# Neutron decay

Neutrinos undergo only weak interactions, which are associated with slow decays. For example, a neutron (electric charge 0) outside a nucleus (a “free” neutron) decays due to the weak interaction into a proton (electric charge +1), an electron (electric charge -1), and an (anti)neutrino (electric charge 0) with a mean life of about 15 minutes:

$n \Rightarrow p^+ + e^- + \overline{\nu}$

At the other extreme, decays associated with the strong/nuclear interaction typically have a lifetime of about the time required for light to move the distance of a diameter of a proton, about (3 × 10–15 m) / (3 × 108 m/s), about 1 × 10–23 seconds. Any decay that takes a lot longer than 1 × 10–23 seconds is typically an indication that it is associated with the weak interaction (though some “electromagnetic” decays may also have long mean lives).

For example, the positively charged pion decays into a low-energy positive muon (a heavy positron — a heavy anti-electron) and a low-energy neutrino with a mean life of about 25 nanoseconds (25 × 10–9 seconds), a time vastly longer than 1 × 10–23 seconds, and this is a weak decay. (The energies are low because the pion mass is only slightly larger than the muon mass).

$\pi^+ \Rightarrow \mu^+ + \nu$

It is pion decay that is the major source of neutrinos made in accelerators. The pions are made at high energy and move at high speed, with the result that the neutrinos emitted in the direction of motion of the pion get thrown forward with high energy. This is the mechanism for producing copious beams of high-energy neutrinos. There are low-energy neutrinos produced by nuclear reactors and by fusion reactions in our Sun.

One can say that there are three classes of fundamental particles: (1) particles made of quarks, called hadrons, including protons, neutrons, and pions, (2) particles that are not made of quarks, called leptons, including electrons, muons, and neutrinos, and (3) “glue” particles that mediate interactions among particles (for example, the photon mediates electromagnetic interactions). There exist purely leptonic interactions and decays, such as muon decay into electron, neutrino, and antineutrino, with a mean life of about 2 microseconds (2 × 10–6 seconds, a long time in this scheme of things). There also exist semileptonic weak interactions such as neutron decay, in which the neutron and proton are hadrons but the electron and antineutrinos are leptons. Similarly, in pion decay the pion is a hadron but the muon and neutrino are leptons. There is a beautiful picture that unifies these various kinds of interactions, having to do with the exchange of particles.

The modern quantum field theory view of electron-electron repulsion is that one electron emits a (“virtual”) photon, with a change of energy and momentum by the emitting electron, and this (“virtual”) photon is absorbed by the other electron, so the energy and momentum of this electron also change. The electron is called “virtual” because it is not directly observable and can have a relation between energy and momentum that is not possible for a real photon. Photon exchange is considered to be the fundamental basis for electromagnetic interactions.

Similarly, remarkably similarly, weak interactions such as muon or neutron decay can be modeled as the exchange of positive or negative W particles. In this view, the free neutron decays into a proton and a W (charge is conserved: the neutron has no electric charge, the proton has +1 unit of electric charge, and the W has -1 unit of electric charge). Next, the W decays into an electron and an antineutrino (“lepton” number is conserved: the W has lepton number zero, the electron has lepton number +1, and the antineutrino has lepton number -1).

$n \Rightarrow p^+ + W^-$

$W^- \Rightarrow e^- + \overline{\nu}$

An even more fundamental picture of neutron decay is that a quark with charge -1/3 in the neutron emits a W and changes into a quark with charge +2/3, a net change of +1, corresponding to the neutron changing into a proton, but with a change that’s actually associated with the change of just one of its quarks; the other two quarks are mere spectators in the process.

$q^{-1/3} \Rightarrow q^{+2/3} + W^-$

$W^- \Rightarrow e^- + \overline{\nu}$

Click in this frame to see an animated view of neutron decay:

A key concept is the interaction “vertex”: In electron-electron repulsion, one vertex is the point where one of the electrons emits a photon, and the electron and photon paths diverge. A second vertex is where the other electron absorbs the photon and changes its direction. “Feynman diagrams” are little pictures of these vertex interactions. In neutron decay one vertex is the quark – quark – W, and a second vertex is W – electron – antineutrino.

Consider positive pion decay. The positively charged pion with charge +1 consists of a quark with charge +2/3 and an antiquark of charge +1/3. One vertex is quark – antiquark – W+, and the other vertex is W+ – muon – neutrino.

$q^{+2/3} + \overline{q}^{+1/3} \Rightarrow W^+$

$W^+ \Rightarrow \mu^+ + \nu$

Consider the purely leptonic decay of a negative muon. One vertex is muon – W – neutrino, and the other is W – electron – antineutrino.

$\mu^- \Rightarrow W^- + \nu$

$W^- \Rightarrow e^- + \overline{\nu}$

Feynman diagrams consist of interaction vertices with exchanges of virtual particles such as the photon (electromagnetism) or the W (weak interactions). In fact, the first big unification was the recognition that electromagnetism (photon exchange) and weak interactions (W exchange) were basically the same thing, which is called the “electroweak” interaction.

Summary: Weak interactions involve interaction vertices that include the W+ or W, and they are slow compared to strong/nuclear interactions. W’s “couple” to quarks, and they also “couple” to leptons, hence such “semileptonic” phenomena as neutron decay, where one vertex is quark – quark – W and the other vertex is W – electron – antineutrino.

I should mention that in addition to the photon, W+, and W, there is also an electrically neutral Z particle that is exchanged in certain kinds of weak interactions where no change in electric charge occurs at a vertex. Also, when a W decays into an electron and an antineutrino, the antineutrino is an electron-type antineutrino, whereas when a W decays into a (negative) muon and an antineutrino, the antineutrino is a muon-type antineutrino. The neutrinos and antineutrinos associated with positrons and electrons are different from the neutrinos and antineutrinos associated with positive and negative muons.

Bruce Sherwood

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