Massive celestial amplitudes and celestial amplitudes beyond four points

We compute scalar three-point celestial amplitudes involving two and three massive scalars. The three-point coefficient of celestial amplitudes with two massive scalars contains a hypergeometric function, and the one with three massive scalars can be represented as a triple Mellin-Barnes integral. Using these three-point celestial amplitudes, we investigate the conformal block expansions of five- and six-point scalar celestial amplitudes in the comb channel. We observe the presence of two-particle operators in the conformal block expansion of five-point celestial amplitudes, which confirms the previous analysis by taking multi-collinear limit. Moreover, we find that there are new three-particle operators in the conformal block expansion of six-point celestial amplitudes. Based on these findings, we conjecture that exchanges of $n$-particle operators can be observed by considering the comb channel conformal block expansion of $(n+3)$-point massless celestial amplitudes. Finally, we show that a new series of operators appears when turning on the mass of the first incoming particle. The leading operator in this series can be interpreted as a two-particle exchange in the OPE of one massive and one massless scalars.