Fermionic Bubble Loop in Cosmological Collider Revisited: Exact signals from spectral and Mellin-Barnes methods

Fermionic degrees of freedom are essential ingredients in cosmological collider physics and are well motivated by many phenomenological models beyond the Standard Model, but their signals remain largely unexplored due to the difficulty of computing loop diagrams. In this work, we ask how fermionic bubble loops contribute to cosmological collider signals and provide an exact answer for arbitrary couplings. We develop two parallel analytical methods whose agreement provides a non-trivial check of the result. The first method is similar in spirit to spectral decomposition and is built directly from an identity for the product of propagators, which turns the bubble signal into an infinite sum of tree-level exchange signals. The second method is based on the Mellin-Barnes representation, where the result is reconstructed from the residues of distinct families of poles. We also show that the fermionic bubble can be generated from the scalar bubble by the action of appropriate differential operators. As a phenomenologically important application, we consider Yukawa interactions between fermions and the inflaton, finding that the resulting bispectrum signal vanishes identically. Through the spectral decomposition, this vanishing can be traced to a field redefinition of the associated tree-level counterparts.