Charm baryons

After some claim of baryon charm decay seen at Fermilab the first actual complete reconstruction of a charm baryon event has come from leptonic (neutrino induced) reactions (Angelini et al, 1979) at CERN where all the momenta have been measured and the particles identified, allowing the determination of both the proper decay time and mass. The event corresponds to the decay of the charm baryon A+ ucd)... 

A large part of the present experimental activity concerns baryons with heavy flavours, Qqq or Qqs or Qss, where q means u or d. These states, with their helium-like structure, are much more asymmetric the two light quarks are rotating rather fast around a flavoured quark which remains almost static. In the near future, double-charm baryons QQq should provide interesting information on quark dynamics with the superposition, within the same hadron, of the slow motion of two heavy quarks experiencing the short-range QCD potential, and of the fast motion of a light quark around them [7,8]. 

Next comes a discussion on the quark-diquark approximation which is suited for angular excitations of ordinary baryons, and a discussion on the Bom-Oppenheimer approximation which provides a simple picture of double-charm baryons OOq. While discussing several variational expansions or possible approximation schemes, we shall present numerical illustrations based on the simple potential model S rf, with selected values of jS and the same quark masses, so that the merits of the various methods can easily be compared. 

For the numerical illustration, let us consider again a linear potential T, r j and the sets of constituent masses (1,1,5) and (1,1,0.2) which are relevant for qqc and ccq charmed baryons, respectively. We display in table 4.3 the behaviour of the ground state energy as a function of the maximal number of quanta, N, introduced in the expansion. Also shown is the order N to which the oscillator parameter K has been optimized. Some remarks are in order. 

These two models predict very similar - m but differ widely in the charm sector. The situation for charmed baryons is analysed by Capstick [106] with references to earlier works. 

Further topics of interest that can be studied at PEP-II include semileptonic decays of D s and the spectroscopy of D mesons. There are interesting predictions concerning the spins and decay patterns of excited D meson states [26] that result from the simplicity of a heavy quark - light quark bound state. In addition, charmed baryons will be copiously produced and their spectroscopy and decay patterns can be studied. The sample will be more than an order of magnitude larger than that currently available. 

Isospin T 1 z Baryon Ba Strangeness St Charm Ch Beauty By Truth Tr Composition... 

Nuclei that are found in nature consist of nucleons (protons and neutrons) which themselves are made of u (up) and d (down) quarks. However, there also exist s (strange) quarks and even heavier flavors, called charm, bottom, top. The latter has just recently been discovered. Let us stick to the s quarks. They are foimd in the strange relatives of the nucleons, the so-called hyperons A, S, a, i2). The yl-particle, e.g., consists of one u, d and s quark, the S-particle even of an u and two s quarks, while the (sss) contains strange quarks only. Figure 8.19 gives an overview of the baryons, which are of interest here, and their quark content. 

The quark model is a mine of exercises for those who have the chance of teaching quantum mechanics, once they have exhausted the charm of the Stark effect and other examples borrowed from atomic physics. The baryon sector is particularly rich. For instance, it illustrates how antisymmetrization is important, in a situation intermediate between the trivial two-body case and the limit of a large number of constituents, where second-quantization techniques are applied. It is also amazing to show that, if qqq is bound by a pairwise potential, V= E whose strength is half of that of the qq potential, i.e., u(r) = V r), then the energies or masses of ground-state mesons and baryons fulfil the inequality 2(qqq) > 3(qq). This is a simple consequence of the variational principle, as shown in chapter 9. 

In both charm and noncharm sectors, new problems have been raised in hadron spectroscopy. One question concerns the existence of localized diquark clusters inside baryons [11]. Another hot topic concerns the possible hybrid states qqqg with a valence gluon and, possibly, exotic quantum numbers. We find it important to analyse carefully the dynamics of ordinary qqq baryons before concluding the need for new configurations. 

Ground-state baryons with ordinary, strange or charmed flavour. Here q denotes u or d, and qq or qqq stands for a properly symmetrized or antisymmetrized isospin wave function. Masses are in MeV. 

Detailed numerical studies of the Born-Oppenheimer approximation have been performed in the context of studies of baryons with double charm [7,73]. The method works quite well for ccq configurations, as expected, but also for the ssq or even qqq cases. In table 7.1, we display a comparison of the extreme and uncoupled adiabatic approximations with exact results for the mmm system with masses m = l and m = 0.2,0.5 and 1, bound by the smooth 2 S r potential. The quality of the approximation is impressive for both the energy of the first levels and the short-range correlation. 

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