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# Gravitational form factors of light mesons

## Abstract

Here, we calculate the gravitational form factors of the pion, $$\sigma$$ meson, and $$\rho$$ meson in the Nambu-Jona-Lasinio 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 0.32 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.

- Authors:

- Argonne National Lab. (ANL), Argonne, IL (United States)

- Publication Date:

- Research Org.:
- Argonne National Lab. (ANL), Argonne, IL (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)

- OSTI Identifier:
- 1563916

- Alternate Identifier(s):
- OSTI ID: 1532793

- Grant/Contract Number:
- [AC02-06CH11357]

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physical Review C

- Additional Journal Information:
- [ Journal Volume: 100; Journal Issue: 1]; Journal ID: ISSN 2469-9985

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 73 NUCLEAR PHYSICS AND RADIATION PHYSICS

### Citation Formats

```
Freese, Adam, and Cloët, Ian C. Gravitational form factors of light mesons. United States: N. p., 2019.
Web. doi:10.1103/PhysRevC.100.015201.
```

```
Freese, Adam, & Cloët, Ian C. Gravitational form factors of light mesons. United States. doi:10.1103/PhysRevC.100.015201.
```

```
Freese, Adam, and Cloët, Ian C. Wed .
"Gravitational form factors of light mesons". United States. doi:10.1103/PhysRevC.100.015201.
```

```
@article{osti_1563916,
```

title = {Gravitational form factors of light mesons},

author = {Freese, Adam and Cloët, Ian C.},

abstractNote = {Here, we calculate the gravitational form factors of the pion, $\sigma$ meson, and $\rho$ meson in the Nambu-Jona-Lasinio 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 0.32 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.},

doi = {10.1103/PhysRevC.100.015201},

journal = {Physical Review C},

number = [1],

volume = [100],

place = {United States},

year = {2019},

month = {7}

}

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