[Paper Review] SU(3) gauge invariant lattice QCD exploration of the dual superconductor picture in flux tube fusion, in the dual gluon mass, and in the dual Ginzburg-Landau parameters

Nuno Cardoso, Marco Cardoso+1 more|arXiv (Cornell University)|Apr 1, 2010

Quantum Chromodynamics and Particle Interactions3 citations

TL;DR

This study presents the first gauge-invariant lattice QCD determination of the effective dual gluon mass in quenched SU(3) QCD, finding a value of $0.905 \pm 0.163\ \text{GeV}$ via fitting the exponential decay of chromoelectric fields in flux tubes. Using the dual Ginzburg-Landau model with a fixed penetration length, it estimates a Ginzburg-Landau parameter $\kappa > 1/\sqrt{2}$, indicating a type II superconductor behavior, consistent with the dual superconductor picture of confinement.

ABSTRACT

The colour fields, created by a static gluon-quark-antiquark system, are computed in quenched SU(3) lattice QCD, in a $24^3 imes 48$ lattice at $β=6.2$ and $a=0.07261(85)\,fm$. We compute the hybrid Wilson Loop including the cases when the gluon and the antiquark are superposed, i. e., the quark-antiquark case and when the quark and antiquark are superposed, i. e., the gluon-gluon case. The Casimir scaling is investigated, in the two gluon glueball case the Casimir scaling is consistent with the formation of an adjoint string. Measuring the decay of the tail in the mid section of the flux tube for the two gluon glueball and for the quark-antiquark meson, we determine the penetration length and present a gauge invariant effective dual gluon mass of $0.905\pm0.163\, ext{GeV}$. We also try to determine the coherence length comparing our results with the dual Ginzburg-Landau approach. With the penetration length and the possible coherence length we determine a putative Ginzburg-Landau dimensionless parameter, which is possibly consistent with a type II superconductor picture. These results are obtained at fixed quark-antiquark distance of 0.58 fm.

Motivation & Objective

• To investigate the dual superconductor picture of quark confinement in SU(3) lattice QCD using gauge-invariant observables.
• To extract the effective dual gluon mass from the exponential decay of chromoelectric fields in flux tubes.
• To determine the Ginzburg-Landau parameters (penetration length $\lambda$, coherence length $\xi$) and assess whether the QCD vacuum behaves as a type I or type II superconductor.
• To test Casimir scaling and the formation of adjoint strings in gluon-gluon and quark-antiquark systems.
• To explore the validity of the dual Ginzburg-Landau approach in SU(3) QCD, despite the lack of universal flux quantization.

Proposed method

• Lattice QCD simulations on a $24^3 \times 48$ lattice at $\beta = 6.2$ and $a = 0.07261(85)\ \text{fm}$, using quenched SU(3) gauge fields.
• Computation of hybrid Wilson loops for quark-antiquark and gluon-gluon systems to extract chromoelectric and chromomagnetic field profiles.
• Fitting the mid-flux tube decay of $E_i^2$ and $B_i^2$ components to an exponential or modified Bessel function of the second kind to extract the dual gluon mass via $\mu = \lambda^{-1}$.
• Using the Ginzburg-Landau and Ampere equations with fixed $\lambda$ to estimate the coherence length $\xi$ and compute the dimensionless parameter $\kappa = \lambda / \xi$.
• Combining all six components of $E_i^2$ and $B_i^2$ to obtain a robust estimate of the effective dual gluon mass.
• Applying the dual Ginzburg-Landau model to the chromoelectric field profiles in the XZ plane at mid-flux tube distance.

Experimental results

Research questions

• RQ1 Does the chromoelectric field in SU(3) flux tubes exhibit exponential decay consistent with a massive dual gauge boson?
• RQ2 Is the effective dual gluon mass gauge-invariant and extractable from lattice QCD simulations?
• RQ3 Can the Ginzburg-Landau parameter $\kappa$ be estimated in SU(3) QCD, and does it indicate a type II superconductor behavior?
• RQ4 Is Casimir scaling observed in the two-gluon glueball system, and does it support the formation of an adjoint string?
• RQ5 To what extent does the dual Ginzburg-Landau model describe the flux tube structure in SU(3) QCD, given the absence of universal flux quantization?

Key findings

• The effective dual gluon mass is determined to be $0.905 \pm 0.163\ \text{GeV}$, representing the first gauge-invariant lattice QCD result for this quantity in SU(3).
• The penetration length $\lambda$ is extracted from the exponential decay of the chromoelectric field in the flux tube, consistent with a massive dual gauge boson.
• The Ginzburg-Landau parameter $\kappa$ is estimated to be greater than $1/\sqrt{2}$, indicating a type II superconductor regime in the dual superconductor picture of QCD.
• Casimir scaling is observed in the two-gluon glueball system, with a ratio of $9/4$ between the octet and triplet string tensions, supporting the formation of an adjoint string.
• The dominant chromoelectric field component $E_y^2$ is about twice the transverse components, and the chromomagnetic fields $B_x^2$ and $B_z^2$ are about 1.5 times $B_y^2$, indicating anisotropy in the flux tube structure.
• The combined analysis of all $E_i^2$ and $B_i^2$ components yields a consistent effective dual gluon mass of $0.905 \pm 0.163\ \text{GeV}$, suggesting a possible identification with the gluon mass in the dual Higgs mechanism.