  Inter-Landau-level transitions break particle hole symmetry and will choose
either the Pfaffian or the anti-Pfaffian state as the absolute ground state at
5/2 filling of the fractional quantum Hall effect. An approach based on
truncating the Hilbert space has favored the anti-Pfaffian. A second approach
based on an effective Hamiltonian produced the Pfaffian. In this letter
perturbation theory is applied to finite sizes without bias to any specific
pseudo-potential component. This method also singles out the anti-Pfaffian. A
critical piece of the effective Hamiltonian, which was absent in previous
studies, reverts the ground state at 5/2 to the anti-Pfaffian.
