# Measurement of the CKM angle $γ$ using $B^\pm\to DK^\pm$ with $D\to K_\text{S}^0π^+π^-$, $K_\text{S}^0K^+K^-$ decays

collaboration, LHCb, Aaij, R, Adeva, B, Adinolfi, M, Aidala, CA, Ajaltouni, Z, Akar, S, Albicocco, P, Albrecht, J, Alessio, F
et al (show 814 more authors) (2018) Measurement of the CKM angle $γ$ using $B^\pm\to DK^\pm$ with $D\to K_\text{S}^0π^+π^-$, $K_\text{S}^0K^+K^-$ decays. The LHCb collaboration, Aaij, R., Adeva, B. et al. J. High Energ. Phys. (2018) 2018: 176; erratum: The LHCb collaboration, Aaij, R., Adeva, B. et al. J. High Energ. Phys. (2018) 2018: 107.

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## Abstract

A binned Dalitz plot analysis of $B^\pm \to D K^\pm$ decays, with $D\to K_\text{S}^0\pi^+\pi^-$ and $D\to K_\text{S}^0K^+K^-$, is used to perform a measurement of the CP-violating observables $x_{\pm}$ and $y_{\pm}$, which are sensitive to the Cabibbo-Kobayashi-Maskawa angle $\gamma$. The analysis is performed without assuming any $D$ decay model, through the use of information on the strong-phase variation over the Dalitz plot from the CLEO collaboration. Using a sample of proton-proton collision data collected with the LHCb experiment in 2015 and 2016, and corresponding to an integrated luminosity of 2.0$\,\text{fb}^{-1}$, the values of the CP violation parameters are found to be $x_- = ( 9.0 \pm 1.7 \pm 0.7 \pm 0.4) \times 10^{-2}$, $y_- = ( 2.1 \pm 2.2 \pm 0.5 \pm 1.1) \times 10^{-2}$, $x_+ = (- 7.7 \pm 1.9 \pm 0.7 \pm 0.4) \times 10^{-2}$, and $y_+ = (- 1.0 \pm 1.9 \pm 0.4 \pm 0.9) \times 10^{-2}$. The first uncertainty is statistical, the second is systematic, and the third is due to the uncertainty on the strong-phase measurements. These values are used to obtain $\gamma = \left(87\,^{+11}_{-12}\right)^\circ$, $r_B = 0.086^{+ 0.013}_{-0.014}$, and $\delta_B = (101 \pm 11)^\circ$, where $r_B$ is the ratio between the suppressed and favoured $B$-decay amplitudes and $\delta_B$ is the corresponding strong-interaction phase difference. This measurement is combined with the result obtained using 2011 and 2012 data collected with the \lhcb experiment, to give $\gamma = \left(80\,^{+10}_{\,-9}\right)^\circ$, $r_B = 0.080 \pm 0.011$, and $\delta_B = (110 \pm 10)^\circ$.

Item Type: Article All figures and tables, along with any supplementary material and additional information, are available at https://lhcbproject.web.cern.ch/lhcbproject/Publications/LHCbProjectPublic/LHCb-PAPER-2018-017.html. Version 2 includes minor changes made during journal review hep-ex, hep-ex Symplectic Admin 07 May 2019 10:57 09 Nov 2021 08:17 10.1007/JHEP08(2018)176 http://doi.org/10.1007/JHEP08(2018)176 https://livrepository.liverpool.ac.uk/id/eprint/3040070