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Using the Virasoro conditions to revise the model of a quark-gluon string fragmentation

Roman Nikolaenko

Abstract

Quark-gluon string fragmentation is usually seen as a universal process with its physics remaining unchanged for different colliding systems and center-of-mass energy. However, there is a way to go beyond this assumption by considering the angular momentum of the fragmenting system. An accurate calculation of the spin of the string requires a specific definition of the initial state of the string. In this paper, I present a new method for defining the initial data for the Nambu-Goto relativistic string and derive the basics of its fragmentation process using the so-called Virasoro conditions. It is shown that very non-trivial consequences arise for non-zero mass strings, including the discrete spectrum of string spin, the discreteness of the possible string breaking points, the close-to-Regge behavior of the spin-mass relation for the light string fragments, and the natural stopping mechanism for fragmentation.

Using the Virasoro conditions to revise the model of a quark-gluon string fragmentation

Abstract

Quark-gluon string fragmentation is usually seen as a universal process with its physics remaining unchanged for different colliding systems and center-of-mass energy. However, there is a way to go beyond this assumption by considering the angular momentum of the fragmenting system. An accurate calculation of the spin of the string requires a specific definition of the initial state of the string. In this paper, I present a new method for defining the initial data for the Nambu-Goto relativistic string and derive the basics of its fragmentation process using the so-called Virasoro conditions. It is shown that very non-trivial consequences arise for non-zero mass strings, including the discrete spectrum of string spin, the discreteness of the possible string breaking points, the close-to-Regge behavior of the spin-mass relation for the light string fragments, and the natural stopping mechanism for fragmentation.

Paper Structure

This paper contains 24 sections, 187 equations, 6 figures.

Table of Contents

  1. Introduction
  2. Main principles of the Nambu-Goto string hadronization model
  3. On the problem of defining the initial conditions for massive relativistic string
  4. The FOEE method to define the initial conditions
  5. The FOEE(1)-string
  6. The FOEE(1)-string in the rest frame
  7. A string moving with momentum P relative to the rest frame
  8. The FOEE(1)-string defined in the arbitrary frame of reference
  9. Generalization to the string with oscillation defined by eigenharmonic of arbitrary order
  10. The algorithm to calculate the motion of the FOEE(1) relativistic string
  11. String fragmentation
  12. The boundary-value problem for the motion of a daughter string
  13. The single-point fragmentation of the FOEE(1)-string
  14. Virasoro conditions and conservation laws for the daughter strings
  15. The fragmentation of the FOEE(1)-string with energy release
  16. ...and 9 more sections

Figures (6)

  • Figure 1: The FOEE(1)-string in its rest frame rotates as a rigid rod.
  • Figure 2: The scheme of the rotation of the coordinate system axis. Rotation is performed in the center-of-mass system of the string.
  • Figure 3: Motion of the FOEE(1)-string defined with total momentum $P_z = 2$ GeV.
  • Figure 4: Frame-by-frame motion of the FOEE(1)-string defined with total momentum $P_z = 200$ GeV.
  • Figure 5: A schematic representation of the string fragmentation process. The generation of daughter strings is marked on the vertical axis. The shape of the different strings is intentionally shown to be very different in order to emphasize their independent existence.
  • ...and 1 more figures