Reply to the comment of Huey-Wen Lin and Keh-Fei Liu on "Controversy concerning the definition of quark and gluon angular momentum" by E. Leader (arXiv:1111.0678, PRD 83, 096012 (2011))

TL;DR

This paper defends the gauge-invariance of certain nucleon matrix elements against recent critiques, clarifying misconceptions and highlighting a lattice paradox related to the non gauge-invariant canonical quark momentum operator.

Contribution

It provides a rebuttal to Lin and Liu's evaluation, reaffirming the gauge-invariance of physical matrix elements despite non gauge-invariant operators.

Findings

Lin and Liu's lattice results do not disprove gauge-invariance.

The argument that physical matrix elements are gauge-invariant remains valid.

A lattice paradox related to the non gauge-invariant operator is discussed.

Abstract

Lin and Liu evaluate the nucleon expectation value of the non gauge-invariant canonical quark momentum operator on a lattice, and obtain zero. They conclude that my argument that, despite the non gauge-invariance of the operator, its physical matrix elements \emph{are} gauge-invariant, cannot be correct. I show that their result has no bearing on the question of gauge-invariance, and also point to an amusing lattice paradox.