= Solution
The QCD <Yang-Mills theta term> is
$$
\mathcal L_\theta=\frac{\theta g_s^2}{32\pi^2}
G_{\mu\nu}^A\widetilde G^{A\mu\nu}
\propto\theta\,\mathbf E^A\mathbin\cdot\mathbf B^A.
$$
The chromoelectric field is a spatial vector and the chromomagnetic field is a pseudovector, so their scalar product is odd under parity. It is also odd under <time-reversal symmetry> because time reversal reverses $\mathbf B^A$ but not $\mathbf E^A$. Charge conjugation reverses both color fields in the gauge-invariant trace and leaves the product even. The term therefore violates P, T, and CP, while it preserves CPT because the two sign reversals from P and T cancel.
Back to article page
