Paired Hall States versus Unidirectional CDW in Tilted Field for $\nu={5/2}$

We formulate the composite fermions in the presence of an in-plane magnetic field. As the in-plane field increases, if we assume the state at $\nu=5/2$ turns into the mixed state between the unidirectional charge density wave domains and paired Hall state, we can phenomenologically fit the theoretically defined gap to the experimental measured results. We explain the destruction of the paired Hall states and then a phase transition from the paired Hall state to the unidirectional charge density wave from a symmetry point of view.