$SU(3{)}_F$ breaking through final state interactions and $CP$ asymmetries in $D\to PP$ decays

We analyze $D$ decays to two pseudoscalars $(\pi ,K)$ assuming the dominant source of $\mathrm{SU}(3{)}_F$ breaking lies in final state interactions. We obtain an excellent agreement with experimental data and are able to predict $CP$ violation in several channels based on current data on branching ratios and ${\mathrm{\Delta }\mathrm{A}}_{CP}$. We also make predictions for ${\delta }_{K\pi }$ and the branching fraction for the decay $D_s^{+}\to K^{+}{K}_L$.

Figure 1

The correlations between $\mathcal{P}/T$ and the $CP$ asymmetries (given in %). HFLAV world average of $\mathrm{\Delta }{\mathrm{A}}_{CP}$ has been used for the fit and these $CP$ asymmetries correspond to the negative solution for the phases. The orange, red, and green regions are the 68%, 95%, and 99% probability regions, respectively. The bottom right-most panel shows the fit to $(P+{\mathrm{\Delta }}_3)/T=\mathcal{P}/T-1$. The green, red, and orange regions are the 68%, 95%, and 99% probability regions, respectively.

Figure 2

Fit results for $R(D^0,{\pi }^0)$, $R(D^{+},{\pi }^{+})$, and $R(D_s^{+},K^{+})$ using the branching fraction data in Table 2 and the HFLAV world average of $\mathrm{\Delta }{\mathrm{A}}_{CP}$. The green, red, and orange regions are the 68%, 95%, and 99% probability regions respectively.

Figure 3

Fit results for $\mathrm{\Delta }R$, ${\epsilon }_1$, and ${\epsilon }_2$ using the branching fraction data in Table 2 and the HFLAV world average of $\mathrm{\Delta }{\mathrm{A}}_{CP}$. The green, red, and orange regions are the 68%, 95%, and 99% probability regions respectively.

Figure 4

Correlations between asymmetries (in %) as given in Eq. (37) using the branching fraction data in Table 2 and the HFLAV world average of $\mathrm{\Delta }{\mathrm{A}}_{CP}$ quoted in Sec. 3. The orange, red, and green regions are the 68%, 95%, and 99% probability regions, respectively.

Figure 5

Fit results for $\mathcal{P}/T$ using the branching fraction data in Table 2 and $CP$ asymmetries listed in Table 6. The green, red, and orange regions are the 68%, 95%, and 99% probability regions, respectively. (BII-50: Belle II $50{\mathrm{ab}}^{-1}$; LHCb-50: LHCb $50{\mathrm{fb}}^{-1}$.)

Figure 6

The marginalized posterior distributions of the parameters from the fit as given in Table 3. The green, red, and orange regions are the 68%, 95%, and 99% probability regions respectively. The bottom three 2D marginalized plots show the correlations between the parameters ${\delta }_0$, ${\delta }_0^{\prime }$, and $\varphi$, The orange, red, and green regions are the 68%, 95%, and 99% probability regions, respectively.