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 the constraints time reversal might have on these matrix elements and their crossing channel counterparts, 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 spin-$J$, twist-2, helicity-flip quark (gluon) operators are 2J-1 (2J-2) if J is odd, and 2J-2(2J-1)if J is even, with J>=1 (J>=2). We also analysis and write down the tensorial/Lorentz structure and kinematic factors of the quark operator matrix elements' expansion in terms of the independent form factors. These generalized form factors define the off-forward quark and gluon helicity-flip distributions in the literature.Keywords
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