Target normal single-spin asymmetry in inclusive electron-nucleon scattering in the 1/Nc expansion

Abstract

The target normal single-spin asymmetry in inclusive electron-nucleon scattering is studied in the low-energy regime that includes the $\mathrm{\ensuremath{\Delta}}$ resonance. The particular interest in the asymmetry resides in that it is driven by two-photon exchange effects. It probes the spin-dependent absorptive part of the two-photon exchange amplitude, which is free of infrared and collinear singularities and represents the most pristine expression of two-photon exchange dynamics. The study presented here uses the $1/{N}_{c}$ expansion of QCD, which combines the $N$ and $\mathrm{\ensuremath{\Delta}}$ through the emergent $SU(4)$ spin-flavor symmetry in the baryon sector and allows for a systematic construction of the transition electromagnetic (EM) currents. The analysis includes the first subleading corrections in the $1/{N}_{c}$ expansion and presents results for elastic and inelastic final states. The asymmetry is found to be in the range ${10}^{\ensuremath{-}3}\ensuremath{-}{10}^{\ensuremath{-}2}$. The $\mathrm{\ensuremath{\Delta}}$ resonance plays an important role as an intermediate state in the elastic asymmetry and as a final state in the inclusive asymmetry.