On model-independent searches for direct CP violation in multi-body decays

Techniques for performing model-independent searches for direct ${CP}$ violation in three and four-body decays are discussed. Comments on the performance and the optimisation of a binned ${\chi }^{2}$ approach and an unbinned approach, known as the energy test, are made. The use of the energy test in the presence of background is also studied. The selection and treatment of the coordinates used to describe the phase-space of the decay are discussed. The conventional model-independent techniques, which test for P-even ${CP}$ violation, are modified to create a new approach for testing for P-odd ${CP}$ violation. An implementation of the energy test using graphical processing units is described.