Graphs showing $ 1-{\rm CL}$ for (a) $\delta_B^K$ , (b) $ r_B^K$ , and (c) $\gamma$ , for the $ DK^\pm$ combination of the two- and four-body GLW/ADS and the $ DK^\pm$ GGSZ measurements. The reported numbers correspond to the best-fit values and the uncertainties are computed using the respective $68.3\%$ CL confidence interval shown in Table 5.

Graphs showing $ 1-{\rm CL}$ for (a) $\delta_B^{\pi}$ , (b) $ r_B^{\pi}$ , and (c) $\gamma$ , for the $ D\pi^\pm$ combination of the two- and four-body GLW/ADS measurements. The reported numbers correspond to the best-fit values and the uncertainties are computed using appropriate $68.3\%$ CL confidence intervals shown in Table 6.

Graphs showing $ 1-{\rm CL}$ for (a) $\delta_B^K$ , (b) $\delta_B^{\pi}$ , (c) $ r_B^K$ , (d) $ r_B^{\pi}$ , and (e) $\gamma$ , for the full $ DK^\pm$ and $ D\pi^\pm$ combination. The reported numbers correspond to the best-fit values and the uncertainties are computed using appropriate $68.3\%$ CL confidence intervals shown in Table 7.

Profile likelihood contours of (a) $\gamma$ vs. $ r_B^K$ , (b) $\gamma$ vs. $\delta_B^K$ , (c) $\gamma$ vs. $ r_B^{\pi}$ , and (d) $\gamma$ vs. $\delta_B^{\pi}$ , for the full $ DK^\pm$ and $ D\pi^\pm$ combination. The contours are the $n\sigma$ profile likelihood contours, where $\Delta\chi^2=n^2$ with $n=1,2$. The markers denote the best-fit values. Subfigures (b) and (d) show the full angular range to visualize the symmetry, while subfigures (a) and (c) are expressed modulo $180^{\circ}$.

Graphs showing $ 1-{\rm CL}$ for $\delta_B^K$ , $ r_B^K$ , and $\gamma$ , separately for the GLW/ADS (light green) and GGSZ (dark purple) parts of the $ DK^\pm$ -only combination.

Profile likelihood contours, separately for the GGSZ (blue) and two-body and four-body GLW/ADS (orange) parts of the $ DK^\pm$ only combination. The contours are the usual $n\sigma$ profile likelihood contours, where $\Delta\chi^2=n^2$ with $n=1,2$. The markers correspond to the best-fit points.

Graphs showing $ 1-{\rm CL}$ for $\gamma$ , separately for the $ DK^\pm$ -only combination (dark purple) and $ D\pi^\pm$ -only combination (light green).

Animated gif made out of all figures.

Free parameters used in the combined fit. The phase differences $\delta_{K\pi}$ and $\delta_{K3\pi}$ are defined in accordance with Refs. [13,4,5], they are shifted by $180^{\circ}$ with respect to the HFAG. Also, $\gamma$ gains a sign for the conjugated modes, $A( B ^+ \rightarrow D ^0 h^+ )/A( B ^+ \rightarrow \overline{ D }{} ^0 h^+ ) = r_B^h e^{i(\delta_B^h +\gamma )}$, with $h=K,\pi$.

Statistical correlations of the $ B ^\pm \rightarrow Dh^\pm$, $ D\rightarrow hh$ analysis [25].

Statistical correlations of the $ B ^\pm \rightarrow Dh^\pm$, $ D\rightarrow K\pi\pi\pi$ analysis [26].

Results of the CLEO measurement [13].

Confidence intervals and best-fit values of the $ DK^\pm$ combination for $\gamma$ , $\delta_B^K$ , and $ r_B^K$ .

Confidence intervals and best-fit values for the $ D\pi^\pm$ combination for $\gamma$ , $\delta_B^{\pi}$ , and $ r_B^{\pi}$ . The corrections to the $\gamma$ intervals for undercoverage and neglected systematic correlations, as described in Sect. 5, are not yet applied.

Confidence intervals and best-fit values for the $ DK^\pm$ and $ D\pi^\pm$ combination for $\gamma$ , $ r_B^K$ , $\delta_B^K$ , $ r_B^{\pi}$ , and $\delta_B^{\pi}$ . The corrections to the $\gamma$ intervals for undercoverage and neglected systematic correlations, as described in Sect. 5, are not yet applied.

Numbers of observables $n_{\rm obs}$, numbers of free parameters in the fit $n_{\rm fit}$, the minimum $\chi^2$ at the best-fit point, and fit probabilities of the best-fit point for the three combinations. The quoted uncertainties are due to the limited number of pseudoexperiments.

Coverage fraction $f_{\rm in} = N_{\rm in}/N$ for $\gamma$ at its best measured value for 1-, 2-, and $3\sigma$ intervals, for the plug-in method and the simpler approach based on the profile likelihood. The quoted uncertainties are due to the limited number of pseudoexperiments.