Small amplitude effects in $B^0\to D^+D^-$ and related decays

Abstract

Intrigued by a recent Belle result for a large direct CP asymmetry in $B^0\to D^+D^-$, we study the effects of a $\bar b\to \bar uu\bar d$ quark transition by combining the asymmetry information with rates and asymmetries in isospin-related decays. Arguing for a hierarchy among several contributions to these decays, including an exchange amplitude which we estimate, we present tests for factorization of the leading terms, and obtain an upper bound on the ratio of $\bar b\to \bar uu\bar d$ and $\bar b\to \bar cc\bar d$ amplitudes. We prove an approximate $\Delta I=1/2$ amplitude relation for $B\to D\bar D$, and an approximate equality between CP asymmetries in $B^0\to D^+D^-$ and $B^+\to D^+\bar D^0$. Violations of these relations by Belle measurements, at $1.8\sigma$ and $3.6\sigma$ respectively, if confirmed, would indicate a possible New Physics contribution in $\bar b\to \bar uu\bar d$. Applying flavor SU(3), we extend this study to a total of ten processes including $\Delta S=0$ decays involving final $D_s$ and initial $B_s$ mesons, and $\Delta S=1$ decays of $B$ and $B_s$ mesons into pairs of charmed pseudoscalar mesons. The decays $B_s\to D\bar D$ provide useful information about a small exchange amplitude, responsible for a decay rate difference between $B^+\to D^+\bar D^0$ and $B^0\to D^+D^-$. A method for determining the weak phase $\gamma$, based on CP asymmetries in $B^0(t)\to D^+D^-$ and the decay rate for $B_s\to D^+_sD^-_s$ or $B^{+(0)}\to D^+_s\bar D^0 (D^-)$, is shown to involve high sensitivity to SU(3) breaking.