Importance of pseudoscalar-axial-vector mixing in calculation of the properties of the pi, eta, and eta ' mesons

In this work we resolve a problem that arises in the calculation of the two -photon decay of the pi(0), eta, and eta' mesons, when use is made of the N ambu-Jona-Lasinio (NJL) model. It has been found that satisfactory results for the widths are obtained if a momentum cutoff is not introduced in the e valuation of the (convergent) integrals obtained from an analysis of the tr iangle diagram, while only about one-half of the experimental value is obta ined, if the cutoff used for the (divergent) loop integrals of the NJL mode l is introduced. The resolution of this problem lies in the introduction of pseudoscalar-axial-vector mixing for both the pi(0) and the eta-eta' syste m. (In addition, one has singlet-octet mixing for the eta and eta', requiri ng the study of T matrices of dimension four in that case.) Since we have u sed a relativistic quark model that includes ii (covariant) confinement mod el, we are able to treat the eta' and eta mesons on the same basis. We foun d that the 't Hooft interaction does not work well in our study of eta-eta' mixing, while the parametrization of nonperturbative effects due to coupli ng to gluonic modes, which affects the strength of the interaction for sing let states only, yields satisfactory results. In the case of a pion, our re sults may be understood by the observation that the vertex iP gamma(5)/root P-2 yields a much larger amplitude for two-photon decay of a meson of mome ntum P than the vertex i gamma(5) Therefore, quite small mixing angles can yield a large modification of the calculated width. We have found that our results are sensitive to the form of regulator used. For example, with a sh arp cutoff, Gamma(eta'-->gamma gamma) is overestimated by about a factor of 3, while the use of a Gaussian regulator leads to a satisfactory fit to th e experimental value. [S0556-2813(99)04505-7].