# Charmonium

# CHARMONIUM

Charmonium refers to a class of composite particles formed when a charm quark binds to a charm antiquark. The study of this system offers a unique probe into the force between quarks, known as the strong force and also into quantum chromodynamics.

Any type of quark can bind together with any type of antiquark to make the composite particles known as mesons. However, only the charm (*c* ) and bottom (*b* ) quarks form bound states having spectra and energy levels reminiscent of atoms. The charm quark, discovered in 1974, has a mass of approximately 1,500 MeV/*c*^{2}, or 2.7 10^{-27} kg.

The hydrogen atom is formed from a proton and an electron bound together by the electric field; charmonium's quarks are bound together by the strong interquark force. The relative motion of the particles gives rise to orbital angular momentum, measured in whole-number multiples of Planck's constant *h* , which contributes to the total energy of the system. The quarks, like the proton and electron, also possess some intrinsic angular momentum called spin.

Quantization of these angular momenta results in a unique set of allowed energy levels for the system. The spacings between these energy levels are determined by the particle masses and angular momenta and depend on how the force between the bound particles varies with their separation. The energy levels can be inferred by measuring the energies of light emitted when the atomic system relaxes from a higher-energy state *E*_{n} to a lower state *E*_{m}; the emitted photon has energy *E*_{n} - *E*_{m}.

Figure 1 shows the spectrum of photon energies observed when one of the excited energy states of charmonium (the so-called *ψ´* particle) relaxes to lower-energy levels. The *ψ´* charmonium state has a mass of 3,684 MeV/*c*^{2}. There are higher-mass charmonium states, such as *ψ˝* (3770), which prefer to decay into a pair of D (1865) particles (the meson formed from a *c* quark and a *u* antiquark) rather than de-excite by photon emission. This type of decay is not possible for *ψ´* because its mass is less than 2m_{D}; it must decay into lower-energy states by radiating one or more photons.

**FIGURE 1**

The energy levels of charmonium are governed by three quantum numbers. The radial quantum number (integer *n* ) describes the successive quantum energy steps of a given configuration (e.g., the difference between the *n* = 2 *ψ'* and the *n* = 1 *ψ* . Next, there is the total spin of the two c quarks. Each quark has an intrinsic angular momentum of ±½*h* , resulting in a total spin angular momentum *s* of 0 or 1*h* . Finally, there is the orbital angular momentum *L* , in whole-number multiples of *h* . Spectroscopic notation (from atomic physics) is used to label the charmonium states shown in Figure 1; the nomenclature is ^{2s + 1}*L*_{J}, where *J* is the total angular momentum and *L* is denoted by the historical notation S for *L* = 0, *P* for *L* = 1*h* , and so on. In quantum mechanics the various angular momenta add vectorially. For instance, with *s* = 1 and *L* = 1, *J* can take on the values 0, 1, or 2; in the figure this is evident for the *s* = 1 *P* states (*L* = 1*h* ) that split into three energy levels.

The observation of the charmonium energy levels has verified the spin of the c quark and, more importantly, provided a better idea of the behavior of the strong force. Although the strong force increases linearly with quark separation for distances greater than 10^{15} meters (and this is why one never sees single quarks!), charmonium tells us that the behavior is like that of the electric force for distances between 10^{-14} and 10^{-15} meters.

## Bibliography

Bloom, E. D., and Feldman, G. J. "Quarkonium." *Scientific American***246** (5), 66–77 (1982).

*Mark J. Oreglia*

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**Charmonium**