Leading Chiral Corrections to the Nucleon Generalized Parton Distributions

Generalized parton distributions (GPDs) describe how quarks are arranged inside the proton: they combine the one-dimensional parton distribution functions with elastic form factors into a more complete picture of the proton's internal structure. The moments of these distributions, integrals over the momentum fraction x, are quantities that lattice QCD can compute. Current lattice calculations use quark masses heavier than in nature, so one must extrapolate to the physical point. Chiral perturbation theory, the low-energy effective theory of QCD, predicts how these moments depend on the pion mass and on momentum transfer, including square-root and logarithmic terms that cannot be reproduced by simple polynomials.

Using heavy baryon chiral perturbation theory, the authors compute the leading mass and momentum-transfer dependence for the complete set of eight quark GPDs, extending earlier work that covered only the spin-averaged and helicity cases. They also discuss the tensor (transversity) GPDs and the gluon GPDs. The leading non-analytic corrections are clean predictions: they depend only on known low-energy constants such as the pion decay constant and the axial coupling, together with moments of the pion distribution. Many of their results reduce to known form factors in special limits, which serves as a check.

The authors then apply the corrected moments to impact parameter distributions, which show where partons sit in the transverse plane. They find that for several isovector GPDs the transverse size squared grows as 1/m_pi^2 as the pion mass goes to zero, a signature of the pion cloud. For the pion-pole term in the pseudoscalar GPD, the transverse size is exactly 4/m_pi^2. These are concrete, testable predictions for future lattice and experiment comparisons.