CP violation effects on the measurement of $\gamma$ from $B\to DK$

Abstract

Inspired by the unexpectedly large difference between the CP violation of $D$ decays into $K^{+}{K}^{-}$ and ${\pi }^{+}{\pi }^{-}$, we explore the impact on the extraction of $\gamma$ via the $B\to DK$ process with the $D$ meson reconstructed in the $K^{+}{K}^{-},{\pi }^{+}{\pi }^{-}$ final state. We show that the extracted results for $\gamma$ can be shifted by $\mathcal{O}(A_{CP}/r_B^K)$, where $A_{CP}$ is the direct CP asymmetry in $D$ decays and $r_B^K$ is the ratio of the decay amplitudes of $B^{-}\to {\bar{D}}^0{K}^{-}$ and $B^{-}\to D^0{K}^{-}$. Using the recent data on CP asymmetry, we demonstrate the correction to physical observables in $B\to DK$ can reach 6%, which corresponds to the shift of $\gamma$ by roughly $5^{\circ }$. The remanent corrections depend on the strong phase of the $D$ decays, but are less than $0.5^{\circ }$. With the increasing precision in the $\gamma$ determination on the LHCb experiment and Super B factories, the inclusion of CP violation of $D$ decays will therefore soon become important.

arXiv comment4 pages, 1 figure, accepted for publication in Physical Review Letters

References in corpus (14)

• CP Violation and the CKM Matrix: Assessing the Impact of the Asymmetric B Factories
• Enhanced CP Violation with $B\to K{D}^0({\overline{D}}^0)$ Modes and Extraction of the CKM Angle gamma
• Determining $\gamma$ using $B^{\pm }\to D{K}^{\pm }$ with multibody D decays
• Improved Methods for Observing CP Violation in B+/- --> K+/- D0 and Measuring the CKM Phase gamma
• Evidence for CP violation in time-integrated D0 -> h-h+ decay rates
• Measurement of the difference of CP-violating asymmetries in D0 -> K+K- and D0 ->pi+pi- decays at CDF
• Measurement of CP--violating asymmetries in D0 --> pi+ pi- and D0 --> K+K- decays at CDF
• New ways to explore factorization in b decays
• The Effect of $D-\bar{D}$ Mixing on the Measurement of $\gamma$ in $B\to DK$ Decays
• Impact of D0-D0bar mixing on the experimental determination of gamma
• Detecting new physics contributions to the D0-D0bar mixing through their effects on B decays
• The $B(B_s)\to D_{(s)}({\bar{D}}_{(s)})T$ and $D_{(s)}^{\ast }({\bar{D}}_{(s)}^{\ast })T$ decays in perturbative QCD approach
• Yet another way to measure $\gamma$
• Determining CP violation angle $\gamma$ with B decays into a scalar/tensor meson

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• Heavy Flavour Physics and CP Violation at LHCb: a Ten-Year Review
• S-wave contributions in ${\bar{B}}_s^0\to (D^0,{\bar{D}}^0){\pi }^{+}{\pi }^{-}$ within perturbative QCD approach
• Effect of direct CP violation in charm on gamma extraction from B->DK, D->K0Spi+pi- Dalitz plot analysis
• Measurement of $CP$ observables in $B^{\pm }\to D{K}^{\ast \pm }$ decays using two- and four-body $D$ final states
• Shift in weak phase $\gamma$ due to CP asymmetries in $D$ decays to two pseudoscalar mesons
• Recent Developments on the CKM Matrix
• Electroweak effects in the extraction of the CKM angle $\gamma$ from $B\to D\pi$ decays
• $B\to D{K}_{0,2}^{\ast }$ Decays: PQCD analysis to determine CP violation phase angle $\gamma$