First moments of nucleon generalized parton distributions in chiral perturbation theory at full one-loop order

In this paper we present chiral extrapolation formulas for the generalized form factors connected to the first moments of chiral-even generalized parton distributions. For the description of QCD at low energies we employ the framework of two-flavor covariant baryon chiral perturbation theory at full one-loop accuracy. Our results are well suited for the extrapolation of lattice QCD data to physical quark masses.

Figure 1

Feynman diagrams needed for the full one-loop calculation. Diagram (f) only contributes to the (isosinglet) vector current. Diagram (a) has to be multiplied with a $Z$ factor if the operator insertion is of zeroth or first order. Additional Feynman diagrams containing quark mass insertions from the second-order pion-nucleon Lagrangian are not shown explicitly.