Isospin breaking in the pion-nucleon coupling from QCD sum rules

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 $g_{\mathrm{NN}\pi }$ coming from isospin violation in the strong interaction. The effect can be attributed primarily to the difference of the quark condensates $〈ūu〉$ and $〈\mathrm{d¯}d〉$. For the splitting ${(g}_{\mathrm{pp}{\pi }_0}-g_{\mathrm{nn}{\pi }_0}{)/g}_{\mathrm{NN}\pi }$ we obtain an interval of $1.2\times {10}^{-2}$ to $3.7\times {10}^{-2}$, the uncertainties coming mainly from the input parameters. The charged pion nucleon coupling is found to be the average of $g_{\mathrm{pp}{\pi }_0}$ and $g_{\mathrm{nn}{\pi }_0}$. Electromagnetic effects are not included.