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 $\langle r^2_{GT}\rangle \approx (0.57-0.60\,{\rm fm})^2$, in agreement with $\langle r^2_{GT}\rangle \approx (0.62\,{\rm fm})^2$ as extracted from the overall numerical lattice data, and empirical GlueX data. The scalar mass radius is found to be slightly larger $\langle r^2_{GS}\rangle \approx (0.7\,{\rm fm})^2$.