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Description
Chiral symmetry breaking by instantons converts low-energy QCD into an effective dynamics of massive fermions with chiral spin-flavor interactions. The same mechanism converts QCD operators with gauge fields into effective multifermion operators. Large instanton effects are observed in the twist-3 part of the QCD quark energy-momentum tensor [1], which controls the decomposition of the quark angular momentum in spin and orbital parts. We compute the instanton effect on the flavor-nonsinglet quark angular momenta $S_{u-d} + L_{u-d} = J_{u-d}$ and show that the large negative $L_{u-d}$ partly cancels the positive $S_{u-d}$ in the spin sum rule [2]. We discuss the mechanical interpretation of the instanton-induced orbital angular momentum in the mean-field picture of the nucleon in the large-$N_c$ limit. We also study the instanton effects in spin-orbit correlations governed by the parity-odd analog of the energy-momentum tensor [3].
[1] J.-Y. Kim, C. Weiss, Phys. Lett. B 848 (2024) 138387
[2] J.-Y. Kim, H.-Y. Won, C. Weiss, to appear (2026)
[3] J.-Y. Kim, H.-Y. Won, H.-C. Kim, C. Weiss, Phys. Rev. D 110, 054026 (2024)