Paired composite fermion wavefunctions for excitations at 5/2

The Pfaffian wave function, which is thought to be relevant for the ground state at filling fraction $\frac{5}{2}$, represents a paired state of composite fermions. It can be expressed as an antisymmetrized bilayer (331) wave function. This formulation can be extended to construct wave functions for neutral as well as charged excitations of the Pfaffian. The space spanned by the quasihole excitations exactly matches that of the previously known quasihole wave functions. By comparison to exact results with up to 14 particles, we find that our neutral excitations and also the quasiparticle excitations describe well the actual excitations of the model three body interaction for which the Pfaffian ground state wave function is exact. The relevance to the solutions of the second Landau level Coulomb interaction is less conclusive. Also, the counting of states on the quasihole and quasiparticle sides is significantly different. Relation of our wave functions to other ansatz wave functions in the literature will be discussed.