Comment on "Taming the pion cloud of the nucleon"

TL;DR

This paper clarifies that pseudoscalar and pseudovector pion-nucleon interactions produce different self-energy results for the nucleon, especially regarding their nonanalytic behavior in the chiral limit.

Contribution

It demonstrates the fundamental differences between PS and PV couplings in nucleon self-energy calculations, correcting a previous claim of their equivalence.

Findings

PV coupling yields m_pi^3 dependence in self-energy

PS coupling involves additional m_pi^2 log(m_pi^2) term

PV and PS interactions are not equivalent in nucleon self-energy

Abstract

In a recent Letter, Alberg and Miller presented a calculation of the pion contributions to the self-energy of the nucleon computed from a pseudoscalar (PS) pion-nucleon interaction, with the claim that the result would be equivalent to that with the pseudovector (PV) form. We demonstrate that the PV and PS pion-nucleon couplings do in fact lead to different results for the self-energy. In particular, for the model-independent, leading nonanalytic behavior of the self-energy, the PV theory yields the well-known m_\pi^3 dependence in the chiral limit, while the PS interaction involves an additional, lower-order term ~ m_\pi^2 log(m_\pi^2).