Charge Radii and Magnetic Polarizabilities of the Rho and K* Mesons in QCD String Theory

TL;DR

This paper uses QCD string theory to calculate the charge radii and magnetic polarizabilities of rho and K* mesons, providing theoretical estimates based on the effective meson action in external electromagnetic fields.

Contribution

It introduces a novel approach using QCD string theory and the Nambu-Goto approximation to estimate meson properties without spin interactions.

Findings

Estimated charge radii of rho and K* mesons.

Calculated diamagnetic polarizabilities for rho and K* mesons.

Validated the use of the Airy function in meson wave functions.

Abstract

The effective action for light mesons in the external uniform static electromagnetic fields was obtained on the basis of QCD string theory. We imply that in the presence of light quarks the area law of the Wilson loop integral is valid. The approximation of the Nambu-Goto straight-line string is used to simplify the problem. The Coulomb-like short-range contribution which goes from one-gluon exchange is also neglected. We do not take into account spin-orbital and spin-spin interactions of quarks and observe the $\rho$ and $K^*$ mesons. The wave function of the meson ground state is the Airy function. Using the virial theorem we estimate the mean charge radii of mesons in terms of the string tension and the Airy function zero. On the basis of the perturbative theory, in the small external magnetic field we find the diamagnetic polarizabilities of $\rho$ and $K^*$ mesons: $\beta_\rho =-0.8\times 10^{-4} {fm}^3$, $\beta_{K^*}=-0.57\times 10^{-4} {fm}^3$