Dispersion relations for non-helicity-conserving CFFs

Derive dispersion relations for the non-helicity-conserving Compton form factors (CFFs) \(\mathcal{H}^{+-}\) and \(\mathcal{H}^{0+}\), whose real and imaginary parts are currently modeled independently because the relevant relations are unknown.

Background

The theory-augmented extraction model exploits known dispersion relations to reduce the number of independently parameterized functions for helicity-conserving CFFs. However, the corresponding relations for the helicity-flip amplitudes $\mathcal{H}^{+-}$ and $\mathcal{H}^{0+}$ have not been established, preventing the same reduction for these sectors. Deriving such relations would allow their real and imaginary parts to be constrained consistently within the dispersion-based framework.