New tests for experiments producing pentaquarks

The distribution of the squared momentum difference |P_A|^2 - |P_B|^2 between the momenta in the laboratory system of two experimentally observed particles A and B provides a test for whether an observed mass peak indicates a real resonance rather than nonresonant background or kinematic reflection. The angular distribution of the relative momenta in the center-of-mass system exhibits a forward-backward symmetry in the production and decay of any resonance with a definite parity. This symmetry is not expected in other nonresonant processes and can be expressed without needing angular distributions in terms of the easily measured momenta in the laboratory frame that are already measured and used to calculate the invariant mass of the system. Our test is especially useful for low statistics experiments where the full angular distribution cannot be determined. It can be applied to both fixed-target and collider searches for the Theta^+ and Theta_c pentaquarks.