Quark splitting in non-trivial \theta-vacuum

Quark splitting in non-trivial $\theta$-vacuum with a given helicity is investigated in pQCD with a modified quark propagator. We found that the quark splitting functions were modified by the presence of a topologically non-trivial QCD background field, though there is no explicit helicity flip associated with the radiative processes. The interaction with the topological non-trivial field leads to the degeneracy of the quark splitting functions for left- and right-handed quarks. Such degeneracy can lead to imbalance of left- and right-handed quarks in quark jet showers. We also discuss phenomenological consequences of such imbalance if there exists non-trivial topological gluon field configuration in heavy-ion collisions.