List of mesons

This is a list of known and predicted mesons. Mesons are made of quarks and as such are part of the subatomic particle family called the hadrons. Mesons are the sub-family of hadrons with a baryon number of 0, as opposed to the baryons which are the sub-family of hadrons with a baryon number of 1. Since mesons are composed of quarks they participate in the strong interaction. Leptons are not composed of quarks and as such do not participate in the strong interaction.

Traditionally, mesons were believed to be composed of only one quarks and one antiquark (diquarks) (quarks have a baryon number of $1/3$ and antiquarks have a baryon number of −$1/3$). Recently, physicists have reported the existence of tetraquarks—"exotic" mesons made of two quarks and two antiquark, but their existence is not generally accepted. Each meson has a corresponding antiparticle (antimeson) where quarks are replaced by their corresponding antiquarks and vice versa. For example, a positive rho meson is made of one up quark and one down antiquark; thus, its corresponding antiparticle is made of an up antiquark and one down quark (the negative rho meson).

Spin, orbital angular momentum, and total angular momentum
Spin (quantum number S) is a vector quantity that represents the "intrinsic" angular momentum of a particle. It comes in increments of $1/2$ ℏ (pronounced "h-bar"). The ℏ is often dropped because it is the "fundamental" unit of spin, and it is implied that "spin 1" means "spin 1 ℏ". In some systems of natural units, ℏ is chosen to be 1, therefore does not appear anywhere.

Quarks are fermionic particles of spin $1/2$ (S = $1/2$). Because spin projections varies in increments of 1 (that is 1 ℏ), a single quark has a spin vector of length $1/2$, and has two spin projections (Sz = +$1/2$ and Sz = −$1/2$). Two quarks can have their spins aligned, in which case the two spin vectors add to make a vector of length S = 1 and three spin projections (Sz = +1, Sz = 0, and Sz = −1). If two quarks have unaligned spins, the spin vectors add up to make a vector of length S = 0 and has only one spin projection (Sz = 0), etc. Since baryons are made of three quarks, their spin vectors can add to make a vector of length S = $3/2$ which has four spin projections (Sz = +$3/2$, Sz = +$1/2$, Sz = −$1/2$, and Sz = −$3/2$), or a vector of length S = $1/2$ with two spin projections (Sz = +$1/2$, and Sz = −$1/2$).

There is another quantity of angular momentum, called the orbital angular momentum (quantum number L), that comes in increments of 1 ℏ, which represent the angular moment of due to particles orbiting around each other. The total angular momentum (quantum number J) of a particle is therefore the combination of intrinsic angular momentum (spin) and orbital angular momentum (J = S + L).

Particles physicists are most interested in mesons with no orbital angular momentum (L = 0), therefore the two groups of mesons most studied are the S = 1; L = 0 and S = 0; L = 0, which corresponds to J = 1 and J = 0, although they are not the only ones. It is also possible to obtain J = 1 particles from S = 0 and L = 1. How to distinguish between the S = 1, L = 0 and S = 0, L = 1 mesons is an active area of research in meson spectroscopy.

Parity
Parity refers to whether the wavefunction of a particle is even or odd. A positive parity (P = +) means that the wavefunction is even, while a negative (P = −) means the wavefunction is odd.
 * $$|\Psi(x)\rangle = x^3e^{-x^2}$$ is an odd 1-dimensional wavefunction because $$|\Psi(x)\rangle=-|\Psi(-x)\rangle$$
 * $$|\Psi(x)\rangle = x^4e^{-x^2}$$ is an even 1-dimensional wavefunction because $$|\Psi(x)\rangle=|\Psi(-x)\rangle$$

For mesons, parity is related to the orbital angular momentum by the relation:
 * $$P=(-1)^{L+1}$$.

Physicists are often particularly interested in mesons with no orbital angular momentum (L = 0), which are of odd parity (P = −).

Isospin and charge


Observation of baryons prior to the development of the quark model led particle physicists to believe that some particles were so similar in how they interact with the strong nuclear force, and so similar in mass, that they were really the same particle even though they had different charge. This was due to the fact that prior to the development of the quark model, only baryons made of u, d and s quarks were known (although this was not known at the time). Since the mass of the u and d quarks are very similar, particles made of the same number of u and d quarks have the same mass, and the exact u and d quark composition specifies the charge (u carries charge +$2/3$ while d carries charge −$1/3$. For example the four Deltas have different charges ( (uuu), (uud),  (udd),  (ddd)), but the same mass (~1,232 MeV/c2), and was considered to be a single particle in different charged states.

To explain the different charges, particles physicist came up with the concept of isospin, whose projections varied in increments of 1 just like spin, where the charges corresponded to different isospin projections. Since the "Delta particle" had four "charged states" of mass 1,232 MeV/c2, the delta was said to be of isospin I = $3/2$ whose four charged state, , , and corresponded to Iz = +$3/2$, Iz = +$1/2$, Iz = −$1/2$, and Iz = −$3/2$ respectively. Another example is the two nucleons (the proton (uud) and neutron (udd)). The positive nucleon (proton) and the neutral nucleon  (neutron)—each of mass ~938 MeV/c2—were given isospin I = $1/2$, and the projections Iz = +$1/2$ and Iz = −$1/2$ respectively.

In the "isospin picture", the four Deltas and the two nucleons were thought to be the different states of two particles. However in the quark model, Deltas are different states of nucleons (the N++ or N− are forbidden by Pauli's exclusion principle). Isospin, although conveying an inaccurate picture of things, is still used to classify baryons, leading to unnatural and often confusing nomenclature. It was noted that the isospin projections were related to the up and down quark content of particles by the relation:
 * $$I_z=\frac{1}{2}[(n_u-n_\bar{u})-(n_d-n_\bar{d})]$$

where the n's are the number of up and down quarks and antiquarks.

Flavour quantum numbers
The strangeness flavour quantum number S (not to be confused with spin) was noticed to go up and down along with particle mass. The higher the mass, the lower the strangeness (the more s quarks). Particles could be described with isospin projections (related to charge) and strangeness (mass) (see the uds octet and decuplet figures on the right). As other quarks where discovered, new quantum numbers were made to have similar description of udc and udb octets and decuplets. Since only the u and d mass are similar, this description of particle mass and charge in terms of isospin and flavour quantum numbers only works well for octet and decuplet made of one u, one d and one other quark and breaks down for the other octets and decuplets (for example ucb octet and decuplet). If the quarks all had the same mass, their behaviour would be called symmetric, as they would all behave in exactly the same way with respect to the strong interaction. Since quarks do not have the same mass, they do not interact in the same way (exactly like an electron placed in an electric field will accelerate more than a proton placed in the same field because of its lighter mass), and the symmetry is said to be broken.

It was noted that charge (Q) was related to the isospin projection (Iz), the baryon number (B) and flavour quantum numbers (S, C, B&prime;, T) by the Gell-Mann–Nishijima formula:
 * $$Q=I_z+\frac{1}{2}(B+S+C+B^\prime+T)$$

S, C, B&prime;, and T represent the strangeness, charmness, bottomness and topness flavour quantum numbers respectively. They are related to the number of strange, charm, bottom, and top quarks and antiquark according to the relations:
 * $$S=-(n_s-n_\bar{s})$$
 * $$C=+(n_c-n_\bar{c})$$
 * $$B^\prime=-(n_b-n_\bar{b})$$
 * $$T=+(n_t-n_\bar{t})$$

meaning that the Gell-Man–Nishijima formula is equivalent to the expression of charge in terms of quark content:
 * $$Q=\frac{2}{3}[(n_u-n_\bar{u})+(n_c-n_\bar{c})+(n_t+n_\bar{t})]-\frac{1}{3}[(n_d-n_\bar{d})+(n_s-n_\bar{s})+(n_b+n_\bar{b})]$$

Particle classification
Mesons are classified according to quark content, quantum numbers I, J, P, C, and G.

Pseudoscalar mesons
[a] Makeup inexact due to non-zero quark masses [b] Strong eigenstate. No definite lifetime (see kaon notes below) [c] Weak eigenstate. Makeup is missing small CP–violating term (see notes on neutral kaons below)

Vector mesons
[d] See charmonium [e] See bottomonium

Notes on neutral kaons
There are two complications with neutral kaons:


 * 1) Due to neutral kaon mixing, the and  are not eigenstates of strangeness.  However, they are eigenstates of the weak force, which determines how they decay, so these are the particles with definite lifetime.
 * 2) Furthermore, the linear combinations given in the table for the and  are not exactly correct, since there is a small correction due to CP violation.  See CP violation in kaons.

Note that these issues also exist in principle for other neutral flavored mesons; however, the weak eigenstates are considered separate particles only for kaons because of their dramatically different lifetimes.

______________________________________________________________________________________ Too much technical gibber and not enough thought. There need to be four K mesons, two neutrally charged and one + and one -, all with approximate mass 892.2 Mev corresponding to Strangeness +1 and Strangeness -1 multiplied by isospin +1/2 and -1/2. Elsewhere in Wickipedia you have the correct hexagonal diagram for vector mesons --- check it up. More staggering is the omission of the omega0 vector meson of mass783.4 Mev. If you add these it will make your table of vector mesons compatible with your diagrams that appear elsewhere.