Universality of the Spectral Memory Scale Across Few-Body Nuclear Systems

Abstract

In standard nuclear Effective Field Theory (EFT), the ultraviolet (UV) sensitivity of the three-body sector (Thomas collapse) is resolved by introducing a phenomenological, cutoff-dependent three-nucleon force (3NF) counterterm. In this work, part of the History-Dependent Gravity (HDG) series, we demonstrate that temporal nonlocality, encoded as a spectral memory kernel, naturally acts as an intrinsic, cutoff-independent regulator for few-body nuclear systems. We rigorously test the universality of the spectral memory scale μ∗μ∗. By applying a multiplicative deformation to the coupled-channel Faddeev kernel, we show that a single value of μ∗μ∗, calibrated exclusively from the two-body deuteron sector (Bd=2.224Bd=2.224 MeV), yields a parameter-free prediction for the triton binding energy (B3≈8.90B3≈8.90 MeV). We introduce a "Reverse Test": extracting the μ∗μ∗ required to reproduce the empirical triton binding energy (8.488.48 MeV) yields 166.42166.42 MeV, differing from the two-body prediction (175.93175.93 MeV) by only 5.4%5.4%. This minor discrepancy perfectly matches the well-documented ss-wave overbinding systematic of separable Yamaguchi potentials, confirming that no ad hoc 3NF is required. Crucially, we prove strict Renormalization Group (RG) invariance by decoupling the physical memory scale from the numerical quadrature grid scale. Varying the numerical cutoff from 100100 to 300300 MeV yields a required physical scale with a standard deviation of σ≈0.00σ≈0.00 MeV. Furthermore, eigenvalue diagnostics confirm that the HDG kernel actively suppresses UV modes (tail slope ≈−5.3≈−5.3) without inducing unphysical blow-up. This bidirectional consistency proves that μ∗μ∗ is a universal, RG-invariant constant of the nuclear memory sector, suggesting that conventional three-nucleon forces are emergent artifacts of neglecting temporal nonlocality. This submission includes the complete, fully reproducible Python (NumPy/SciPy) numerical pipeline used to generate all results and figures, adhering to open-science standards.