2025/02/27 by Hideo Suganuma, Suganuma, Hideo, Atsuya Tokutake +3 · 1 citation
Physics and Astronomy · #Quantum Chromodynamics and Particle Interactions #Advanced Condensed Matter Physics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2502.19874
Motivated by color-magnetic instabilities in QCD, we investigate field-strength correlations in both SU(2) and SU(3) lattice QCD. In the Euclidean Landau gauge, we numerically calculate the perpendicular-type color-magnetic correlation, C⊥(r) ≡ g2 ⟨ Hza(s)Hza(s + r ⊥)) ⟩ with ⊥ ≡ x, y, and the parallel-type one, C∥(r) ≡ g2 ⟨ Hza(s)Hza(s + r ∥) ⟩ with ∥~≡ z, t. In the Landau gauge, all two-point field-strength correlations g2 ⟨ Gaμν(s)Gbαβ(s')⟩ are described by these two quantities, due to the Lorentz and global SU(Nc) color symmetries. Curiously, the perpendicular-type color-magnetic correlation C⊥(r) is found to be always negative for arbitrary r, except for the same point of r=0. The parallel-type color-magnetic correlation C∥(r) is always positive. In the infrared region, C⊥(r) and C∥(r) strongly cancel each other, which leads to an approximate cancellation for the sum of the field-strength correlations as ∑μ, ν ⟨ Gaμν(s)Gaμν(s')⟩ ∝ C⊥(|s-s'|)+ C∥(|s-s'|) ≃ 0. Next, we decompose the perpendicular-type color-magnetic correlation C⊥(r) into quadratic, cubic and quartic terms of the gluon field Aμ. The quadratic term is always negative, which is explained by the Yukawa-type gluon propagator ⟨ Aaμ(s)Aaμ(s')⟩ ∝ e-mr/r with r≡ |s-s'| in the Landau gauge. The quartic term gives a relatively small contribution. In the infrared region, the cubic term is positive and tends to cancel with the quadratic term, resulting in a small value of C⊥(r).