Abstract

On the basis of a compactification of the (3+1) into (1+1) dimensional space-time [1], the quark states inside the 2D flux tube are studied for the case of a linear transverse confining potential. The derived states are classified by both the projections of the orbital momentum and the spin along the tube direction. The spectrum of the fermion states is evaluated. It is found that the energy eigenvalues of the quarks appear to be approximately related to the square root of the eigenvalues of the two-dimensional harmonic oscillator.

Highlights

  • The three-dimensional QCD flux tube between a quark and an antiquark and its idealization as a one-dimensional string are useful concepts

  • On the basis of a compactification of the (3+1) into (1+1) dimensional space-time [1], the quark states inside the 2D flux tube are studied for the case of a linear transverse confining potential

  • We show how the quark and the gluon in QCD2 acquire masses arising their being confined within the tube, and how all these quantities depend on the transverse wave functions of the quarks in the tube

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Summary

Introduction

The three-dimensional QCD flux tube between a quark and an antiquark and its idealization as a one-dimensional string are useful concepts (for a review see [2]). To describe the transverse dynamics, it is necessary to examine the structure and the states of particles in the flux tube. The knowledge of these states furnishes useful information for the investigation of the transverse momentum distribution of the produced particles, for which a wealth of information have been collected recently [6,7,8,9,10,11,12].

Equations of Motion for Transverse Dynamics of Quarks
Axisymmetric Potential
Eigenvalue equation
Effective Masses of Quarks and Gluons and 2D coupling constant
Conclusion

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