Massive celestial amplitudes and celestial amplitudes beyond four points

TL;DR

This work advances celestial holography by deriving three-point celestial amplitudes involving multiple massive scalars, revealing a hypergeometric structure for two-mass cases and a triple Mellin-Barnes representation for three-mass cases. Exploiting the split representation, the authors perform conformal partial wave analyses of four-, five-, and six-point celestial amplitudes in comb-channel topologies, uncovering double-trace exchanges as well as new multi-particle operators (notably two- and three-particle exchanges) whose presence depends on spacetime dimension. They show that turning on masses introduces a rich spectrum of operator exchanges and that higher-point amplitudes encode intricate OPE data that extends beyond single-particle exchanges. A key conjecture is that exchanges of $n$-particle operators can be observed in the comb-channel expansion of $(n+3)$-point massless celestial amplitudes, pointing to a broader, AdS-like structure in CCFT and offering a path for exploring OPE consistency and factorization in celestial holography.

Abstract

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.

Figures (2)

• Figure 1: A tree-level diagram for $1_{0}^{0}+2_{0}^{0}+3_{0}^{0}\to 4_{0}^{0}+5_{0}^{0}$. The external and internal particles are all massless scalars.
• Figure 2: A tree-level diagram for $1_{0}^{0}+2_{0}^{0}+3_{0}^{0}+4_{0}^{0}\to 5_{0}^{0}+6_{0}^{0}$. The external and internal particles are all massless scalars.