Cumulants, coherence, and contamination in multiparticle Bose-Einstein interferometry

We examine the formalism of multiparticle correlations used in Bose-Einstein interferometry with pions produced in ultrarelativistic heavy ion collisions. We include incoherent and quantum optics coherent contributions as well as the effect of contamination from particles included in the correlation that are not pions. We give expressions for the correlation functions and normalized cumulants for orders 2-5 in the presence of these effects. We show that in the presence of coherence the normalized cumulants include an additional contribution besides that usually called the ''true'' multiparticle correlation. We also consider the Q=0 intercepts of the correlation functions and normalized cumulants in the presence of coherence and of contamination and show that values of the intercept of the normalized cumulant as a function of order can distinguish these two effects.