The period-index problem of the canonical gerbe of symplectic and orthogonal bundles

We consider regularly stable parabolic symplectic and orthogonal bundles over an irreducible smooth projective curve over an algebraically closed field of characteristic zero. The morphism from the moduli stack of such bundles to its coarse moduli space is a μ2-gerbe. We study the period and index of this gerbe, and solve the corresponding period-index problem.