Abstract
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.
RESONANCES AND WEAK INTERACTIONS IN D+→ π+π−π+ DECAYS