Masses of the Multiquark States in the MIT Bag Model with the Pion-Cloud

Abstract

We study the masses of the low-lying multiquark states, especially the dibaryon states, within the framework of the MIT bag model with the pion-cloud, in which the non-local pion-quark· interaction is taken into account. We find that the pionic effect does not greatly alter the original predictions of the MIT bag model for the dibaryon states with Y = 1 and 2, while it increases the mass of the lowest Y = 0 dibaryon state. The Y = 0 dihyperon predicted by Jaffe may be either unbound or very weakly bound. In this letter we wish to study the low-lying multiquark states in the MIT bag model with the pion-cloud. In the original MIT bag model some authors calculated the masses of the multiquark states and discussed their properties. 1l • 2 ) Recent1y' however, it ~as pointed out that the contribu­ tion of the pion-cloud to the masses of the ordi­ nary hadrons amounts to about 100 MeV and especially the pion-cloud plays an important role in the origin of the N-LJ and the .E-A mass differences. 3 )A) We should, therefore, estimate the effect of the pion-cloud on the masses of the multiquark states. Of special interest is the deep­ ly bound state of the dihyperon UI=OO+) predicted by Jaffe. 2 ) (This state is 70~80 MeV lower than the A-A threshold in the MIT bag model.) Here we will use the chiral and the cloudy bag models with the non-local interaction between the quark and pion,a) in which the extent of the pion is taken into account. The pionic corrections will be treated as a perturbation to the masses of the multiquark states. In the naive chiral S ) and cloudy 6) bag models there are two difficulties, i.e., the collapse of the bag and the divergence of the quark self-energy, which are due to the pion­ cloud. In the first order of the pionic correction we can, however, avoid these difficult problems by using the non-local description of the quark-pion interaction. In the limit of a static and spherical cavity with the radius R the usual mass formula for the N­ quark state is given by