Hadronic decays of B_c mesons with flavor SU(3)_F symmetry

We study implications of a recent observation of non-leptonic $B^+_c\to D^0 K^+$ decay and a bound on $B^+_c\to D^0 \pi^+$ transition on CP-violating asymmetries in $B_c$ decays. In the U-spin symmetry limit, we derive a relation between the CP-asymmetries in the $B^+_c\to D^0 K^+$ and $B^+_c\to D^0 \pi^+$ channels and the corresponding branching ratios. We also derive several relations between non-leptonic $B_c$ decays into the final states with $D$ mesons in the flavor $SU(3)_F$ limit. We point out that a combined study of $SU(3)_F$ amplitudes in these decays can be used to constrain the angle $\gamma$ of the Cabibbo-Kobayashi-Maskawa (CKM) matrix.Comment: 12 pages, 2 tables, no figure

Cross ratios between Dalitz plot amplitudes in three-body D0D^0 decays

A recent study of $D^0 \to \pi^0 K^+ K^-$ and $D^0 \to K_S \pi^+\pi^-$ describes a flavor-symmetric approach to calculate relative amplitudes and phases, for characteristic interferences between $D$ decays to a light pseudoscalar $P$ and a light vector $V$, on Dalitz plots for $D \to PPP$ decays. The flavor-symmetric approach used an earlier fit to $D \to P V$ decay rates and was found to agree fairly well with experiments for $D^0 \to \pi^0 \pi^+ \pi^-$ but not as well for $D^0 \to \pi^0 K^+ K^-$ and $D^0 \to K_S \pi^+\pi^-$. The present work extends this investigation to include $D^0 \to K^- \pi^+ \pi^0$. We use an SU(3) flavor symmetry relationship between ratios of Cabibbo-favored (CF) $D \to P V$ amplitudes in $D^0 \to K^- \pi^+ \pi^0$ and ratios of singly- Cabibbo-suppressed (SCS) $D \to P V$ amplitudes in $D^0 \to \pi^0 K^+ K^-$ and $D^0 \to \pi^0 \pi^+ \pi^-$. We observe that experimental values for Dalitz plot cross ratios obey this relationship up to discrepancies noted previously. The need for an updated Dalitz plot analysis of $D^0 \to K^- \pi^+ \pi^0$ is emphasized.Comment: 9 pages, one figure. Submitted to Phys. Rev. D (Brief Reports). Additional comparisons with previous result

Charmed meson decays to two pseudoscalars

A recent update of data on the decays of $D^0$, $D^+$, and $D_s^+$ to pairs of light pseudoscalars calls for a renewed analysis of key decay amplitudes and tests of flavor symmetry. The present data change our previous understanding of relative phases between amplitudes that describe Cabibbo-favored decays of the charmed mesons. The new data also seem to favor a smaller octet-singlet mixing angle for the $\eta$ and $\eta'$ mesons when singly-Cabibbo-suppressed processes are taken into account. We also discuss the effects of the new data on interference between Cabibbo-favored and doubly-Cabibbo-suppressed decays.Comment: 15 pages, 7 figures, to be submitted to Phys. Rev.

Relative phases in Dalitz plot amplitudes for D0→KSπ+π−D^0 \to K_S \pi^+ \pi^- and D0→π0K+K−D^0 \to \pi^0 K^+ K^-

Relative phases of amplitudes for $D$ meson decays to a light pseudoscalar meson $P$ and a light vector meson $V$ decaying to two pseudoscalar mesons will lead to characteristic interferences on the three-body Dalitz plot. These phases may be compared with predictions of a flavor-symmetric treatment which extracts contributing amplitudes and their relative phases from a fit to $D \to PV$ decay rates. Good agreement was found previously for the cases of $D^0 \to K^- \pi^+ \pi^0$ and $D^0 \to \pi^+ \pi^- \pi^0$. The present work is devoted to the decays $D^0 \to K_S \pi^+ \pi^-$ and $D^0 \to \pi^0 K^+ K^-$, for which agreement is not found. Several suggestions are offered for this discrepancy.Comment: 11 pages, 3 figures, to be published in Phys. Rev. D. Additonal figure, text, and references; minor correction