A global analysis of $\bar{B}\to DP$ and $\bar{B}\to \bar{D}P$ decays

Abstract

Recently, a fit to the 10 measured branching ratios of $\bar{B}\to DP$ decays ($B=\{B^{+},B^0,B_s^0\}$, $D=\{D^0,D^{+},D_s^{+}\}$, $P\in \{\pi ,K\}$) was performed under the assumption of flavor SU(3) symmetry [SU(3)${}_F$]. A terrible fit was found: there was a $>5\sigma$ disagreement with the SU(3)${}_F$ limit of the Standard Model [SM${}_{{\mathrm{SU}(3)}_{\mathrm{F}}}$]. It was also found that this discrepancy can be removed by adding $\sim 20\%$ SU(3)${}_F$-breaking effects. Now, the $\bar{B}\to D^{0}P$ amplitudes can contribute to other observables (direct and indirect CP asymmetries) if they interfere with the amplitudes for $\bar{B}\to {\bar{D}}^{0}P$ decays. This happens if the $D^0$ and ${\bar{D}}^0$ decay to the same final state (e.g., $K^{+}{K}^{-}$, ${\pi }^{+}{\pi }^{-}$, $K^{\pm }{\pi }^{\mp }$, etc.). In this paper, we perform a combined fit of $\bar{B}\to DP$ and $\bar{B}\to \bar{D}P$ decays, including all observables. We again find a $>5\sigma$ disagreement with the SM${}_{{\mathrm{SU}(3)}_{\mathrm{F}}}$, and we find that the data can be explained if $\sim 60\%$ SU(3)${}_F$-breaking effects are included.

arXiv comment36 pages, 3 figures, submitted to a volume of "Journal of Physics G" honouring Ashutosh Kumar Alok; typos corrected in this version 2