# Gravitational form factors of light mesons

## TL;DR

This paper computes the gravitational form factors of light mesons using the NJL model, revealing insights into their internal structure and mass distribution, and compares these with charge radii and experimental data.

## Contribution

It introduces a method to calculate meson gravitational form factors using the canonical EMT and demonstrates the importance of dressing the graviton vertex for accurate results.

## Key findings

- Light cone mass radii: pion 0.27 fm, sigma 0.32 fm, rho 0.25 fm.
- Pion and rho mass radii are smaller than their charge radii.
- The pion mass radius agrees with KEKB experimental data.

## Abstract

We calculate the gravitational form factors of the pion, sigma meson, and rho meson in the Nambu-Jona-Lasinio (NJL) model of quantum chromodynamics. The canonical energy-momentum tensor (EMT) is used in their derivation, allowing the possibility of an antisymmetric contribution when the hadron has intrinsic spin. We show that the asymmetric graviton vertex arising from the canonical EMT satisfies a simpler Ward-Takahashi identity (WTI) than the symmetric graviton vertex of the Belinfante EMT. The necessity of fully dressing the graviton vertex through the relevant Bethe-Salpeter equation is demonstrated for observing both the WTI and a low-energy pion theorem. Lastly, we calculate static moments of the meson EMT decompositions, obtaining predictions for the meson mass radii. We find light cone mass radii of 0.27 fm for the pion, 0.32 fm for the sigma, and 0.25 fm for the rho. For the pion and rho, these are smaller than the light cone charge radii, respectively 0.51 fm and 0.45 fm, while we have a sigma charge radius of zero. Our light cone pion mass radius agrees with a phenomenological extraction from KEKB data.