Counting and Tensorial Properties of Twist-Two Helicity-Flip Nucleon Form Factors

Abstract

We perform a systematic analysis on the off-forward matrix elements of the twist-two quark and gluon helicity-flip operators. By matching the allowed quantum numbers and their crossing channel counterparts (a method developed by Ji & Lebed), we systematically count the number of independent nucleon form factors in off-forward scattering of matrix elements of these quark and gluon spin-flip operators. In particular, we find that the numbers of independent nucleon form factors twist-2, helicity flip quark (gluon) operators are $2n-1$ ($2n-5$) if $n$ is odd, and $2n-2$ ($2n-6$) if $n$ is even, with $n\ge2$ ($n\ge 4$). We also analysis and write down the tensorial/Lorentz structure and kinematic factors of the expansion of these operators' matrix elements in terms of the independent form factors. These generalized form factors define the off-forward quark and gluon helicity-flip distributions in the literature.