Measuring $CP$ violation and mixing in charm with inclusive self-conjugate multibody decay modes

TL;DR

This paper proposes a method using inclusive charm decays to multibody self-conjugate final states to measure $CP$ violation and mixing parameters with improved sensitivity, especially highlighting the $D o \pi^+\pi^-\pi^0$ channel.

Contribution

It introduces a novel approach leveraging the fractional $CP$-even content of multibody decays to enhance measurements of $CP$ violation and mixing in charm mesons.

Findings

The method can significantly improve sensitivity over traditional $CP$ eigenstate decays.

The $D o \pi^+\pi^-\pi^0$ channel is particularly effective due to its large branching ratio and high $F_+$.

Recent measurements of $F_+$ support the feasibility of this approach.

Abstract

Time-dependent studies of inclusive charm decays to multibody self-conjugate final states can be used to determine the indirect $CP$-violating observable $A_\Gamma$ and the mixing observable $y_{CP}$, provided that the fractional $CP$-even content of the final state, $F_+$, is known. This approach can yield significantly improved sensitivity compared with the conventional method that relies on decays to $CP$ eigenstates. In particular, $D \to \pi^+\pi^-\pi^0$ appears to be an especially powerful channel, given its relatively large branching fraction and the high value of $F_+$ that has recently been measured at charm threshold.