CP violation effects on the measurement of $\gamma$ from $B\to DK$

TL;DR

This paper investigates how CP violation in D meson decays affects the measurement of the CKM angle gamma from B→DK decays, showing that recent data can cause shifts of several degrees in gamma.

Contribution

It quantifies the impact of D decay CP violation on gamma extraction and highlights the necessity to include these effects in future high-precision measurements.

Findings

Corrections to gamma can reach about 5 degrees.

The impact depends on the CP asymmetry and strong phase.

Remanent corrections are less than 0.5 degrees.

Abstract

Inspired by the unexpectedly large difference between the CP violation of $D$ decays into $K^+K^-$ and $\pi^+\pi^-$, we explore the impact on the extraction of $\gamma$ via the $B\to DK$ process with the $D$ meson reconstructed in the $K^+K^-,\pi^+\pi^-$ final state. We show that the extracted results for $\gamma$ can be shifted by ${\cal O}(A_{CP} / r_B^K)$, where $A_{CP}$ is the direct CP asymmetry in $D$ decays and $r_B^K$ is the ratio of the decay amplitudes of $B^-\to \bar D^0K^-$ and $B^-\to D^0K^-$. Using the recent data on CP asymmetry, we demonstrate the correction to physical observables in $B\to DK$ can reach 6%, which corresponds to the shift of $\gamma$ by roughly $5^\circ$. The remanent corrections depend on the strong phase of the $D$ decays, but are less than $0.5^\circ$. With the increasing precision in the $\gamma$ determination on the LHCb experiment and Super B factories, the inclusion of CP violation of $D$ decays will therefore soon become important.