Study of intermediate states in the inclusive semi-leptonic $B \to X_c \ell\nu$ decay structure functions

We analyze the inclusive semileptonic $B \to X_c \ell\nu$ structure functions in 2+1-flavor lattice QCD. The M\"obius domain-wall fermion action is used for light, strange, charm and bottom quarks. The structure function receives contributions from various exclusive modes, including the dominant S-wave states $D^{(*)}_s$ as well as the P-wave states $D_s^{**}$. We can identify them in the lattice data, from which we put some constraints on the $B_s \to D_s^{**}\ell\nu$ form factors.