meson

Other Definitions
meson (dict)

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.)

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 |L−S| to L+S in one-unit steps. The different possibilities are summarized with the use of the term symbol ^2S+1L_J (a letter code is used instead of the actual value of L, see the spectroscopic notation) and the symbol J^PC (here only the sign is used for P and C). The different possibilities and the corresponding meson symbol are given in the following table:

	J^PC =	(0, 2)^{− +}	(1, 3)^{+ −}	(1,2)^{− −}	(0, 1)^{+ +}
Quark composition	^2S+1L_J = ^*	¹(S, D)_J	¹(P, F)_J	³(S, D)_J	³(P, F)_J
$u \bar d\mbox{, }u \bar u - d\bar d\mbox{, }d\bar u$ ^†	I = 1	π	b	ρ	a
$u \bar u + d \bar d \mbox{, }s \bar s$ ^‡	I = 0	η, η	h, h	$\phi\,\!$ , ω	f, f
$c \bar c$	I = 0	η_c	h_c	ψ ^•	χ_c
$b \bar b$	I = 0	η_b	h_b	Υ ^**	χ_b

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

s\bar s

state, and ω a

u \bar u + d \bar d

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, ³S₁ form of ψ is called J/ψ

^** 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 J^P = 0⁻ are known as pseudoscalars, and mesons with J^P = 1⁻ are called vectors. For particles other than those, the number J is added as a subindex: a₀, a₁, χ_c1, etc.
For most of ψ, Υ and χ states is common to include the spectroscopic information: &Upsilon(1S), Upsilon(2S). The first number is the principal quantum number, and the letter is the spectroscopic notation for L. Multiplicity is ommited since is implied by the symbol, and J appears as a subindex when needed: χ_b2(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 J^PC = 0^{− −}, 0^{+ −}, 1^{− +}, 2^{+ −}, 3^{− +}... would use the same convention as the meson with identical J^P numbers, but adding a J subindex. A meson with isospin 0 and J^PC = 1^{− +} would be denoted ω₁.

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.

align="center" width="100px" style="border-top: 2px solid windowtext; border-bottom: 2px solid windowtext" \| quark	align="center" width="100px" style="border-top: 2px solid windowtext; border-bottom: 2px solid windowtext; border-right: 2px solid windowtext;" \| symbol	align="center" width="100px" style="border-top: 2px solid windowtext; border-bottom: 2px solid windowtext" \| quark	align="center" width="100px" style="border-top: 2px solid windowtext; border-bottom: 2px solid windowtext" \| symbol
align="center" \| c	align="center" style="border-right: 2px solid windowtext;" \| D	align="center" \| t	align="center" \| T
align="center" style="border-bottom: 2px solid windowtext" \| s	align="center" style="border-bottom: 2px solid windowtext; border-right: 2px solid windowtext;" \| $\bar K$	align="center" style="border-bottom: 2px solid windowtext" \| b	align="center" style="border-bottom: 2px solid windowtext" \| $\bar B$

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 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. J^{P = 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: align="center" width="100px" style="border-top: 2px solid windowtext; border-bottom: 2px solid windowtext" | quark composition align="center" width="100px" style="border-top: 2px solid windowtext; border-bottom: 2px solid windowtext; border-right: 2px solid windowtext;" | Isospin align="center" width="100px" style="border-top: 2px solid windowtext; border-bottom: 2px solid windowtext" | J^P = 0⁻, 1⁺, 2⁻... align="center" width="100px" style="border-top: 2px solid windowtext; border-bottom: 2px solid windowtext" | J^P = 0⁺, 1⁻, 2⁺...
align="center" | $\bar su,\ \bar sd$ align="center" style="border-right: 2px solid windowtext;" | 1/2 align="center" | $K_J$ ^† align="center" | $K^*_J$
align="center" | $c \bar u,\ c\bar d$ align="center" style="border-right: 2px solid windowtext;" | 1/2 align="center" | $D_J$ align="center" | $D^*_J$
align="center" | $c \bar s$ align="center" style="border-right: 2px solid windowtext;" | 0 align="center" | $D_{sJ}$ align="center" | $D^*_{sJ}$
align="center" | $\bar bu,\ \bar bd$ align="center" style="border-right: 2px solid windowtext;" | 1/2 align="center" | $B_J$ align="center" | $B^*_J$
align="center" | $\bar bs$ align="center" style="border-right: 2px solid windowtext;" | 0 align="center" | $B_{sJ}$ align="center" | $B^*_{sJ}$
align="center" style="border-bottom: 2px solid windowtext" | $\bar bc$ align="center" style="border-bottom: 2px solid windowtext; border-right: 2px solid windowtext;" | 0 align="center" style="border-bottom: 2px solid windowtext" | $B_{cJ}$ align="center" style="border-bottom: 2px solid windowtext" | $B^*_{cJ}$

† J is omitted for 0⁻ and 1⁻

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

See also
List of particles

External links
http://hyperphysics.phy-astr.gsu.edu/hbase/particles/meson.html#c1
Authoritative information on particle properties is compiled by the Particle Data Group http://pdg.lbl.gov
hep-ph/0211411: The light scalar mesons within quark models

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