Transcendental structure of the one-loop four-site correlator

Determine whether the one-loop four-site cosmological correlator can be expressed in terms of multiple polylogarithms or instead requires more general transcendental functions, and determine its transcendental weight and whether that weight is uniform.

Background

The paper proposes extending its Landau-singularity and consistency-condition bootstrap from the one-loop three-site triangle to higher-point one-loop cosmological correlators. For the one-loop four-site correlator, the authors state that leading singularities, algebraic units, branch-point loci, permutation symmetries, and conformal Ward identities appear accessible, but the correlator’s function class and weight properties remain unresolved. A detailed analysis is explicitly deferred to future work.

References

A more basic question, however, must first be addressed: whether the box can still be expressed in terms of multiple polylogarithms or requires more general transcendental functions, what its transcendental weight is, and whether it has uniform weight. We expect that these questions can also be explored using the dressed representation. A detailed analysis is beyond the scope of the present paper and is left for future work.

— A compact analytic formula for the one-loop triangle cosmological correlator  (2608.17877 - Henn et al., 18 Aug 2026) in Section 6, Bootstrapping the correlator from Landau singularities