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New Solutions for RG Equations in QCD

R. M. Iakhibbaev, D. I. Kazakov, D. M. Tolkachev

Abstract

We construct simple analytical solutions of renormalization group equations for the running coupling and for the Green functions in QCD in the asymptotic regime. These solutions have an explicit form and subsequently sum up the leading, subleading, and so on logarithms in all orders of PT. They easily reproduce the inverse logarithm expansion and allow for further summation and improvement of the asymptotic behaviour.

New Solutions for RG Equations in QCD

Abstract

We construct simple analytical solutions of renormalization group equations for the running coupling and for the Green functions in QCD in the asymptotic regime. These solutions have an explicit form and subsequently sum up the leading, subleading, and so on logarithms in all orders of PT. They easily reproduce the inverse logarithm expansion and allow for further summation and improvement of the asymptotic behaviour.

Paper Structure

This paper contains 5 sections, 32 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Perturbative Expansion and New Solutions
  3. Vertical Summation and Nested Logs
  4. Solution for the Green Functions
  5. Conclusion

Figures (2)

  • Figure 1: Comparison of the three-loop running coupling $\bar{\alpha}_s(Q^2)$ in the first, second and third 'nested' approximations.
  • Figure 2: Comparison of the one-loop and improved two-loop and three-loop running coupling $\bar{\alpha}_s(Q^2)$.