πNNform factor for explaining sea-quark distributions in the nucleon

We reinvestigate a soft {π}NN form factor with a monopole cutoff parameter Λ₁0.5 GeV obtained by Frankfurt, Mankiewicz, and Strikman for explaining sea-quark distributions in the nucleon. It is found that their estimate is small in comparison to the limit Λ₁0.65--0.7 GeV estimated in this investigation. Studying processes involving {π}NN and {π}N{Δ} vertices, we find that the limit for the dipole form factor is Λ₂0.95 GeV (which corresponds to Λ₁0.6 GeV). Therefore, a typical {π}NN form factor with Λ₁{~}0.6 GeV in quark models could be consistent with deep-inelastic experimental data at this stage. However, it is softer than a {π}NN form factor with Λ₁{~}1 GeV widely used in nuclear physics. Using the cutoff Λ₂=0.95 GeV, we investigate pionic contributions to a SU(2)f-breaking distribution u{}(x)-d{}(x) in the nucleon. We find that the pionic contributions to u{}(x)-d{}(x) are negative and a contribution to the deviation from the Gottfried sum rule is estimated to be -0.041, which could explain a part of the discrepancies indicated by recent New Muon Collaboration experiments.