Spin precession and anomalous dipole couplings in a plane-wave Yang-Mills background
We investigate the fermion spin dynamics and induced dipole interactions in an external Yang-Mills gauge field that represents a non-Abelian plane wave. We use the exact solutions of the Dirac equation in the external gauge field, the exact fermion Green's function, and the renormalized one-loop fermion-gluon vertex in the axial gauge. The exact propagator produces spin-dependent structures proportional to $σ^{μν}F_{μν}^{a} $. The external field induces spin precession at tree level through a non-Abelian extension of the Bargmann-Michel-Telegdi equation, coupled with Wong color transport. The exact vertex produces a phase-dependent Pauli form factor $F_{2}^{a}\left( 0;φ,φ^{\prime }\right) $ beyond tree level, which serves as an anomalous chromomagnetic dipole coupling. For monochromatic two-color noncommuting plane waves, explicit weak-field expressions are derived for the induced Pauli coefficient and the anomalous spin-precession frequency. The commutator term $gf^{abc}A_{μ}^{b}A_{ν}^{c}$ in this case, generates additional field-strength components and dynamically induced precession axes not present in Abelian backgrounds, resulting in coupled spin-color precession. The exact one-loop coefficient is provided as a harmonic expansion suitable for periodic Yang-Mills waves. Explicit expressions for spin-dependent amplitudes, spin-flip probabilities, and polarization asymmetries are provided. These results establish a direct connection between exact background-field propagators, renormalized vertex functions, anomalous dipole interactions, and observable spin effects in strong non-Abelian gauge fields.