Target normal single-spin asymmetry in inclusive electron-nucleon scattering with two-photon exchange: Analysis using $1\mathrm{/}{N}_c$ expansion

We calculate the target normal single-spin asymmetry caused by two-photon exchange in inclusive electron-nucleon scattering in the resonance region. Our analysis uses the $1\mathrm{/}{N}_c$ expansion of low-energy QCD and combines $N$ and $\mathrm{\Delta }$ intermediate and final states using the contracted $SU(4)$ spin-flavor symmetry. The normal spin asymmetry obtained in leading-order accuracy in $1\mathrm{/}{N}_c$ has magnitude $\sim {10}^{-2}$ and different sign in $ep$ and $en$ scattering. It can be measured in electron scattering at lab energies $\sim$ 0.5-1.5 GeV and provides a clean probe of two-photon exchange dynamics.