Heavy quark mass expansion for the operator Q̄γ5Q and the charm content of η,η′

Recently in the context of studies of the intrinsic charm content of the nucleon and of the η′ meson two groups have arrived at different results for the 1/m3 term of the heavy quark expansion for operator Q̄γ5Q differing by the factor of six. We show that the form of both results violates certain general principles. Using the expression for the axial anomaly with the finite Pauli-Villars regularization we obtain a new expression for the 1/m3 term of the heavy quark expansion for Q̄γ5Q. With this new result we obtain an estimate for the constant fη′(c)≈−112mc2〈0|αs4πGμνaG̃μν,a|η′〉≈−2 MeV