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Title: 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:
 [1];  [1]
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  1. Argonne National Lab. (ANL), Argonne, IL (United States)
Publication Date:
Research Org.:
Argonne National Laboratory (ANL), Argonne, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Nuclear Physics (NP)
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.
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Freese, Adam, & Cloët, Ian C. Gravitational form factors of light mesons. United States. https://doi.org/10.1103/PhysRevC.100.015201
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Freese, Adam, and Cloët, Ian C. Wed . "Gravitational form factors of light mesons". United States. https://doi.org/10.1103/PhysRevC.100.015201. https://www.osti.gov/servlets/purl/1563916.
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@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 = {Wed Jul 10 00:00:00 EDT 2019},
month = {Wed Jul 10 00:00:00 EDT 2019}
}
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https://doi.org/10.1103/PhysRevC.100.015201
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Figures / Tables:

FIG. 1 FIG. 1: Diagrammatic depiction of the inhomogeneous Bethe-Salpeter equation for the two-body T-matrix in the NJL model.
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      FIG. 1 (p. 2)figure
      TABLE I (p. 3)table
      FIG. 2 (p. 5)figure
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      FIG. 5 (p. 8)figure
      FIG. 6 (p. 8)figure
      FIG. 7 (p. 11)figure
      FIG. 8 (p. 11)figure
      TABLE II (p. 13)table
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