Holographic description of the kaon gravitational form factor

TL;DR

This work computes the kaon gravitational form factor $A_K(Q^2)$ within a $N_f=3$ bottom-up holographic QCD model that incorporates $SU(3)$ flavor breaking through the strange quark mass. By solving for the kaon bulk profile $\phi_K(z)$ and the graviton bulk-to-boundary propagator $h(q,z)$, the authors obtain $A_K(Q^2)=\int_{0}^{z_0} \frac{dz}{z^3} h(q,z) |\phi_K(z)|^2$, with $A_K(0)=1$ and a high-$Q^2$ falloff $A_K(Q^2) \sim \frac{16 \pi^2 f_K^2}{Q^2}$, consistent with perturbative QCD. The extracted gravitational radius is $\langle r_G^2\rangle_K = (0.35\ \mathrm{fm})^2$, slightly smaller than the pion’s, indicating a marginally more compact mass distribution due to $SU(3)$ breaking. Overall, the holographic approach captures the kaon’s internal energy–momentum distribution and its similarity to the pion, while confirming PQCD scaling at large $Q^2$ and pointing toward extensions to heavier quarks.

Abstract

We compute the kaon gravitational form factor (GFF) using a bottom-up holographic QCD approach that incorporates SU(3) flavor symmetry breaking through the strange quark mass. We present the resulting Q^2 dependence of the kaon GFF and compare it with that of the pion. In the high-energy limit, the kaon GFF exhibits a 1/Q^2 falloff, in agreement with perturbative QCD. Furthermore, we extract the gravitational radius of the kaon and find it to be almost the same as that of the pion, with a slightly smaller value.

Figures (1)

• Figure 1: The gravitational form factors as a function of $Q^2$. The solid and dashed curves represent the kaon and pion results Liu:2025vfeAbidin:2008hn, respectively.