  The triaxial quadrupole collective Hamiltonian, based on relativistic energy
density functionals, is extended to include a pairing collective coordinate. In
addition to triaxial shape vibrations and rotations, the model describes
pairing vibrations and the coupling between triaxial shape and pairing degrees
of freedom. The parameters of the collective Hamiltonian are determined by a
covariant energy density functional, with constraints on the intrinsic triaxial
shape and pairing deformations. The effect of coupling between triaxial shape
and pairing degrees of freedom is analyzed in a study of low-lying spectra and
transition rates of $^{128}$Xe. When compared to results obtained with the
standard triaxial quadrupole collective Hamiltonian, the inclusion of dynamical
pairing compresses the low-lying spectra and improves interband transitions, in
better agreement with data. The effect of zero-point energy (ZPE) correction on
low-lying excited spectra is also discussed.
