Isospin Breaking in the Pion-Nucleon Coupling from QCD Sum Rules

Abstract

We use QCD sum rules for the three point function of a pseudoscalar and two nucleonic currents in order to estimate the charge dependence of the pion nucleon coupling constant $g_{NN\pi}$ coming from isospin violation in the strong interaction. The effect can be attributed primarily to the difference of the quark condensates $<{\bar u}u>$ and $<{\bar d}d>$. For the splitting $(g_{pp\pi_0} - g_{nn\pi_0}) / g_{NN\pi}$ we obtain an interval of $1.2 * 10^{-2}$ to $3.7 * 10^{-2}$, the uncertainties coming mainly from the input parameters. The charged pion nucleon coupling is found to be the average of $g_{pp\pi_0}$ and $g_{nn\pi_0}$. Electromagnetic effects are not included.