# Meson

In particle physics, a meson is a strongly interacting boson, that is, it is a hadron with integral spin. In the Standard Model, mesons are composite (non-elementary) particles composed of an even number of quarks and antiquarks. Until the discovery of the tetraquark, all known mesons were believed to consist of a quark-antiquark pair - the so-called valence quarks - plus a "sea" of virtual quark-antiquark pairs and virtual gluons. 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) have the lowest rest energy, where the quark and antiquark have opposite spin, and then the 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. Most of a meson's mass comes from binding energy, rather than the sum of the mass of its components. All mesons are unstable.

Mesons were originally predicted as carriers of the force that bind 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 hadrodynamics for a discussion of modern theories in which nucleon-nucleon interactions are mediated by meson exchange.)

Yukawa was awarded Nobel Prize in Physics for this. He originally named it 'mesotron', but was famously corrected by Werner Heisenberg (whose father was a professor in Greek at University of Munich) that there are no 'tr' in 'mesos'.

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## 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, depending on whether the meson has a flavor or not.

### Flavorless mesons

Flavorless mesons are mesons whose flavor quantum numbers are all equal to zero. This means that these quarks are quarkonium states (quark-antiquark 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 for the meson. 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 symbol are given in the following table:

</table> Notes:
*</span> 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 [itex]s\bar s[itex] state, and ω a [itex]u \bar u + d \bar d[itex] state. on the other cases it is not known the exact composition 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 were 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 on 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 is common to include the 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 is implied by the symbol, and J appears as a subindex when needed: χb2(1P). If the spectroscopic information is not available, the 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 simplier.

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.

JPC

(0, 2)− +

<p>(1, 3)+ − <p>(1,2)− − <p>(0, 1)+ +
Quark composition <p>2S+1LJ* <p>1(S, D)J <p>1(P, F)J <p>3(S, D)J <p>3(P, F)J
<p>[itex]u \bar d\mbox{, }u \bar u - d\bar d\mbox{, }d\bar u[itex] <p>I = 1 <p>π <p>b <p>ρ <p>a
<p>[itex]u \bar u + d \bar d \mbox{, }s \bar s[itex] <p>I = 0 <p>η, η <p>h, h <p>[itex]\phi\,\![itex], ω <p>f, f
<p>[itex]c \bar c[itex] <p>I = 0 <p>ηc <p>hc <p>ψ <p>χc
<p>[itex]b \bar b[itex] <p>I = 0 <p>ηb <p>hb <p>Υ ** <p>χb
quark symbol quark symbol
c D t T
s [itex]\bar K[itex] b [itex]\bar B[itex]
Note the fact that for s and b quarks we get an antiparticle symbol. This is because it is adopted the convention 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 than 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</sub> = 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+...
[itex]\bar su,\ \bar sd[itex] 1/2 [itex]K_J[itex] [itex]K^*_J[itex]
[itex]c \bar u,\ c\bar d[itex] 1/2 [itex]D_J[itex] [itex]D^*_J[itex]
[itex]c \bar s[itex] 0 [itex]D_{sJ}[itex] [itex]D^*_{sJ}[itex]
[itex]\bar bu,\ \bar bd[itex] 1/2 [itex]B_J[itex] [itex]B^*_J[itex]
[itex]\bar bs[itex] 0 [itex]B_{sJ}[itex] [itex]B^*_{sJ}[itex]
[itex]\bar bc[itex] 0 [itex]B_{cJ}[itex] [itex]B^*_{cJ}[itex]
J is omitted for 0 and 1

In some cases, particles can mix between them. For example, the neutral kaon, [itex]K^0\,(\bar sd)[itex] and its antiparticle [itex]\bar K^0\,(s\bar d)[itex] can combine in a symmetric or antisymmetric manner, originating two new particles, the short-lived and the long-lived neutral kaons [itex]K^0_S = \begin{matrix}{\sqrt 2 \over 2}\end{matrix}(K^0-\bar K^0),\;K^0_L = \begin{matrix}{\sqrt 2 \over 2}\end{matrix}(K^0 + \bar K^0)[itex] .

## List of some mesons

The various types of meson (not comprehensive)
Particle Symbol Anti-
particle
Makeup Rest mass
MeV/c2
s
Pion π+ π- [itex]\mathrm{u \bar{d}}[itex] 139.6 0 0 0 2.60×10-8
Pion π0 Self [itex]\mathrm{\frac{u\bar{u} + d \bar{d}}{\sqrt{2}}}[itex] 135.0 0 0 0 0.84×10-16
Kaon K+ K- [itex]\mathrm{u\bar{s}}[itex] 493.7 +1 0 0 1.24×10-8
Kaon [itex]\mathrm{K_S^0}[itex] [itex]\mathrm{K_S^0}[itex] [itex]\mathrm{\frac{d\bar{s} - s\bar{d}}{\sqrt{2}}}[itex] 497.7 +1 0 0 0.89×10-10
Kaon [itex]\mathrm{K_L^0}[itex] [itex]\mathrm{K_L^0}[itex] [itex]\mathrm{\frac{d\bar{s} + s\bar{d}}{\sqrt{2}}}[itex] 497.7 +1 0 0 5.2×10-8
Eta η0 Self [itex]\mathrm{\frac{u\bar{u} + d\bar{d} - 2s\bar{s}}{\sqrt{6}}}[itex] 547.8 0 0 0 0.5×10-18
Rho ρ+ ρ- [itex]\mathrm{u\bar{d}}[itex] 776 0 0 0 0.4×10-23
Phi φ Self [itex]\mathrm{s\bar{s}}[itex] 1019 0 0 0 16×10-23
D D+ D- [itex]\mathrm{c\bar{d}}[itex] 1869 0 +1 0 10.6×10-13
D D0 [itex]\mathrm{\bar{D^0}}[itex] [itex]\mathrm{c\bar{u}}[itex] 1865 0 +1 0 4.1×10-13
D [itex]\mathrm{D_S^+}[itex] [itex]\mathrm{D_S^-}[itex] [itex]\mathrm{c\bar{s}}[itex] 1968 +1 +1 0 4.9×10-13
J/Psi J/ψ Self [itex]\mathrm{c\bar{c}}[itex] 3096.9 0 0 0 0.8×10-20
B B- B+ [itex]\mathrm{b\bar{u}}[itex] 5279 0 0 -1 1.7×10-12
B B0 [itex]\mathrm{\bar{B^0}}[itex] [itex]\mathrm{d\bar{b}}[itex] 5279 0 0 -1 1.5×10-12
Upsilon Υ Self [itex]\mathrm{b\bar{b}}[itex] 9460 0 0 0 1.3×10-20

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