CP Violation in Correlated Production and Decay of Unstable Particles

TL;DR

This paper investigates CP violation in the production and decay of unstable scalar particles at colliders, deriving conditions for observable CP asymmetries and applying the results to supersymmetric top quark pairs at the LHC.

Contribution

It establishes a theoretical framework for CP violation in correlated scalar particle processes and introduces a new spinorial trace technique for amplitude calculations.

Findings

At least three decay matrices are needed for CP violation in 2-->2 scatterings.

Only two decay matrices suffice for 2-->4 correlated production and decay processes.

CP asymmetries in supersymmetric top pair production could reach order one at the LHC.

Abstract

We study resonant CP-violating Einstein--Podolsky--Rosen correlations that may take place in the production and decay of unstable scalar particles at high-energy colliders. We show that as a consequence of unitarity and CPT invariance of the S-matrix, in 2 --> 2 scatterings mediated by mixed scalar particles, at least three linearly independent decay matrices associated with the unstable scalar states are needed to obtain non-zero CP-odd observables that are also odd under C-conjugation. Instead, for the correlated production and decay of two unstable particle systems in 2 --> 4 processes, we find that only two independent decay matrices are sufficient to induce a net non-vanishing CP-violating phenomenon. As an application of this theorem, we present numerical estimates of CP asymmetries for the correlated production and decay of supersymmetric scalar top--anti-top pairs at the LHC, and demonstrate that these could reach values of order one. As a byproduct of our analysis, we develop a novel spinorial trace technique, which enables us to efficiently evaluate lengthy expressions of squared amplitudes describing the resonant scalar transitions.