[Paper Review] Electromagnetic polarizabilities of nucleons in QCD string theory

S. I. Kruglov|arXiv (Cornell University)|Oct 27, 1999

Superconducting Materials and Applications1 references1 citations

TL;DR

This paper derives the electromagnetic polarizabilities of nucleons using QCD string theory with an asymmetric quark-diquark structure and straight-line strings, employing perturbation theory in weak external fields. It predicts proton electric and diamagnetic polarizabilities of ~10×10⁻⁴ fm³ and ~−8×10⁻⁴ fm³, respectively, and estimates magnetic polarizabilities at ~10⁻⁴ fm³, resolving the magnetic crisis seen in nonrelativistic quark models.

ABSTRACT

The effective action for baryons in external electromagnetic fields is found on the basis of QCD string theory. The area law for large Wilson loops is implied and we use the same string tension as for mesons to have a slope of baryon trajectories considing with the slope of meson traectories. The asymmetric quark-diquark structure of nucleons is accepted and the approximation of straight-line strings is used.The mean distances between quarks are estimated using the virial theorem. We calculate the electric and diamagnetic polarizabilities of a proton $\\bar{\\alpha}_p= 10\ imes 10^{-4} fm^3$, $\\beta_p^{dia}=-8\ imes 10^{-4} fm^3$ and neutron fm^3$ on the basis of the perturbative theory in small external electromagnetic fields. Using the $\\Delta$ contribution to the paramagnetic polarizability of the nucleons, the reasonable values of magnetic polarizabilities 10^{-4} fm^3$ are estimated. As a result there is no magnetic crisis as one occures in the nonrelativistic quark model.

Motivation & Objective

• To derive the electromagnetic polarizabilities of nucleons using QCD string theory with a consistent string tension matching meson trajectories.
• To address the magnetic crisis in nonrelativistic quark models by incorporating the Δ resonance contribution to paramagnetic polarizability.
• To model nucleons as asymmetric quark-diquark systems with straight-line strings to estimate quark separations via the virial theorem.
• To compute electric, diamagnetic, and magnetic polarizabilities perturbatively in weak external electromagnetic fields.
• To ensure baryon trajectory slopes match meson slopes by using the same string tension as in mesonic systems.

Proposed method

• Adopting QCD string theory with the area law for large Wilson loops to model baryons as strings with quark-diquark structure.
• Using the same string tension as in mesons to ensure consistency in the slope of baryon trajectories with that of meson trajectories.
• Applying the virial theorem to estimate mean quark-diquark distances in the nucleon within the string model.
• Formulating an effective action for baryons in external electromagnetic fields using perturbation theory in small fields.
• Including the Δ resonance contribution to paramagnetic polarizability to estimate magnetic polarizabilities.
• Solving for electric, diamagnetic, and magnetic polarizabilities using the string model and perturbative expansion in external field strength.

Experimental results

Research questions

• RQ1 What are the electromagnetic polarizabilities of the proton and neutron derived from QCD string theory with a quark-diquark structure?
• RQ2 How does the inclusion of the Δ resonance contribution affect the estimation of magnetic polarizabilities in the nucleon?
• RQ3 Can the string tension used for mesons be consistently applied to baryons to reproduce the observed slope of baryon trajectories?
• RQ4 Does the QCD string model resolve the magnetic crisis present in nonrelativistic quark models?
• RQ5 What are the quantitative values of electric and diamagnetic polarizabilities for the proton under this string-theoretic framework?

Key findings

• The proton electric polarizability is calculated as $\bar{\alpha}_p = 10 \times 10^{-4} \, \text{fm}^3$.
• The proton diamagnetic polarizability is found to be $\beta_p^{\text{dia}} = -8 \times 10^{-4} \, \text{fm}^3$.
• The magnetic polarizability of the nucleon is estimated at approximately $10^{-4} \, \text{fm}^3$ using the $\Delta$ resonance contribution.
• The model successfully avoids the magnetic crisis observed in nonrelativistic quark models by incorporating relativistic string dynamics.
• The quark-diquark string model with consistent string tension reproduces baryon trajectory slopes matching those of mesons.
• The virial theorem is used to estimate mean quark-diquark distances, supporting the internal structure assumptions of the model.