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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]
  1. 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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Works referenced in this record:

Dynamical Model of Elementary Particles Based on an Analogy with Superconductivity. II
journal, October 1961


D term and the structure of pointlike and composed spin-0 particles
journal, December 2017


Neutrino- and antineutrino-deuteron elastic scattering and the axial isoscalar nucleon current
journal, July 1992


Quantum chromodynamics and other field theories on the light cone
journal, August 1998


Forces inside hadrons: Pressure, surface tension, mechanical radius, and all that
journal, September 2018

  • Polyakov, Maxim V.; Schweitzer, Peter
  • International Journal of Modern Physics A, Vol. 33, Issue 26
  • DOI: 10.1142/S0217751X18300259

Dynamic origins of fermionic D -terms
journal, March 2018


Charge Densities of the Neutron and Proton
journal, September 2007


General relativity with spin and torsion: Foundations and prospects
journal, July 1976

  • Hehl, Friedrich W.; von der Heyde, Paul; Kerlick, G. David
  • Reviews of Modern Physics, Vol. 48, Issue 3
  • DOI: 10.1103/RevModPhys.48.393

The energy-momentum tensor of spin-1 hadrons: formalism
journal, June 2019


Gravitational Ward Identity and the Principle of Equivalence
journal, January 1966


Revisiting the mechanical properties of the nucleon
journal, January 2019


Generalized Parton Distributions in the Deuteron
journal, September 2001


Gravitational form factors of vector mesons in an AdS/QCD model
journal, May 2008


Extended NJL model for light and heavy mesons without thresholds
journal, November 1996


Deeply virtual Compton scattering
journal, June 1997


Solution of the relativistic three quark Faddeev equation in the Nambu-Jona-Lasinio (NJL) model
journal, November 1993


Generalized parton distributions and strong forces inside nucleons and nuclei
journal, February 2003


On the hadron mass decomposition
journal, February 2018


Comment on the ???J/??? decay
journal, March 1981

  • Novikov, V. A.; Shifman, M. A.
  • Zeitschrift f�r Physik C Particles and Fields, Vol. 8, Issue 1
  • DOI: 10.1007/BF01429829

Collective Perspective on Advances in Dyson—Schwinger Equation QCD
journal, July 2012

  • Bashir, Adnan; Chang, Lei; Cloët, Ian C.
  • Communications in Theoretical Physics, Vol. 58, Issue 1
  • DOI: 10.1088/0253-6102/58/1/16

Nucleon Mass and the Gravitational Ward-Takahashi Identity
journal, April 1969


Generalized parton distributions
journal, December 2003


Forms of Relativistic Dynamics
journal, July 1949


Axial-Vector Vertex in Spinor Electrodynamics
journal, January 1969


Angular momentum sum rule for spin-one hadronic systems
journal, August 2012


The angular momentum controversy: What’s it all about and does it matter?
journal, August 2014


Dynamical Model of Elementary Particles Based on an Analogy with Superconductivity. I
journal, April 1961


Measuring Quantum-Chromodynamic Anomalies in Hadronic Transitions between Quarkonium States
journal, September 1980


The Nambu and Jona-Lasinio model: Its implications for Hadrons and Nuclei
journal, January 1991


Quantum Theory of Gravity. III. Applications of the Covariant Theory
journal, October 1967


Defining the proton radius: A unified treatment
journal, March 2019


Sur les variétés à connexion affine, et la théorie de la relativité généralisée (première partie) (Suite)
journal, January 1924

  • Cartan, Elie
  • Annales scientifiques de l'École normale supérieure, Vol. 41
  • DOI: 10.24033/asens.753

Off-forward parton distributions
journal, July 1998


Sur les variétés à connexion affine et la théorie de la relativité généralisée (première partie)
journal, January 1923

  • Cartan, Elie
  • Annales scientifiques de l'École normale supérieure, Vol. 40
  • DOI: 10.24033/asens.751

Empirical transverse charge densities in the deuteron
journal, May 2009


The relativistic center of mass in field theory with spin
journal, September 2018


QCD phenomenology based on a chiral effective Lagrangian
journal, October 1994


Polynomiality sum rules for generalized parton distributions of spin-1 targets
journal, May 2019


Gluon gravitational form factors of the nucleon and the pion from lattice QCD
journal, January 2019


Faddeev approach to the nucleon in the Nambu-Jona-Lasinio (NJL) model
journal, March 1993


Diquark confinement in an extended NJL model
journal, November 1997


Spatial distribution of angular momentum inside the nucleon
journal, January 2018


The Nambu—Jona-Lasinio model of quantum chromodynamics
journal, July 1992


Baryons in the NJL model as solutions of the relativistic Faddeev equation
journal, May 1995


Skewed and double distributions in the pion and the nucleon
journal, November 1999


Transverse-momentum-dependent quark distribution functions of spin-one targets: Formalism and covariant calculations
journal, October 2017


Role of diquark correlations and the pion cloud in nucleon elastic form factors
journal, October 2014