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Azimuthal asymmetries from $θ$ Vacuum

We present the complete azimuthal asymmetries at leading twist in terms of fragmentation functions in dihadron production semi-inclusive electron positron annihilation process. When the non-trivial $θ$ vacuum is taken into consideration, the parity symmetry of quantum chromodynamics is violated. As a consequence of the $local$ $\mathcal{P}$-odd effects, $\mathcal{P}$-odd fragmentation functions would contribute to the azimuthal asymmetries. Azimuthal asymmetry coming from two interference terms with opposite signs vanishes when sum over many events. This symmetry only survives on the event-by-event basis. Azimuthal asymmetry coming from two interference terms with same signs survives and can be measured to extract the $\mathcal{P}$-odd fragmentation functions. We also present the hadron polarizations.