Off forward non-SCHC contributions to exclusive vector quarkonium production from the "spin dependent BFKL Pomeron"

A novel contribution to off-forward, exclusive vector quarkonium production, $\gamma^{(*)}+p \to V+p$, at high energy is derived which corresponds to a $t$-channel exchange of a BFKL hard Pomeron, with a helicity flip of the proton. This ``spin-dependent BFKL Pomeron" is required in a consistent expansion in powers of the momentum transfer $t \approx -\Delta_\perp^2$ beyond first order. The spin-dependent Pomeron violates $s$-channel helicity conservation (SCHC) at ${\cal O}(\Delta_\perp^2)$, and beyond. Expanding to leading twist only, it corresponds to GPD $E_g(x,t)$ for vanishing skewness. We derive explicit expressions for the eikonal BFKL amplitudes, to all orders in dipole size times momentum transfer, for all helicity configurations of the particles in the initial and final states. We also provide numerical estimates of the helicity flip two gluon exchange amplitude at moderate $x$ from a light-cone quark model of the proton. The spin dependent BFKL Pomeron could, in principle, be discovered via double spin asymmetries in $e+p \to e+p+J/\psi$ with transversely polarized proton and longitudinally polarized electron in the initial state.