Alberg and Miller Reply to arXiv:arXiv:1206.3671

TL;DR

The authors clarify that their pion-nucleon effective theory aligns with pseudovector results due to the equivalence theorem, and they address misconceptions about their approach's accuracy in calculating pion momentum distributions.

Contribution

They clarify the theoretical basis of their calculations and defend the validity of their results against recent comments questioning their methodology.

Findings

Their theory reproduces PV results due to the equivalence theorem.

Discrepancies in pion momentum distribution are within uncertainties.

Their conclusions remain unaffected by the recent comment.

Abstract

In a recent Comment [arXiv:1206.3671] on our calculation of the pion contributions to the self-energy of the nucleon [arXiv:1201.4184], Ji, Melnitchouk and Thomas (JMT) correctly state that we obtain the same result as given by the pseudovector (PV) theory. We point out that this result is expected by the equivalence theorem, since our pion-nucleon effective theory puts the intermediate nucleon on its mass shell. We make no claim that pseudoscalar (PS) and pseudovector interactions are equivalent in general. JMT also argue that our theory will not give the correct PV result for the pion momentum distribution $f^N_{\pi}$. We note that the discrepancies are much smaller than the uncertainties due to $\pi N$ form factors. To summarize, nothing in the Comment by JMT changes the conclusions or numerical results of our work in any substantive way.