Pion
The pion is a subatomic particle belonging to the meson family. It is a composite particle, consisting of a quark - antiquark pair, and therefore it is not a fundamental constituent of matter.
A pion is built from a light up (u) or down (d) quark together with a corresponding light antiquark.
$$ q \overline{q} $$
The pion participates in the strong interaction because it is composed of quarks carrying color charge. Any system containing quarks necessarily interacts through the strong force.
Types of pions
There are three pion states with nearly identical masses but different electric charges:
- \( \pi^+ \) positive pion, composed of an up quark and a down antiquark \( \pi^+ = u \bar d \)
- \( \pi^- \) negative pion, composed of a down quark and an up antiquark \( \pi^- = d \bar u \)
- \( \pi^0 \) neutral pion, a quantum superposition of \( u\bar u \) and \( d\bar d \)
As an example, the positive pion is a meson formed by an up quark and a down antiquark, and its electric charge (+1) follows directly from summing the charges of its constituents. The positive pion \( \pi^+ \) consists of an up quark and a down antiquark $$ \pi^+ = u \bar d $$ Since the up quark carries charge \( +\tfrac{2}{3} \) and the down antiquark carries charge \( +\tfrac{1}{3} \), their sum is +1, which is exactly the electric charge of the positive pion. $$ +\tfrac{2}{3} + \tfrac{1}{3} = +1 $$
As a meson, the pion has baryon number zero and vanishing total spin.
Fundamental properties
The fundamental properties of the pion are summarized below.
| Property | Value | Note |
|---|---|---|
| Spin (S) |
0 | The pion is a spin-zero particle. |
| Mass | about 140 MeV | |
| Mean lifetime | very short | |
| Baryon number | 0 | |
| Orbital angular momentum (L) | 0 |
The pion has spin zero because the quark and the antiquark, each with spin $ \tfrac 12 $, are coupled into a singlet state with zero total spin.
Explanation. Both the quark and the antiquark have spin \( \tfrac12 \). When combined, they can form two possible spin configurations: $$ \tfrac12 \otimes \tfrac12 = [ \tfrac12 - \tfrac12 ] , [ \tfrac12 + \tfrac12 ] = 0 \oplus 1 $$ Here 0 denotes a singlet state, while 1 denotes a triplet state. The pion corresponds to the singlet configuration with total spin \( S = 0 \). This is the antisymmetric combination in which the two spins are antiparallel and their vector sum vanishes: $$ \frac{1}{\sqrt{2}} \left( \lvert \uparrow \downarrow \rangle - \lvert \downarrow \uparrow \rangle \right) $$ By contrast, the triplet state \( S = 1 \) consists of symmetric spin configurations and does not describe the pion, but rather vector mesons such as the \( \rho \): $$ \lvert \uparrow \uparrow \rangle , \quad \frac{1}{\sqrt{2}} \left( \lvert \uparrow \downarrow \rangle + \lvert \downarrow \uparrow \rangle \right), \quad \lvert \downarrow \downarrow \rangle $$
The pion occupies a central position in particle and nuclear physics for three main reasons.
- It mediates the nuclear interaction
The pion is the particle responsible for transmitting the residual strong force between protons and neutrons inside atomic nuclei. In this respect, it plays a role analogous to that of the photon in electromagnetism. - It acts as a “bridge” particle
The pion is produced through the strong interaction but decays through the weak or electromagnetic interaction, thereby linking different fundamental interactions. - It is the lightest meson
Its low mass makes it the easiest meson to produce in high-energy collisions and the most frequently observed meson in hadronic decays.
In short, the pion is one of the simplest particles, yet also one of the most significant in particle physics.
Pion decay
The pion is an unstable particle and decays very rapidly into lighter particles.
This behavior reflects the fact that pions are not fundamental objects but unstable composite states.
- The weak interaction governs the decay of charged pions.
- The electromagnetic interaction dominates the decay of the neutral pion.
In other words, the pion is a transitional particle, created by the strong interaction but destined to disappear through weaker interactions.
There are two main cases to consider: the decay of charged pions and the decay of the neutral pion.
Decay of the charged pion
The charged pion has a mean lifetime of approximately
$$ 2.6 \times 10^{-8} \ s $$
which is very long on a subnuclear timescale, even though it is exceedingly short on everyday timescales.
A] Decay of the positive pion
The dominant decay mode of the positive pion \( \pi^+ \) produces a positive muon and a muon neutrino:
$$ \pi^+ \rightarrow \mu^+ + \nu_\mu $$
The pion has spin zero, so the total spin of the final state must also be zero. Consequently, the muon and the neutrino must be produced with opposite helicities.
Since neutrinos are always left-handed, the positive muon must be right-handed, meaning that its spin is aligned with its direction of motion.
B] Decay of the negative pion
For the negative pion, the charge-conjugate process takes place. The decay produces a negative muon and a muon antineutrino:
$$ \pi^- \rightarrow \mu^- + \bar{\nu}_\mu $$
In this case, because the antineutrino is always right-handed, the negative muon must be left-handed.
Note. In principle, the pion could also decay through the channel $$ \pi^+ \rightarrow e^+ + \nu_e $$ but this process is strongly suppressed. The reason is quantum mechanical and is tied to the structure of the weak interaction and helicity conservation. The muon, being much more massive than the electron, allows the decay to satisfy angular momentum conservation more readily. The electron is too light to efficiently reverse its helicity. As a consequence, more than 99% of charged pions decay into muons.
Decay of the neutral pion
The mean lifetime of the neutral pion is much shorter than that of the charged pion, approximately
$$ 8.4 \times 10^{-17} \ s $$
The neutral pion decays almost exclusively into photons:
$$ \pi^0 \rightarrow \gamma + \gamma $$
This decay proceeds via the electromagnetic interaction and is extremely rapid.
Parity
The pion is a pseudoscalar meson with spin 0 and intrinsic parity -1 $$ P(\pi) = -1 $$
In other words, under a spatial inversion, that is, a parity transformation, the pion’s momentum reverses direction while its spin remains unchanged. As a result, the helicity of the pion changes sign.
Why does it have parity -1?
For mesons composed of a quark - antiquark pair, the total parity is given by:
$$ P = (-1)^{L+1} $$
Here \( L \) denotes the relative orbital angular momentum of the quark - antiquark system, and the additional factor of -1 arises from the intrinsic parity of the antiquark.
Accordingly, the parity of a meson depends on \( L \).
- vector mesons with \( L = 0 \) have \( P = -1 \), as do pseudoscalar mesons
- scalar mesons with \( L = 1 \) have \( P = +1 \), as do axial-vector mesons
As a pseudoscalar meson, the pion occupies its ground state with \( L = 0 \).
$$ P = (-1)^{0+1} = -1 $$
This explains why the pion has intrinsic parity $ P = -1 $.
And so on.
