# Gluon gravitational form factors of the nucleon and the pion from lattice QCD

## Abstract

A future electron-ion collider will enable the gluon contributions to the gravitational form factors of the proton to be constrained experimentally for the first time. Here, the first calculation of these form factors from lattice quantum chromodynamics is presented. The calculations use a larger-than-physical value of the light quark mass corresponding to m _{π} ~ 450 MeV . All three form factors, which encode the momentum dependence of the lowest moment of the spin-independent gluon generalized parton distributions and are related to different components of the energy-momentum tensor, are resolved. In particular, the gluon *D*-term form factor, related to the pressure distribution inside the nucleon, is determined for the first time. The gluon contributions to the two gravitational form factors of the pion are also determined, and are compared to existing lattice determinations of the quark contributions to the gravitational form factors and to phenomenology.

- Authors:

- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); Perimeter Institute for Theoretical Physics, Waterloo, ON (Canada)
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

- Publication Date:

- Research Org.:
- Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1491778

- Alternate Identifier(s):
- OSTI ID: 1544130

- Grant/Contract Number:
- AC02-05CH11231; SC0010495

- Resource Type:
- Published Article

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Volume: 99; Journal Issue: 1; Journal ID: ISSN 2470-0010

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

### Citation Formats

```
Shanahan, P. E., and Detmold, W. Gluon gravitational form factors of the nucleon and the pion from lattice QCD. United States: N. p., 2019.
Web. doi:10.1103/PhysRevD.99.014511.
```

```
Shanahan, P. E., & Detmold, W. Gluon gravitational form factors of the nucleon and the pion from lattice QCD. United States. doi:10.1103/PhysRevD.99.014511.
```

```
Shanahan, P. E., and Detmold, W. Wed .
"Gluon gravitational form factors of the nucleon and the pion from lattice QCD". United States. doi:10.1103/PhysRevD.99.014511.
```

```
@article{osti_1491778,
```

title = {Gluon gravitational form factors of the nucleon and the pion from lattice QCD},

author = {Shanahan, P. E. and Detmold, W.},

abstractNote = {A future electron-ion collider will enable the gluon contributions to the gravitational form factors of the proton to be constrained experimentally for the first time. Here, the first calculation of these form factors from lattice quantum chromodynamics is presented. The calculations use a larger-than-physical value of the light quark mass corresponding to mπ ~ 450 MeV . All three form factors, which encode the momentum dependence of the lowest moment of the spin-independent gluon generalized parton distributions and are related to different components of the energy-momentum tensor, are resolved. In particular, the gluon D-term form factor, related to the pressure distribution inside the nucleon, is determined for the first time. The gluon contributions to the two gravitational form factors of the pion are also determined, and are compared to existing lattice determinations of the quark contributions to the gravitational form factors and to phenomenology.},

doi = {10.1103/PhysRevD.99.014511},

journal = {Physical Review D},

number = 1,

volume = 99,

place = {United States},

year = {2019},

month = {1}

}

DOI: 10.1103/PhysRevD.99.014511

*Citation information provided by*

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