The Phase in Three-Pion Correlations

We discuss the complex phase generated in three pion correlation functions. The lowest order contribution to the phase is of order $q^2 R/K$, where $q$ is a typical relative momentum, $K$ is a typical center of mass momentum and $R$ is a typical radius parameter. This contribution is of purely kinematic origin. At next order we find a generic contribution of order $(qR)^3$ which is a result of odd modifications to the source emission function. We argue, that the scale for typical HBT correlations in ultrarelativistic heavy ion collisions is $q/K \ll qR \sim 1$, so that the third order correction actually dominates the phase in the experimentally relevant momentum range. We study in detail such contributions which arise from source asymmetries generated by flow, the source geometry and resonance decays.