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Measurement of the CKM angle $\gamma$ from a combination of $B^{\pm} \to Dh^{\pm}$ analyses

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Abstract

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 D0-bar 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 fb-1 of integrated luminosity. Combining results from B->DK decays alone a best-fit 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 best-fit 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 best-fit 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 D0-D0bar mixing.

Figures and captions

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.

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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 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.

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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 best-fit 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 best-fit values. Subfigures (b) and (d) show the full angular range to visualize the symmetry, while subfigures (a) and (c) are expressed modulo $180^{\circ}$.

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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 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.

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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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Tables and captions

Free parameters used in the combined fit. The phase differences $\delta_{K\pi}$ and $\delta_{K3\pi}$ are defined in accordance with Refs. [4,5,13], 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 best-fit values of the $ DK^\pm$ combination for $\gamma$ , $\delta_B^K$ , and $ r_B^K$ .

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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.

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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.

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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 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.

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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 plug-in 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 09 December 2018.Citation count from INSPIRE on 18 December 2018.