Definitions

# Meson

[mee-zon, ‐son, mez-on, mes]

In particle physics, a meson is a strongly interacting boson—that is, a hadron with integer spin. In the Standard Model, mesons are composite (non-elementary) particles composed of an even number of quarks and antiquarks. All known mesons are believed to consist of a quark-antiquark pair—the so-called valence quarks—plus a "sea" of virtual quark-antiquark pairs and virtual gluons. Searches for exotic mesons that have different constituents are ongoing. The valence quarks may exist in a superposition of flavor states; for example, the neutral pion is neither an up-antiup pair nor a down-antidown pair, but an equal superposition of both. Pseudoscalar mesons (spin 0), where the quark and antiquark have opposite spin, have the lowest rest energy. Next lowest in rest energy are vector mesons (spin 1), where the quark and antiquark have parallel spin. Both come in higher-energy versions where the spin is augmented by orbital angular momentum. All mesons are unstable.

Mesons were originally predicted as carriers of the force that binds protons and neutrons together. When first discovered, the muon was identified with this family from its similar mass and was named "mu meson". However it did not show a strong attraction to nuclear matter and is actually a lepton. The pion was the first true meson to be discovered. (The current picture of intranuclear forces is quite complicated; see quantum hydrodynamics for a discussion of modern theories in which nucleon-nucleon interactions are mediated by meson exchange.)

## History

In 1949 Hiideki Yukawa was awarded the Nobel Prize in Physics for predicting the existence of the meson. He called the particle the meson, from mesos, Greek for intermediate, because its mass was between that of the electron and proton. He had originally named it the 'mesotron', but was corrected by Werner Heisenberg (whose father was a professor in Greek at the University of Munich), who pointed out that there is no 'tr' in the Greek word 'mesos'.

## Naming of the mesons

The name of a meson is devised so that its main properties can be inferred. Conversely, given a meson's properties, its name is clearly determined. The naming conventions fall in two categories based on flavor: flavorless mesons and flavored mesons.

### Flavorless mesons

Flavorless mesons are mesons whose flavor quantum numbers are all equal to zero. This means that these quarks are quarkonium states (quark-anti-quark pairs of the same flavor) or a linear superposition of such states.

The name of a flavorless meson is determined by its total spin S and total orbital angular momentum L. As a meson is composed of two quarks with s = 1/2, the total spin can only be S = 1 (parallel spins) or S = 0 (anti-parallel spins). The orbital quantum number L is due to the revolution of one quark around the other. Usually higher orbital angular momenta translate into a higher mass. These two quantum numbers determine the parity P and the charge-conjugation parity C of the meson:

P = (−1)L+1
C = (−1)L+S
Also, L and S add together to form a total angular momentum quantum number J, whose values range from |LS| to L+S in one-unit steps. The different possibilities are summarized with the use of the term symbol 2S+1LJ (a letter code is used instead of the actual value of L, see the spectroscopic notation) and the symbol JPC (here only the sign is used for P and C).

The different possibilities and the corresponding meson symbols are given in the following table:

`  `
`  `
`  `
`  `
`  `
`  `
`  `
`  `
`  `
`  `
`  `
`  `
JPC
`     (0, 2…)− +`
`     (1, 3…)+ −`
`     (1,2…)− −`
`     (0, 1…)+ +`
Quark composition
`    2S+1LJ = *`
`    1(S, D…)J`
`    1(P, F…)J`
`    3(S, D…)J`
`    3(P, F…)J`
$u bar dmbox\left\{, \right\}u bar u - dbar dmbox\left\{, \right\}dbar u$
` I = 1`
π b ρ a
$u bar u + d bar d mbox\left\{, \right\}s bar s$
` I = 0`
η, η h, h’ $phi,!$, ω f, f
$c bar c$
` I = 0`
ηc hc ψ χc
$b bar b$
` I = 0`
` ηb`
hb Υ **
` χb`
Notes:
* Note that some combinations are forbidden: 0− −, 0+ −, 1− +, 2+ −, 3− +...
First row form isospin triplets: π, π0, π+ etc.
Second row contains pairs of elements: φ is supposed to be a $sbar s$ state, and ω a $u bar u + d bar d$ state. In the other cases, the exact composition is not known, so a prime is used to distinguish the two forms.
For historical reasons, 13S1 form of ψ is called J
** The bottomonium state symbol is a capital upsilon (may be rendered as a capital Y depending of the font/browser)

The normal spin-parity series is formed by those mesons where P=(−1)J. In the normal series, S = 1 so PC = +1 (i.e., P = C). This corresponds to some of the triplet states (triplet states appear in the last two columns).

Since some of these symbols can refer to more than one particle, some extra rules are added:

• In this scheme, particles with JP = 0 are known as pseudoscalars, and mesons with JP = 1 are called vectors. For particles other than those, the number J is added as a subindex: a0, a1, χc1, etc.
• For most of ψ, Υ and χ states it is common to include spectroscopic information: Υ(1S), Υ(2S). The first number is the principal quantum number, and the letter is the spectroscopic notation for L. Multiplicity is omitted since it is implied by the symbol, and J appears as a subindex when needed: χb2(1P). If spectroscopic information is not available, mass is used instead: Υ(9460).
• The naming scheme does not differentiate between "pure" quark states and gluonium states, so gluonium states follow the same naming scheme.
• However, exotic mesons with "forbidden" quantum numbers JPC = 0− −, 0+ −, 1− +, 2+ −, 3− +... would use the same convention as the meson with identical JP numbers, but adding a J subindex. A meson with isospin 0 and JPC = 1− + would be denoted ω1.

When the quantum numbers of a particle are unknown, it is designated with an X followed by its mass in parentheses.

### Flavored mesons

For flavored mesons, the naming scheme is a little simpler.

1. The meson name is given by the heaviest of the two quarks. From more to less massive, the order is: t > b > c > s > d > u. However, u and d do not carry any flavor, so they do not influence the naming scheme. Quark t never forms hadrons, but a symbol for t-containing mesons is reserved anyway.

quark symbol quark symbol
c D t T
s $bar K$ b $bar B$
For s and b quarks we get an antiparticle symbol. This is because the adopted convention is that flavor charge and electric charge must agree in sign. This is also true for the third component of isospin: quark up has positive I3 and charge, quark down has negative charge and I3. The effect of that is: any flavor of a charged meson has the same sign as the meson's electric charge.

2. If the second quark has also flavor (it is not u or d) then the identity of that second quark is given by a subindex (s, c or b, and in theory t).

3. Add a "*" superindex if the meson is in the normal spin-parity series, i.e. JP = 0+, 1, 2+...

4. For mesons other than pseudoscalars (0) and vectors (1) the total angular momentum quantum number J is added as a subindex.

To sum it up, we have:

quark composition Isospin JP = 0, 1+, 2... JP = 0+, 1, 2+...
$bar su, bar sd$ 1/2 $K_J$ $K^*_J$
$c bar u, cbar d$ 1/2 $D_J$ $D^*_J$
$c bar s$ 0 $D_\left\{sJ\right\}$ $D^*_\left\{sJ\right\}$
$bar bu, bar bd$ 1/2 $B_J$ $B^*_J$
$bar bs$ 0 $B_\left\{sJ\right\}$ $B^*_\left\{sJ\right\}$
$bar bc$ 0 $B_\left\{cJ\right\}$ $B^*_\left\{cJ\right\}$
J is omitted for 0 and 1

In some cases, particles can mix between them. For example, the neutral kaon, $K^0,\left(bar sd\right)$ and its antiparticle $bar K^0,\left(sbar d\right)$ can combine in a symmetric or antisymmetric manner, originating two new particles, the short-lived and the long-lived neutral kaons $K^0_S = begin\left\{matrix\right\}\left\{1 over sqrt 2\right\}end\left\{matrix\right\}\left(K^0-bar K^0\right),;K^0_L = begin\left\{matrix\right\}\left\{1 over sqrt 2\right\}end\left\{matrix\right\}\left(K^0 + bar K^0\right)$ (neglecting a small CP-violating term).