Present status of the pion-nucleon term

The long-standing discrepancy between the predicted value of the N term in the framework of quantum chromodynamics (QCD) and the value extracted from extrapolated on-mass-shell N scattering data is critically reexamined. Assuming the validity of the Okubo-Zweig-Iizuka (OZI) rule at t=0 and using quark mass ratios extracted from the pseudoscalar-meson mass spectrum one obtains the canonical result N 235 MeV. It is argued that the possibility of readjusting the quark mass ratios to give a term of 60-70 MeV so as to agree with some values extracted from N data is most likely ruled out. In particular this would imply a huge violation of the nonrenormalization theorem in K13 decay. Since the OZI rule is unreliable at t=0, we have recalculated the matrix element p|s»spp(12) (u»u+d»d)|p using the Goldstone-boson-pair mechanism and have found a term of 368 MeV. Other evidence supporting a breakdown of the OZI rule at t=0 is also examined. Another theoretical uncertainty is the effect of higher-order terms in SU(3) breaking. Two recent calculations suggest that such terms could increase the term by another 10 MeV or more. Finally, the whole procedure of extracting a value of the term from N scattering data is reconsidered. The usual evaluations do not include the uncertainties or their correlations in the N amplitude or in the fixed-t dispersion relations. We perform several fits to the N amplitude at =0 that suggest that values of the term in the range 30-70 MeV are not ruled out by the existing data. Also, nonlinearities in the N amplitude lead to another 10 MeV uncertainty in the comparison between theory and experiment. We therefore conclude that both the theoretical and experimental uncertainties in the determination of the term are sufficiently large for the apparent discrepancy to provide neither evidence against QCD nor against the canonical quark mass ratios that one obtains in the conventional (3,3») model.