Isospin Splitting in the Pion-Nucleon Couplings 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 gNNπ coming from isospin violation in the strong interaction. The effect can be attributed primarily to the difference of the quark condensates < ūu > and < d̄d >. Assuming that the π is a pure isostate we obtain for the splitting (|gppπ0 |−|gnnπ0 |)/gNNπ an interval of 0.8∗10−2 to 2.3∗10−2, the uncertainties coming mainly from the input parameters. In order to obtain the coupling to a physical π we have to take π−η mixing into account leading to an interval of 1.2∗10−2 to 3.7∗10−2. The charged pion nucleon coupling is found to be the average of |gppπ0 | and |gnnπ0 |. Electromagnetic effects are not included. The effect of isospin violating meson nucleon couplings is of great importance in the investigation of charge symmetry breaking (CSB) phenomena [1]. On a microscopical level, isospin symmetry is broken by the electromagnetic interaction as well as the mass difference of up and down quarks mu 6= md. We will examine the splitting between the pion nucleon coupling constants gppπ0, gnnπ0 and gpnπ+ using the QCD sum rule method, which has been established as a powerful and fruitful technique for describing hadronic phenomena at intermediate energies. We will only look at effects which arise from isospin breaking in the strong interaction. In the QCD sum rule method this is reflected by mu 6= md as well as by the isospin breaking of the vacuum condensates. Electromagnetic effects are not examined. Details of our calculation have been recently published [2]. We start from the three point function of two nucleonic (Ioffe) currents (ηN ) and one pseudoscalar isovector (P T=1 a ) interpolating current with the appropriate isospin quantum numbers: ANNπa(p1, p2, q) = ∫