A combination of three LHCb measurements of the CKM angle gamma is presented. The decays B>DK and B>Dpi are used, where D denotes an admixture of D0 and D0bar mesons, decaying into K+K, pi+pi, K+pi+, K+pi+pi+pi+, KSpi+pi, or KSK+K final states. All measurements use a dataset corresponding to 1.0 fb1 of integrated luminosity. Combining results from B>DK decays alone a bestfit value of gamma = 72.0 deg is found, and confidence intervals are set gamma in [56.4,86.7] deg at 68 CL, gamma in [42.6,99.6] deg at 95 CL. The bestfit value of gamma found from a combination of results from B>Dpi decays alone, is gamma = 18.9 deg, and the confidence intervals gamma in [7.4,99.2] deg or [167.9,176.4] deg at 68 CL, are set, without constraint at 95 CL. The combination of results from B>DK and B>Dpi decays gives a bestfit value of gamma = 72.6 deg and the confidence intervals gamma in [55.4,82.3] deg at 68 CL, gamma in [40.2,92.7] deg at 95 CL are set. All values are expressed modulo 180 deg, and are obtained taking into account the effect of D0D0bar mixing.
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 fourbody GLW/ADS and the $ DK^\pm$ GGSZ measurements. The reported numbers correspond to the bestfit values and the uncertainties are computed using the respective $68.3\%$ CL confidence interval shown in Table 5. 
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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 fourbody GLW/ADS measurements. The reported numbers correspond to the bestfit values and the uncertainties are computed using appropriate $68.3\%$ CL confidence intervals shown in Table 6. 
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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 bestfit values and the uncertainties are computed using appropriate $68.3\%$ CL confidence intervals shown in Table 7. 
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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 bestfit values. Subfigures (b) and (d) show the full angular range to visualize the symmetry, while subfigures (a) and (c) are expressed modulo $180^{\circ}$. 
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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. 
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Profile likelihood contours, separately for the GGSZ (blue) and twobody and fourbody 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 bestfit points. 
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Graphs showing $ 1{\rm CL}$ for $\gamma$ , separately for the $ DK^\pm$ only combination (dark purple) and $ D\pi^\pm$ only combination (light green). 
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Animated gif made out of all figures. 
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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 $h=K,\pi$. 
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Statistical correlations of the $ B ^\pm \rightarrow Dh^\pm$, $ D\rightarrow hh$ analysis [25]. 
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Statistical correlations of the $ B ^\pm \rightarrow Dh^\pm$, $ D\rightarrow K\pi\pi\pi$ analysis [26]. 
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Results of the CLEO measurement [13]. 
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Confidence intervals and bestfit values of the $ DK^\pm$ combination for $\gamma$ , $\delta_B^K$ , and $ r_B^K$ . 
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Confidence intervals and bestfit 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. 
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Confidence intervals and bestfit 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. 
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Numbers of observables $n_{\rm obs}$, numbers of free parameters in the fit $n_{\rm fit}$, the minimum $\chi^2$ at the bestfit point, and fit probabilities of the bestfit point for the three combinations. The quoted uncertainties are due to the limited number of pseudoexperiments. 
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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 plugin method and the simpler approach based on the profile likelihood. The quoted uncertainties are due to the limited number of pseudoexperiments. 
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Created on 10 July 2020.