Masses and Internal Structure of Mesons in the String Quark Model

TL;DR

This paper applies a relativistic string quark model to mesons, predicting their masses, internal structures, and revealing nonlinear Regge trajectories, with implications for understanding meson spectra and nucleon spin structure.

Contribution

The paper extends the relativistic string quark model to all mesons on Regge trajectories, predicting new meson masses and analyzing their internal spin and energy structures.

Findings

Meson mass spectrum described by the model matches experimental data.

Predicted new mesons, including a $K^*$ at 1910 MeV.

Revealed significant deviations in spin structure from nonrelativistic models.

Abstract

The relativistic quantum string quark model, proposed earlier, is applied to all mesons, from pion to $\Upsilon$, lying on the leading Regge trajectories (i.e., to the lowest radial excitations in terms of the potential quark models). The model describes the meson mass spectrum, and comparison with measured meson masses allows one to determine the parameters of the model: current quark masses, universal string tension, and phenomenological constants describing nonstring short-range interaction. The meson Regge trajectories are in general nonlinear; practically linear are only trajectories for light-quark mesons with non-zero lowest spins. The model predicts masses of many new higher-spin mesons. A new $K^*(1^-)$ meson is predicted with mass 1910 Mev. In some cases the masses of new low-spin mesons are predicted by extrapolation of the phenomenological short-range parameters in the quark masses. In this way the model predicts the mass of $\eta_b(1S)(0^{-+})$ to be $9500\pm 30$ MeV, and the mass of $B_c(0^-)$ to be $6400\pm 30$ MeV (the potential model predictions are 100 Mev lower). The relativistic wave functions of the composite mesons allow one to calculate the energy and spin structure of mesons. The average quark-spin projections in polarized $\rho$-meson are twice as small as the nonrelativistic quark model predictions. The spin structure of $K^*$ reveals an 80% violation of the flavour SU(3). These results may be relevant to understanding the ``spin crises'' for nucleons.