Instanton Effects on the Exotic Meson (Q2Formula2) Spectroscopy

Abstract

The effects of the effective determinantial interaction on the exotic meson (Q'Q') mass spectra are studied. The effective interaction is related to the Fermion zero mode of the background instanton field and is introduced by 't Hooft. The mass shift due to the effective interaction is obtained by the first order perturbation calculation. Our results are expressed by the ground state quark wave function, inside the hadron. The numerical calcula­ tion is carried out by borrowing the quark wave function of the MIT bag model. From our analysis it is found that the study of the pattern of mass shift of Q'Q' states will offer information on the distributions of instantons inside the hadron. is studied in the framework of dilute gas approximation by group. 3' Horn and Yankielowicz 4' studied the effect of the determinantial interaction on ordinary meson and baryon spectra by combined use of QCD and MIT bag model, and succeeded in explaining the n: and r; mass difference. In this article we study its effect on the exotic meson (Q2Q2) spectra. The level shifts due to the determinantial interaction are obtained in the lowest order perturbation calculation. Recently, group has studied the confinement mechanism in QCD, and proposed the Princeton 5' In this model, the instantons and merons conden­ sate in the vacuum, and inside the hadron the perturbative vacuum is realized. And the instantons are distributed in the fringe of the hadron. It is a very in­ teresting problem to study the mass spectra of hadrons in the bag model but it has not been carried out yet. Our results for the level shifts due to the determinantial interaction are ex­ pressed by the quark wave function inside the hadron and are applicable to wider models of hadron. It is more interesting to study the mass shifts of the exotic mesons in the framework of QCD; namely, by using the bag model. But unfortunately we have not obtained the quark wave function inside the Prince­ ton bag. Then in carrying out the numerical calculation of the mass shifts, we have borrowed the quark wave function of the MIT bag model,6''n on the assump-