Taming the Pion Cloud of the Nucleon

Abstract

We present a light-front determination of the pionic contribution to the nucleon self-energy, Σ(π), to second order in pion-baryon coupling constants that allows the pion-nucleon vertex function to be treated in a model-independent manner constrained by experiment. The pion mass μ dependence of Σ(π) is consistent with chiral perturbation theory results for small values of μ and is also linearly dependent on μ for larger values, in accord with the results of lattice QCD calculations. The derivative of Σ(π) with respect to μ(2) yields the dominant contribution to the pion content, which is consistent with the d[over ¯]-u[over ¯] difference observed experimentally in the violation of the Gottfried sum rule.

Light-front field theory in the description of hadrons

“…Thus, one may effectively get the equivalence between the "on-shell" contributions of the PV and PS theories in the self-energy calculation [32]. This also confirms the model-independence of the LNA behavior in the nucleon self-energy regardless whether the PV theory or the PS theory is used.…”

“…The equivalence in the "on-shell" contribution between PV and PS coupling theories is boxed with Ref. [32]. The cancellation between the two light-front zero-mode contributions in the PS coupling is denoted by the double-arrow pointing to those two contributions, i.e.…”

Alberg and Miller Reply:

“…This conclusion is obviously correct, but no claim of general equivalence between PS and PV theory was made in our paper [2].…”

“…To summarize, nothing in the Comment by Ji et al changes the conclusions or numerical results of [2] in any substantive way.…”

Comment on “Taming the Pion Cloud of the Nucleon”

“…In a recent Letter, Alberg and Miller (AM) [1] presented a calculation of the pion contributions to the self-energy of the nucleon, in an attempt to better constrain the role of the pion cloud in the " d À " u asymmetry in the proton sea. In computing the self-energy AE, AM used the on-shell projection of the nucleon propagator, arguing that form factors suppress the off-shell, contact contributions, thereby rendering the pseudovector (PV) and pseudoscalar (PS) pionnucleon interactions equivalent.…”