Light-front diagnostics in the 't Hooft model: II. Boundary cancellations, ERBL spectral sums, and analyticity of the EMT form factor

Abstract

A diagonal light-front overlap contains near-forward energy-momentum-tensor (EMT) information but is not itself a local matrix element. In the large-$N_c$ 't Hooft model we complete the second GPD moment with its ERBL contribution and follow how the two support regions combine. Boundary exponents generate fractional powers and, at $β=1/2$, resonant logarithms in the separate terms. We show that these structures cancel, including the interference of the leading and next indicial families. At the resonance, cancellation of the double and single logarithms also yields an inverse-mass-squared residue sum rule; above it, the two regions combine into a finite fourth-order coefficient. The complete EMT form factor is therefore analytic through curvature order. The ERBL sector leaves the slope unchanged but is essential for curvature and higher derivatives. We extract stable canonical and heavy curvatures, estimates with systematic envelopes for the second and third light excitations, and the longitudinal trace radius. The intermediate-state decomposition further shows how constituent mass and excitation redistribute pole strength and generate removable poles and interference zeros.