Shift in weak phase $\gamma$ due to CP asymmetries in $D$ decays to two pseudoscalar mesons

TL;DR

This paper investigates how CP asymmetries in D meson decays to two pseudoscalar mesons can cause shifts in the weak phase gamma, affecting its precise measurement in B decays, and proposes measurements to reduce uncertainties.

Contribution

It provides an analysis of CP asymmetries in singly-Cabibbo-suppressed D decays and estimates their impact on the gamma measurement, highlighting the importance of specific measurements to improve accuracy.

Findings

CP asymmetries can shift gamma by several degrees.

Certain measurements can reduce the uncertainty in gamma.

Standard model penguin amplitudes influence CP asymmetries.

Abstract

A difference of several tenths of a percent has been observed between the direct CP asymmetries of $D^0\to K^+K^-$ and $D^0\to \pi^+\pi^-$. It has been noted recently that CP asymmetries in such singly-Cabibbo-suppressed (SCS) decays can affect the determination of the weak phase $\gamma$ using the Gronau-London-Wyler method of comparing rates for $B^+ \to D K^+$ and $B^- \to D K^-$, where $D$ is a superposition of $D^0$ and $\od$ decaying to a CP eigenstate. Using an analysis of the CP asymmetries in SCS decays based on a $c \to u$ penguin amplitude with standard model weak phase but enhanced by CP-conserving strong interactions, we estimate typical shifts in $\gamma$ of several degrees and pinpoint measurements which would reduce uncertainties to an acceptable level.