (2.6033×10 seconds), and the neutral pion π
decaying after a much shorter lifetime of 85 attoseconds (8.5×10 seconds). Charged pions most often decay into muons and muon neutrinos, while neutral pions generally decay into gamma rays.
The exchange of virtual pions, along with vector, rho and omega mesons, provides an explanation for the residual strong force between nucleons. Pions are not produced in radioactive decay, but commonly are in high-energy collisions between hadrons. Pions also result from some matter–antimatter annihilation events. All types of pions are also produced in natural processes when high-energy cosmic-ray protons and other hadronic cosmic-ray components interact with matter in Earth's atmosphere. In 2013, the detection of characteristic gamma rays originating from the decay of neutral pions in two supernova remnants has shown that pions are produced copiously after supernovas, most probably in conjunction with production of high-energy protons that are detected on Earth as cosmic rays.
A muon (/ˈm(j)uː.ɒn/ M(Y)OO-on; from the Greek letter mu (μ) used to represent it) is an elementary particle similar to the electron, with an electric charge of −1 e and a spin of 1/2 ħ, but with a much greater mass. It is classified as a lepton. As with other leptons, the muon is not thought to be composed of any simpler particles.
The muon is an unstable subatomic particle with a mean lifetime of 2.2 μs, much longer than many other subatomic particles. As with the decay of the free neutron (with a lifetime around 15 minutes), muon decay is slow (by subatomic standards) because the decay is mediated only by the weak interaction (rather than the more powerful strong interaction or electromagnetic interaction), and because the mass difference between the muon and the set of its decay products is small, providing few kinetic degrees of freedom for decay. Muon decay almost always produces at least three particles, which must include an electron of the same charge as the muon and two types of neutrinos.
A free neutron refers to a neutron that is not part of an atomic nucleus. When embedded in a stable nuclide, neutrons have not been observed to decay. Free neutrons, however, decay with a mean lifetime of 877.75+0.50
−0.44 s or 879.6±0.8 s (about 14 min and 37.75 s or 39.6 s, depending on the specific measurement technique). This corresponds to a half-life of 611±1 s (about 10 min, 11 s).
The free neutron decays primarily by beta decay, with small probability of other channels. Considering the most common decay and only the stable resultant products the process may be described:
The sigma baryons are a family of subatomic hadron particles which have two quarks from the first flavour generation (up and / or down quarks), and a third quark from a higher flavour generation, in a combination where the wavefunction sign remains constant when any two quark flavours are swapped. They are thus baryons, with total isospin of 1, and can either be neutral or have an elementary charge of +2, +1, 0, or −1. They are closely related to the lambda baryons, which differ only in the wavefunction's behaviour upon flavour exchange.
The third quark can hence be either a strange (symbols Σ
, Σ
, Σ
), a charm (symbols Σ
c, Σ
c, Σ
c), a bottom (symbols Σ
b, Σ
b, Σ
b) or a top (symbols Σ
t, Σ
t, Σ
t) quark. However, the top sigmas are expected to never be observed, since the Standard Model predicts the mean lifetime of top quarks to be roughly 5×10 s. This is about 20 times shorter than the timescale for strong interactions, and therefore it does not form hadrons.