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Scenario for quark confinement from infrared safe Yang-Mills dynamics

Marcela Peláez, Urko Reinosa, Julien Serreau, Matthieu Tissier, Nicolás Wschebor

TL;DR

This work presents a semiclassical flux-tube description of quark confinement in infrared-safe Yang-Mills dynamics using a background-field formulation in the Landau gauge. By incorporating an infrared-minite coupling and a gluon mass via the Curci-Ferrari model, the authors obtain a regular flux-tube profile driven by the nonmonotonic background two-point function and a nonanalytic A^4 ln A term from massless ghosts. They demonstrate that a nonzero homogeneous background κ is dynamically favored and that the resulting flux tube yields a string tension in reasonable agreement with lattice data, providing a robust mechanism for confinement rooted in infrared physics. The approach offers a controllable, analytic description of flux tubes and motivates further exploration of nonlinear core regularization, higher representations, and finite-temperature effects within infrared-safe frameworks.

Abstract

We revisit the non-Abelian dipole problem in the context of a simple semiclassical approach that incorporates some essential features of the infrared sector of Yang-Mills theories in the Landau gauge, in particular, the fact that both the running coupling and the gluon propagator remain finite at infrared scales and that the latter shows positivity violations that reflects the presence of massless modes. We obtain a simple flux tube solution in a controlled approximation scheme, which we compare to the results of lattice simulations.

Scenario for quark confinement from infrared safe Yang-Mills dynamics

TL;DR

This work presents a semiclassical flux-tube description of quark confinement in infrared-safe Yang-Mills dynamics using a background-field formulation in the Landau gauge. By incorporating an infrared-minite coupling and a gluon mass via the Curci-Ferrari model, the authors obtain a regular flux-tube profile driven by the nonmonotonic background two-point function and a nonanalytic A^4 ln A term from massless ghosts. They demonstrate that a nonzero homogeneous background κ is dynamically favored and that the resulting flux tube yields a string tension in reasonable agreement with lattice data, providing a robust mechanism for confinement rooted in infrared physics. The approach offers a controllable, analytic description of flux tubes and motivates further exploration of nonlinear core regularization, higher representations, and finite-temperature effects within infrared-safe frameworks.

Abstract

We revisit the non-Abelian dipole problem in the context of a simple semiclassical approach that incorporates some essential features of the infrared sector of Yang-Mills theories in the Landau gauge, in particular, the fact that both the running coupling and the gluon propagator remain finite at infrared scales and that the latter shows positivity violations that reflects the presence of massless modes. We obtain a simple flux tube solution in a controlled approximation scheme, which we compare to the results of lattice simulations.
Paper Structure (8 sections, 36 equations, 4 figures)

This paper contains 8 sections, 36 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Setup
  3. flux tube solution
  4. The homogeneous background
  5. Discussion
  6. Conclusion
  7. Two-point function
  8. Quartic potential

Figures (4)

  • Figure 1: The effective potential \ref{['eq:gammaK']} (arbitrary normalization) for the background $\kappa$ for various values of the flux $\phi$ for $N=2$.
  • Figure 2: The parameter $\kappa_0/m$ as a function of $\phi$ for $N=2$.
  • Figure 3: The lattice data of Ref. Koma:2003hv for the longitudinal chromoelectric field against the present leading-order result $\bar{E}^{a=2}_z(r)=\kappa A(r)=\phi \kappa^2 f(\kappa r)/(4\pi)$.
  • Figure 4: The function \ref{['appeq:g2']} with the counterterm \ref{['appeq:ct']} for the SU(2) parameters $m=0.68~{\rm GeV}$ and $g=7.5$ at $\mu=1~{\rm GeV}$. The nonmonotonous behavior at low momentum is related to the positivity violation of the gluon propagator in the Landau gauge---corresponding to a vanishing background---and is responsible for the nontrivial root at $q=M=0.7~{\rm GeV}$.