Entanglement between Valence and Sea Quarks in Hadrons of 1+1 Dimensional QCD

The conceptual interpretation of valence- and sea-quark separation, which is a key aspect of the parton model and of an intuitive picture of hadron structure, becomes obscured by quantum effects in QCD. This suggests that there may be measures of entanglement between quark degrees of freedom that are present in QCD, but absent in the intuitive picture with a clear valence-sea (VS) separation. In this paper, we define the first rigorous measure of VS entanglement in QCD in an attempt to bring conceptual clarity to this issue, and, potentially, to find a measure of the applicability of the parton model to QCD bound states. This VS entanglement vanishes in the large-$N_c$ limit, and it remains low when finite-$N_c$ states resemble their large-$N_c$ counterparts. We perform a numerical study of VS entanglement in 1+1 dimensional discrete light-cone quantized QCD, and in the process develop a method for building the color-singlet basis of 1+1d QCD that is manifestly complete and orthogonal by construction. We calculate this VS entanglement entropy for the first time and find that it is relatively low for the first few excited states of both mesons and baryons compared to all other states in the spectrum, with the VS entropy of ground state hadrons providing a minimum. We also see that for ground state mesons the entropy is well described in the $1/N_c$ approximation. These results suggest that low energy hadrons may be the only QCD bound states for which the large-$N_c$ expansion, and perhaps the parton model, provide an accurate description. This work also provides the first evidence that the VS entanglement entropy of QCD in 3+1d, which would likely serve as an order parameter for the transition between quark and hadron degrees of freedom, may be perturbatively accessible through a large-$N_c$ expansion.