Pseudoscalar meson dominance, the pion–nucleon coupling constant and the Goldberger–Treiman discrepancy

Abstract We analyze the matrix elements of the pseudoscalar density with pion-quantum numbers $$I^G J^{PC}= 1^- 0^{-+}$$ I G J PC = 1 - 0 - + in the nucleon in terms of dispersion relations, PCAC and pQCD asymptotic sum rules for the pseudoscalar form factor. We show that the corresponding spectral density must have at least one zero. A model based on ChPT at low energies, resonances at intermediate energies, Regge power-like behavior at high energies and pQCD at asymptotically high energies, allows to deduce the pion–nucleon coupling constant and the Goldberger–Treiman discrepancy $$\Delta _\textrm{GT} = 1 -\frac{m_N g_A }{F_{\pi }g_{\pi NN}}$$ Δ GT = 1 - m N g A F π g π N N , yielding the results for the charged channel $$g_{\pi ^+ pn} = 13.14(^{+6}_{-4})(7)_\textrm{IB}, \quad \Delta _\textrm{GT} = 1.26(^{+51}_{-34})(50)_\textrm{IB}\%,$$ g π + p n = 13.14 ( - 4 + 6 ) ( 7 ) IB , Δ GT = 1.26 ( - 34 + 51 ) ( 50 ) IB % , to be compared with the most precise determinations, $$g_{\pi ^+ np} = 13.25(5)$$ g π + n p = 13.25 ( 5 ) (and hence $$\Delta _\textrm{GT}=2.1(4) \%$$ Δ GT = 2.1 ( 4 )