2025/07/14 by Atsuya Tokutake, Tokutake, Atsuya, Kei Tohme +3 · 1 citation
Physics and Astronomy · #Rare-earth and actinide compounds #Quantum Chromodynamics and Particle Interactions #Advanced Condensed Matter Physics
paper · pdf · doi:10.48550/arxiv.2507.10089
We study the two-point field-strength correlation g2 ⟨ Gμνa(s)Gbαβ(s') ⟩ in the Landau gauge in SU(2) and SU(3) quenched lattice QCD, as well as the gluon propagator g2 ⟨ Aμa (s)Aνb(s') ⟩. The Landau-gauge gluon propagator g2 ⟨ Aμa (s)Aμa(s') ⟩ is well described by the Yukawa-type function e-mr/r with r≡ |s-s'| for r=0.1-1.0~\rm fm in both SU(2) and SU(3) QCD. Next, motivated by color-magnetic instabilities in the QCD vacuum, we investigate the perpendicular-type color-magnetic correlation, C⊥(r) ≡ g2⟨ Hza(s)Hza(s + r ⊥)) ⟩ ( ⊥: unit vector on the xy-plane), and the parallel-type one, C∥(r) ≡ g2 ⟨ Hza(s)Hza(s + r ∥) ⟩ ( ∥: unit vector on the tz-plane). These two quantities reproduce all the correlation of g2⟨ Gaμν(s)Gbαβ(s')⟩, due to the Lorentz and global SU(Nc) color symmetries in the Landau gauge. Curiously, the perpendicular-type color-magnetic correlation C⊥(r) is found to be always negative for arbitrary r, except for the same-point correlation. In contrast, the parallel-type color-magnetic correlation C∥(r) is always positive. In the infrared region of r \gtrsim 0.4~\rm fm, C⊥(r) and C∥(r) strongly cancel each other, which leads to a significant cancellation in the sum of the field-strength correlations as ∑μ, ν g2⟨ Gaμν(s)Gaμν(s')⟩ ∝ C⊥(|s-s'|)+ C∥(|s-s'|) ≃ 0. Finally, we decompose the field-strength correlation into quadratic, cubic and quartic terms of the gluon field Aμ in the Landau gauge.