Momentum-projected hadron entanglement from lattice-QCD replica correlators

Abstract

We define a finite-volume lattice-QCD observable for the vacuum-subtracted spatial Rényi response of a source--sink-prepared, momentum-projected hadron. At fixed regulator, integer replica index $n>1$, spatial region and gauge-theory cut prescription, double-sided state projection expresses this response as a ratio of replicated and ordinary hadron correlators. The first numerical target is the $n=2$ ratio; its proposed $L^{-3}$ scaling at fixed physical region is to be tested with matched volumes. We implement the measurement in quenched SU(3) for a charged pseudoscalar meson with heavy degenerate Wilson valence quarks, $a{m}_{\mathrm{eff}}\simeq 2.07$, on two $16^3\times 32$ sheets with a central-plaquette cut. Five finite balls and empty/full controls are measured at nine source/sink placements. Their finite-ball means increase with radius at every placement. At the reference placement the three largest responses are 1.6--2.5 times an ideal single-quasiparticle occupancy reference. A full-covariance fit ${\Delta }_{\mathrm{cp}}={\kappa }_{\mathrm{occ}}{S}_2^{\mathrm{occ}}$ gives ${\kappa }_{\mathrm{occ}}=1.68\pm 0.12$; radius-window and full-control comparisons give values spanning $1.49$--$1.73$. An exact pure-state quark--antiquark pair model interpolates, in the dilute limit, between the unit-occupancy reference (${\kappa }_{\mathrm{occ}}=1$) for an unresolved meson and the double-occupancy reference (${\kappa }_{\mathrm{occ}}=2$) for a separately resolved quark and antiquark, and yields a boundary-area correction governed by their separation.

arXiv commentv5: 19 pages, 8 figures, plus 10-page Supplemental Material with 6 figures. Added exploratory quenched SU(3) lattice results for a heavy charged pseudoscalar meson, including five finite balls and empty/full controls. Added correlated occupancy fits and an exact quark-antiquark pair model deriving a boundary-area correction