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Mechanical Properties of the Proton from a Deformed AdS Holographic Model

Ayrton Nascimento, Henrique Boschi-Filho

Abstract

We study the gravitational form factors of the proton and some of its mechanical properties. We use a holographic model based on the AdS/CFT correspondence, in which a deformation in the anti-de Sitter background geometry is considered. By describing the proton as a Dirac field in this background, we numerically evaluate the gloun contribution of its gravitational form factors $A$ and $C$ from its energy-momentum tensor. A comparison of our numerical results with respect to some lattice QCD results and previous results in holography is made. In general, a good agreement is found. We also evaluate the term $D$ and make use of it to compute the pressure and shear distributions in the system, which result in a stable composed particle interpretation consistent with the von Laue stability condition. The energy distribution in the system is also obtained. Internal forces are investigated to support this picture. We are also able to compute the radii associated with these distributions in the proton.

Mechanical Properties of the Proton from a Deformed AdS Holographic Model

Abstract

We study the gravitational form factors of the proton and some of its mechanical properties. We use a holographic model based on the AdS/CFT correspondence, in which a deformation in the anti-de Sitter background geometry is considered. By describing the proton as a Dirac field in this background, we numerically evaluate the gloun contribution of its gravitational form factors and from its energy-momentum tensor. A comparison of our numerical results with respect to some lattice QCD results and previous results in holography is made. In general, a good agreement is found. We also evaluate the term and make use of it to compute the pressure and shear distributions in the system, which result in a stable composed particle interpretation consistent with the von Laue stability condition. The energy distribution in the system is also obtained. Internal forces are investigated to support this picture. We are also able to compute the radii associated with these distributions in the proton.

Paper Structure

This paper contains 9 sections, 36 equations, 7 figures, 1 table.

Table of Contents

  1. Introduction
  2. Holographic Model
  3. Proton in the deformed AdS background
  4. Gravitational Form Factors
  5. $A(q^2)$ form factor
  6. $D(q^2)$ form factor
  7. Pressure, Shear, and Energy Distributions
  8. Normal and Tangential Forces
  9. Conclusions

Figures (7)

  • Figure 1: $A(q^2)_\text{norm}$ form factor adjusted to the gluon contributions of lattice data of Shanahan:2018pib and Hackett:2023rif. The green dots correspond to the gluonic contribution in lattice QCD of Hackett:2023rif, and the blue curve represents our best-fit normalized holographic form factor $A$ .The purple curve represents the soft-wall result of Mamo & Zahed Mamo:2019mka, compared to the lattice data of Shanahan:2018pib (red dots).
  • Figure 2: Holographic $D(q^2)_\text{norm}$ form factor from deformed AdS model (blue curve) compared to gluon lattice data of Hackett:2023rif (green dots). The purple curve corresponds to the soft-wall model of Mamo:2019mka, which compares to the lattice data of Shanahan:2018pib (red dots).
  • Figure 3: Pressure distribution from the dipole approximation \ref{['eq:DipoleA']}, with a repulsive (red) and confining (green) pressure regions.
  • Figure 5: Energy distribution from the dipole approximations \ref{['eq:DipoleA']} and \ref{['eq:Adipole']}.
  • Figure 6: Normal and tangential forces on a spherical shell of radius $r$ in the nucleon.
  • ...and 2 more figures