Tensor-polarized parton density in the $N\to \mathrm{\Delta }$ transition

The generalized parton distributions for transitions between baryon states with different masses have a forward limit in which they behave as parton densities (light-front momentum transfer ${\mathrm{\Delta }}^{+},{\mathrm{\Delta }}_T=0$, energy transfer ${\mathrm{\Delta }}^{-}\mathrm{\ne }0$). These "transition parton densities’’ can realize spin/isospin quantum numbers not accessible in the ground-state nucleon. The $N\to \mathrm{\Delta }$ transition gives rise to a new parton density proportional to the $1\mathrm{/}2\to 3\mathrm{/}2$ spin transition tensor. Its properties are derived, and its magnitude is estimated in the chiral quark-soliton model based on the large-$N_c$ limit of QCD.