KAHIBARO
Table of Contents
Identity and Role
The muon neutrino, written as $\nu_\mu$, is one of the three known neutrino flavors. It is the neutrino associated with the muon, just as the electron neutrino is associated with the electron and the tau neutrino is associated with the tau lepton.
The muon neutrino is electrically neutral, has very small mass, and interacts only through the weak interaction and gravity. Because it does not feel the electromagnetic force, it does not leave direct ionization tracks like charged particles do. This makes it very difficult to detect.
A muon neutrino is a lepton with electric charge $0$, lepton flavor $\mu$, and very weak interactions with matter.
Relation to the Muon
The muon neutrino appears naturally in processes involving muons. A classic example is the decay of a negatively charged pion:
$$
\pi^- \to \mu^- + \bar{\nu}_\mu
$$
and for a positively charged pion:
$$
\pi^+ \to \mu^+ + \nu_\mu
$$
These reactions show that the muon neutrino is the neutrino partner of the muon. It carries away energy, momentum, and muon lepton number.
Muon decay also involves the muon neutrino. For example,
$$
\mu^- \to e^- + \bar{\nu}_e + \nu_\mu
$$
In this decay, the muon neutrino is produced together with an electron and an electron antineutrino.
In lepton decays, neutrinos are produced in ways that preserve conserved quantities such as energy, momentum, and lepton number.
Basic Properties
The muon neutrino shares many general properties with the other neutrinos, but its flavor label is what makes it distinct in weak interactions.
| Property | Muon neutrino |
|---|---|
| Symbol | $\nu_\mu$ |
| Antiparticle | $\bar{\nu}_\mu$ |
| Electric charge | $0$ |
| Lepton family | Muon family |
| Interaction type | Weak interaction, gravity |
| Mass | Very small, nonzero |
| Spin | $\frac{1}{2}$ |
A muon neutrino is not the same particle as a muon. The muon is charged and relatively easy to detect, while the muon neutrino is neutral and usually passes through matter without interacting.
Production of Muon Neutrinos
Muon neutrinos are commonly produced in high energy particle processes. One important source is pion decay. In particle accelerators, protons strike a target and create many pions. These pions then decay into muons and muon neutrinos.
A simplified chain is
$$
p + \text{target} \to \pi^\pm + \cdots
$$
followed by
$$
\pi^+ \to \mu^+ + \nu_\mu
$$
or
$$
\pi^- \to \mu^- + \bar{\nu}_\mu
$$
Muon neutrinos are also produced in Earth’s atmosphere when cosmic rays collide with air nuclei. These collisions create pions and kaons, which decay and produce muon neutrinos.
Weak Interactions of Muon Neutrinos
The muon neutrino participates in weak interactions in a flavor-specific way. In a charged-current interaction, a muon neutrino can produce a muon if enough energy is available. For example,
$$
\nu_\mu + n \to \mu^- + p
$$
and for the antineutrino,
$$
\bar{\nu}_\mu + p \to \mu^+ + n
$$
These reactions are especially important experimentally, because the produced muon is charged and can be detected. Its appearance is often taken as evidence that a muon neutrino interacted.
A charged-current interaction of a muon neutrino produces a muon, not an electron or tau, at the interaction point.
There are also neutral-current interactions, such as
$$
\nu_\mu + N \to \nu_\mu + N
$$
where $N$ represents a nucleon or nucleus. In this case the neutrino remains a neutrino, and the event is harder to identify as specifically muon flavored.
Detection Signature
Muon neutrinos are often identified indirectly through the muons they create. Since a muon is charged, it can leave a long track in a detector. This is one of the characteristic signs of a muon neutrino charged-current event.
Compared with an electron, a muon usually travels farther through matter before losing all its energy. Because of this, detector images of muon neutrino interactions often show a long, relatively clean track.
In this sketch, the incoming muon neutrino interacts with a neutron and produces a muon and a proton.
Muon Neutrino Versus Muon Antineutrino
It is important to distinguish the muon neutrino $\nu_\mu$ from the muon antineutrino $\bar{\nu}_\mu$. They are different particles, though both are neutral.
Their weak interactions differ. For example, in charged-current reactions:
$$
\nu_\mu + n \to \mu^- + p
$$
but
$$
\bar{\nu}_\mu + p \to \mu^+ + n
$$
So the charge of the produced muon tells us whether the incoming particle was a neutrino or an antineutrino, if the detector can measure that charge.
$\nu_\mu$ produces $\mu^-$ in charged-current interactions, while $\bar{\nu}_\mu$ produces $\mu^+$.
Historical Importance
The muon neutrino played a major role in establishing that there is more than one kind of neutrino. In early experiments, neutrinos produced together with muons created muons in detectors, but not electrons. This showed that the neutrino associated with the muon is distinct from the electron neutrino.
This was a major step in particle physics, because it revealed the existence of separate lepton families.
Muon Neutrinos in Beams
Muon neutrinos are the most common neutrinos used in accelerator experiments. They are relatively practical to produce because pion decay gives intense beams of $\nu_\mu$ or $\bar{\nu}_\mu$.
A typical beam setup works like this. A proton beam strikes a target, producing pions. Magnets select pions of a chosen charge. The pions decay in flight, creating a beam rich in muon neutrinos or muon antineutrinos. The beam is then sent to a detector, sometimes over very long distances.
Role in Oscillation Experiments
Muon neutrinos are central in neutrino oscillation studies. A beam may begin mostly as $\nu_\mu$, but after traveling a distance, some of the muon neutrinos may no longer be detected as muon neutrinos. Instead, fewer muons appear than expected, or neutrinos of another flavor appear.
This behavior is evidence that neutrinos have mass and that flavor states are not identical to mass states. The detailed theory of oscillations belongs to a separate chapter, but the muon neutrino is one of the main particles used to observe this phenomenon.
Summary
The muon neutrino is the neutrino flavor associated with the muon. It is neutral, extremely light, and weakly interacting. It is produced in processes such as pion decay and muon decay, and it is commonly detected through the muons created in charged-current interactions.
Key identification rule: if a neutrino interaction creates a muon at the vertex, the incoming particle was a muon neutrino or muon antineutrino, depending on the muon charge.
Its importance is both practical and fundamental. Practically, it is widely used in neutrino beam experiments. Fundamentally, it helped show that neutrinos come in different flavors.