Measurement of the CKM angle γ in B± → DK± and B± → Dπ± decays with D → $$ {K}_{mathrm{S}}^0 $$h+h−

A measurement of CP-violating observables is performed using the decays B± → DK± and B± → Dπ±, where the D meson is reconstructed in one of the self-conjugate three-body final states $$ {K}_{\mathrm{S}}^0 $$ K S 0 π+π− and $$ {K}_{\mathrm{S}}^0 $$ K S 0 K+K− (commonly denoted $$ {K}_{\mathrm{S}}^0 $$ K S 0 h+h−). The decays are analysed in bins of the D-decay phase space, leading to a measurement that is independent of the modelling of the D-decay amplitude. The observables are inter- preted in terms of the CKM angle γ. Using a data sample corresponding to an integrated luminosity of 9 fb−1 collected in proton-proton collisions at centre-of mass energies of 7, 8, and 13 TeV with the LHCb experiment, γ is measured to be $$ \left({68.7}_{-5.1}^{+5.2}\right){}^{\circ} $$ 68.7 − 5.1 + 5.2 ° . The hadronic parameters $$ {r}_B^{D K},{r}_B^{D\pi},{\delta}_B^{D K},\kern0.5em \mathrm{and}\kern0.5em {\delta}_B^{D\pi} $$ r B DK , r B Dπ , δ B DK , and δ B Dπ , which are the ratios and strong-phase differences of the suppressed and favoured B± decays, are also reported.