Radius-Flow Entanglement in Hadron States and Gravitational Form Factors

TL;DR

This paper introduces a lattice-compatible entanglement measure for hadrons based on radius flow of Rènyi entropy, linking it to gravitational form factors and enabling new tests of boundary dominance in QCD.

Contribution

It proposes a novel entanglement observable for QCD hadrons, connecting lattice measurements with gravitational form factors and providing a method to analyze boundary effects.

Findings

Distinct extremum scales for scalar and spin-2 controls (~0.84 fm and ~0.43 fm)

A lattice stability test for boundary dominance using radius flow data

Model-dependent benchmarks for gravitational form factor ratios

Abstract

We propose a lattice-ready entanglement observable for QCD hadrons: the vacuum-subtracted radius flow of the ball R\'enyi entropy, $\mathfrak{s}_n(R;h)\equiv R\,\partial_R\Delta S_n(B_R;h)$, defined via the Euclidean replica cut-and-glue construction in a rest-frame momentum-projected one-hadron state, with spin averaging performed at the level of the final flow. In the continuum, varying $R$ at fixed shape is equivalent to a Weyl rescaling, so the flow is trace selected and admits a surface-plus-remainder organization on the entangling sphere. We use this to formulate a lattice stability test of boundary dominance: fit the measured flow on local $R$ windows to a low-curvature remainder plus a small template basis built from hadronic gravitational form factors (GFFs). The two endpoint templates are the spin-0/trace shape $\mathfrak{t}_h^{(0)}(R)=R^3\rho_S(R)$ constructed from $A^S(t)$ and a spin-2/TT proxy $\mathfrak{t}_h^{(2)}(R)=R^3\rho_A(R)$ constructed from $A(t)$, together with the mixed family $\mathfrak{t}_h^{\rm mix}(R;c_0,c_2)=c_0\mathfrak{t}_h^{(0)}(R)+c_2\mathfrak{t}_h^{(2)}(R)$. A soft-wall AdS/QCD appendix shows that the pole-subtracted integrated trace--energy correlator closes on this same $\{A^S,A\}$ basis and supplies a model-dependent benchmark ratio for $c_0/c_2$; for lattice comparison the coefficients are left free and extracted from data. For representative nucleon dipole inputs, the pure endpoints predict distinct single-extremum scales, $R_{\rm EE}^{(0)}\sim0.84~\mathrm{fm}$ and $R_{\rm EE}^{(2)}\sim0.43~\mathrm{fm}$, enabling discrimination among scalar control, spin-2 control, and genuine mixing through the turning-point location, the sign change of the slope across it, and the fitted ratio of template weights.