[Paper Review] Chromoelectric and chromomagnetic fields for the static gluon-quark-antiquark system

Marco Cardoso, Nuno Cardoso+1 more|arXiv (Cornell University)|Oct 1, 2009

Quantum Chromodynamics and Particle Interactions2 references3 citations

TL;DR

This lattice QCD study computes chromoelectric and chromomagnetic fields in static gluon-quark-antiquark systems using U- and L-shaped Wilson loops on a 24³×48 lattice at β=6.2. It finds that flux tubes dominate via chromoelectric fields, with field configurations consistent with glueball and quark-antiquark limits when particles are superposed, supporting a type-II superconductor model of QCD confinement with fundamental and adjoint flux tubes.

ABSTRACT

The chromoelectric and chromomagnetic fields, created by a static gluon-quark-antiquark system, are computed in the quenched approximation of lattice QCD, in a $24^3 imes 48$ lattice at $β=6.2$. We study two geometries, one with a U shape and another with an L shape. The degenerate case of the two gluon glueball is also studied. This is relevant to understand the microscopic structure of hadrons, in particular of hybrids. This also contributes to understand confinement with flux tubes of the chromoelectric field, and to discriminate between the models of fundamental or adjoint tubes.

Motivation & Objective

• To investigate the microscopic structure of hybrid hadrons via chromoelectric and chromomagnetic fields in static gluon-quark-antiquark systems.
• To determine the shape and nature of flux tubes in QCD confinement using lattice simulations.
• To test whether flux tubes are fundamental or adjoint by comparing field configurations in U- and L-shaped geometries.
• To validate the type-II superconductor analogy for QCD confinement by analyzing field dominance and string tension scaling.
• To examine field behavior when quark-antiquark or gluon-antiquark are superposed, comparing to glueball and mesonic limits.

Proposed method

• Uses the quenched approximation of lattice QCD on a 24³×48 spatial-temporal lattice at β=6.2.
• Constructs a Wilson loop operator for the gq¯q system using SU(3) octet (gluon), triplet (quark), and antitriplet (antiquark) representations.
• Employs fat links with w=0.2 and 25 iterations to improve signal-to-noise ratio in field measurements.
• Computes chromoelectric and chromomagnetic fields via expectation values of plaquette operators: ⟨E²⟩ = ⟨P₀ᵢ⟩ − ⟨W P₀ᵢ⟩/⟨W⟩ and ⟨B²⟩ = ⟨W Pᵢⱼ⟩/⟨W⟩ − ⟨Pᵢⱼ⟩.
• Derives energy and action densities from field strengths: ε = ½(⟨E²⟩ + ⟨B²⟩), γ = ½(⟨E²⟩ − ⟨B²⟩).
• Analyzes field profiles along symmetry axes in U- and L-shaped configurations, comparing to glueball and mesonic limits.

Experimental results

Research questions

• RQ1 How do chromoelectric and chromomagnetic fields distribute in U- and L-shaped gluon-quark-antiquark systems?
• RQ2 Do the field configurations support a type-II superconductor model of QCD confinement with repelling fundamental strings?
• RQ3 What is the relative dominance of chromoelectric versus chromomagnetic fields in the flux tube structure?
• RQ4 How do field profiles change when quark and antiquark are superposed, and how do they compare to the two-gluon glueball state?
• RQ5 Does the string tension in parallel segments follow Casimir scaling, indicating adjoint string dominance?

Key findings

• The absolute value of the chromoelectric field dominates over the chromomagnetic field in all configurations studied.
• When the quark and antiquark are superposed (d=0), the field profiles match those of the degenerate two-gluon glueball state.
• When the gluon and antiquark are superposed (r₁=0), the results are consistent with the static quark-antiquark mesonic case.
• For the L-shaped geometry with r₁=0, r₂=8, the gluon-antiquark segment field matches the static mesonic potential, confirming consistency with known limits.
• The flux tube shape and field distribution support the type-II superconductor model of QCD confinement, with repelling fundamental strings and higher tension in adjoint channels.
• The field profiles for both U- and L-shaped geometries reinforce previous findings that confinement in hybrid states is mediated by a pair of fundamental flux tubes when segments are perpendicular.