Nucleon mass radii and distribution: Holographic QCD, lattice QCD, and GlueX data

Abstract

We briefly review and expand our recent analysis for all three invariant A, B, D gravitational form factors of the nucleon in holographic QCD. They compare well to the gluonic gravitational form factors recently measured using lattice QCD simulations. The holographic A-term is fixed by the tensor T = 2++(graviton) Regge trajectory, and the D-term by the difference between the tensor T = 2++(graviton) and scalar S = 0++(dilaton) Regge trajectories. The B-term is null in the absence of a tensor coupling to a Dirac fermion in bulk. A first measurement of the tensor form factor A-term is already accessible using the current GlueX data, and therefore the tensor gluonic mass radius, pressure, and shear inside the proton, thanks to holography. The holographic A-term and D-term can be expressed exactly in terms of harmonic numbers. The tensor mass radius from the holographic threshold is found to be (r2GT) ≈(0.57-0.60 fm)2, in agreement with (r2GT) ≈(0.62 fm)2as extracted from the overall numerical lattice data, and empirical GlueX data. The scalar mass radius is found to be slightly larger (r2GS) ≈ (0.7 fm)2