Counting and tensorial properties of twist-two helicity-flip nucleon form factors

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 and 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 of twist-two, helicity-flip quark (gluon) operators are $2n-1$ ($2n-5$) if $n$ is odd, and $2n-2$ ($2n-6$) if $n$ is even, with $n\ge 2$ ($n\ge 4$). We also analyze 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.