Spectroscopy of the -like baryons

Since each baryon is made of three quarks and each quark has a spin, then the same three quarks can align in several different configurations, each of which is a distinct charmed baryon. This complication is somewhat simplified by Heavy Quark Effective Theory which allows us to treat quarks as either heavy (in our case the charm quark) or light (the up, down, and strange quarks). In this theory one imagines a central heavy quark and an outlying pair of light quarks, much in the same way the hydrogen atom is a heavy proton surrounded by a light electron. Each change in the spin configuration gives rise to a change in the energy, or mass of a baryon. Unlike the hyperfine splitting in atoms, these energy level splittings are substantial.

With this simplification, and restricting ourselves to -like baryons with charm, up, and down quarks, we must consider three spin configurations of the quarks. If we denote the three quarks as $[\cq(\qq\qq)]$ (where is a light quark) and their spins as $[\uparrow\!\!(\uparrow\uparrow)]$, we can more easily present the configurations. The first, or ground state, system is formed when the two light quarks are anti-aligned to form a light di-quark with spin 0. In our notation, this is denoted as $[\uparrow\!\!(\uparrow\downarrow)]$. This is the configuration of the , whose quark configuration is $[\cq(\uq\dq)]$ and has total $J = \half$. The next lowest energy configuration, also with $J = \half$, is $[\downarrow\!\!(\uparrow\uparrow)]$ where the light di-quark has spin 1. These states are the baryons: $(\cq\dq\dq)$, $(\cq\uq\dq)$, and $(\cq\uq\uq)$. Finally, we can have the arrangement $[\uparrow\!\!(\uparrow\uparrow)]$ with $J = \threehalf$. These states are the baryons , , and (with the same quark content as the $J = \half$ states). The and states are members of the octet shown in intro:nucleon-plet and the states are members of the decuplet in intro:delta-plet.

In addition to these states, states with angular momentum and radial excitations are also possible, again with various spin configurations. The and baryons are the only observed -like baryons with L=1, but many more must exist. The spectrum of the , , , and baryons and their dominant decay modes is shown in intro:baryon_spect. The $(\cq\sq\qq)$ and $\Omega_c^0$ $(\cq\sq\sq)$ ground states are expected to have similar spectra. Similarly to the de-excitations observed in atomic physics, each of these states decays to its corresponding ground state. However, in hadrons, these decays are often strong decays which can emit pions rather than photons.⁹

 

Figure 1.3: The spectrum of excited charm baryons with two light quarks and the dominant decay modes. The $\scps (2520)$is unobserved.

intro:baryon_spect