Fermionic S-matrix and cosmological correlators: T-violation at O(H)

TL;DR

The paper develops a fermionic de Sitter S-matrix framework (BD and UdW) and links it to cosmological correlators, including a finite-time UdW_T variant that enables $O(H)$ analyses of particle processes. It shows that for fermions the UdW_T S-matrix agrees with the BD S-matrix at leading $H$, while scalars exhibit no $O(H)$ corrections to $|\mathcal{M}|^2$ at this order, explained via symmetry arguments. A key finding is intrinsic T-violation arising in polarized beta decays in the expanding patch, with energy-conserving and energy-nonconserving contributions; the latter can be enhanced only at finely tuned kinematics, while the former yields a lower bound on T-violation in our cosmological setup. The work provides a systematic perturbative approach to cosmological corrections in fermionic processes, clarifies the in-in to in-out correspondence for fermions, and highlights potential links to terrestrial and early-universe phenomenology. These results enrich the de Sitter S-matrix program and offer concrete predictions for T-violating observables in a cosmological context.

Abstract

We study the Bunch-Davies (BD) and Unruh-de Witt (UdW) de Sitter S-matrices in the presence of spin-$1/2$ fermions. Building on recent work, this enables us to correlate the de Sitter S-matrix with cosmological correlators. We consider a finite-time version of the UdW S-matrix to study $O(H)$ corrections to some typical particle physics processes such as beta decay. Owing to the lack of time-reversal symmetry in the expanding Poincaré patch, we find signatures of intrinsic T-violation in polarized beta decay. The observable we study begins at $O(H)$. The possibility of T-violation was examined theoretically in the 1950's by Jackson, Treiman, and Wyld in flat space and has been probed more recently in the emiT experiment, with the purpose of examining fundamental T-violation coming from additional interactions in the Lagrangian. Our analysis places a lower bound on the intrinsic T-violation in the expanding Poincaré patch. At $O(H)$, we find both energy conserving and energy non-conserving contributions. Surprisingly, the energy-violating piece, in principle, can give large T-violation at fine-tuned values of the kinematical variables.

Figures (8)

• Figure 1: (a), (b) were introduced in pimentel1 while (c) was introduced in pajer. $\tau$ here is the conformal time.
• Figure 2: The UdW$_T$ S-matrix. Scattering in our conventions happens between $-T/2$ and $T/2$. $t$ here is the co-moving time.
• Figure 3: Contour for integral
• Figure 4: Leptonic decay of $\pi^+$ via weak interaction.
• Figure 5: 2-2 scattering in de Sitter spacetime Feynman diagrams