A Heavy Quark Symmetry Approach to Baryons

Abstract

We evaluate different properties of baryons with a heavy c or b quark. The use of Heavy Quark Symmetry (HQS) provides with an important simplification of the non relativistic three body problem which can be solved by means of a simple variational approach. This scheme is able to reproduce previous results obtained with more involved Faddeev calculations. The resulting wave functions are parametrized in a simple manner, and can be used to calculate further observables.

Heavy hadron spectroscopy and the bag model

“…We compare our predictions obtained in the modified bag model for baryons from the charm sector (Table 7) and for baryons from the bottom sector (Tables 8 and 9) with some other estimates and experimental data. The works we want to compare our results with are: the baryon mass estimates in relativistic [29,30] and nonrelativistic [25,26] potential models with assumed quark-diquark ansatz, usual nonrelativistic potential model [19], variational calculations [23,24], and estimates obtained using various sum rules [60]. All but the one experimental masses for bottom baryons are from the Particle Data Tables [42].…”

“…Even the early treatments [15][16][17] predict the masses of many hadrons with good accuracy. Among the recent treatments there are extensive developments of the traditional approach [18,19], calculations using the method of hyperspherical harmonics [20], solving the Faddeev equations [21], variational calculations [22][23][24], nonrelativistic calculations using quarkdiquark approximation [25,26], etc. Relativistic effects are taken into account by building up the relativistic quark models based on approximate solution of the Bethe-Salpeter equation [27], or using quark-diquark approximation to simplify relativistic dynamics [28][29][30].…”

Ground-state masses and magnetic moments of heavy baryons

“…Reference [4] investigated heavy-flavor baryons by using the Bethe-Salpeter equation in the heavy-quark limit and calculated the Isgur-Wise function. Albertus et al evaluated different properties of single heavy-flavor baryons using heavyquark symmetry in the non-relativistic quark model [6]. Flynn et al studied charmed baryons and spin-splittings in quenched lattice QCD [7].…”

Mixing of heavy baryons in the bag model calculations

“…Before going to the concluding remarks we want to compare the masses of baryons calculated in our work with the results obtained in other models and experimental data where available. We have chosen for the sake of comparison the baryon mass estimates in nonrelativistic [22] and relativistic [23,24] potential models obtained in the quark-diquark approximation, the estimates obtained in the quark-diquark approximation of the bag model [9], the calculations in the simplified variational approach [25], and predictions provided using various sum rules based partially on the heavy quark symmetry considerations [26,27]. The experimental values are taken from the Particle Data Tables [28].…”