Alberg and Miller Reply to arXiv:arXiv:1206.3671

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.