Radius-Flow Entanglement in Hadron States and Gravitational Form Factors
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918525582442496 |
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| author | Mamo, Kiminad A. |
| author_facet | Mamo, Kiminad A. |
| contents | We define an operational integer-$n$ lattice observable for state-dependent spatial entanglement in QCD hadrons and a falsifiable local-window analysis of its radius dependence. The observable is the vacuum-subtracted logarithmic radius derivative of the ball Rényi entropy, $\mathfrak{s}_n(R;h)=R\partial_RΔS_n(B_R;h)$, evaluated in a rest-frame momentum-projected one-hadron state. At fixed replica/cut prescription, $ΔS_n$ is a direct integer-$n$ replica ratio and $\mathfrak{s}_n$ is obtained as its correlated radius derivative; the intended first target is $n=2$, and spin averaging is performed only after forming the flow. Continuum trace-response identities motivate a trace-channel organization, but the proposed lattice observable and fits are defined directly at fixed integer $n$. We test boundary dominance by fitting local $R$ windows to a low-curvature remainder plus two candidate endpoint templates, $\mathfrak{t}_h^{(0)}(R)=R^3ρ_S(R)$ from the trace gravitational form factor $A^S(t)$ and $\mathfrak{t}_h^{(2)}(R)=R^3ρ_A(R)$ from the spin-2 gravitational form factor $A(t)$. A soft-wall AdS/QCD trace--energy calculation motivates this two-function basis and gives an optional model-dependent fixed-ratio benchmark; the lattice coefficients are left free. For representative nucleon dipole gravitational form factors, the pure endpoint-template peak scales are $R_{\rm peak}^{(0)}\simeq0.84~{\rm fm}$ and $R_{\rm peak}^{(2)}\simeq0.43~{\rm fm}$, so lattice data can distinguish scalar dominance, spin-2 dominance, genuine mixing, or failure of the boundary-dominance ansatz. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_03064 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Radius-Flow Entanglement in Hadron States and Gravitational Form Factors Mamo, Kiminad A. High Energy Physics - Phenomenology High Energy Physics - Lattice High Energy Physics - Theory Nuclear Theory We define an operational integer-$n$ lattice observable for state-dependent spatial entanglement in QCD hadrons and a falsifiable local-window analysis of its radius dependence. The observable is the vacuum-subtracted logarithmic radius derivative of the ball Rényi entropy, $\mathfrak{s}_n(R;h)=R\partial_RΔS_n(B_R;h)$, evaluated in a rest-frame momentum-projected one-hadron state. At fixed replica/cut prescription, $ΔS_n$ is a direct integer-$n$ replica ratio and $\mathfrak{s}_n$ is obtained as its correlated radius derivative; the intended first target is $n=2$, and spin averaging is performed only after forming the flow. Continuum trace-response identities motivate a trace-channel organization, but the proposed lattice observable and fits are defined directly at fixed integer $n$. We test boundary dominance by fitting local $R$ windows to a low-curvature remainder plus two candidate endpoint templates, $\mathfrak{t}_h^{(0)}(R)=R^3ρ_S(R)$ from the trace gravitational form factor $A^S(t)$ and $\mathfrak{t}_h^{(2)}(R)=R^3ρ_A(R)$ from the spin-2 gravitational form factor $A(t)$. A soft-wall AdS/QCD trace--energy calculation motivates this two-function basis and gives an optional model-dependent fixed-ratio benchmark; the lattice coefficients are left free. For representative nucleon dipole gravitational form factors, the pure endpoint-template peak scales are $R_{\rm peak}^{(0)}\simeq0.84~{\rm fm}$ and $R_{\rm peak}^{(2)}\simeq0.43~{\rm fm}$, so lattice data can distinguish scalar dominance, spin-2 dominance, genuine mixing, or failure of the boundary-dominance ansatz. |
| title | Radius-Flow Entanglement in Hadron States and Gravitational Form Factors |
| topic | High Energy Physics - Phenomenology High Energy Physics - Lattice High Energy Physics - Theory Nuclear Theory |
| url | https://arxiv.org/abs/2603.03064 |