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