The Effect of $D-\bar{D}$ Mixing on the Measurement of $\gamma$ in $B\to DK$ Decays

Abstract

$D-\bar{D}$ mixing is the source of the largest theoretical uncertainty in the extraction of $\gamma$ from $B\to DK$ decays. In the Standard Model, the mixing can have a rate close to its current experimental upper bound and is CP-conserving to an excellent approximation. We show that neglecting CP-conserving $D-\bar{D}$ mixing leads to an error in the determination of $\gamma$ only at second order in the small parameters, $\Delta m_D/{\Gamma }_D$ and $\Delta {\Gamma }_D/{\Gamma }_D$, and is therefore very small and can be safely neglected.

arXiv comment8 pages, no figures

References in corpus (27)

• 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
• SU(3) Breaking and D0-D0bar Mixing
• The $D^0-{\bar{D}}^0$ mass difference from a dispersion relation
• $D^0-\overline{D^0}$ Mixing and Rare Charm Decays
• Search for D0-D0B Mixing
• Improving bounds on $\gamma$ in $B^{\pm }\to D{K}^{\pm }$ and $B^{\pm ,0}\to D{X}_s^{\pm ,0}$
• Role of Charm Factory in Extracting CKM-Phase Information via B --> DK
• New, Efficient and Clean Strategies to Explore CP Violation Through Neutral B Decays
• Measuring $\gamma$ in $B^{\pm }\to K^{\pm }(K{K}^{\ast }{)}_D$ decays
• Search for D^0 - barD^0 Mixing in the Dalitz Plot Analysis of D^0 --> K_S^0 pi^+ pi^-
• On ${\varphi }_3$ Measurements Using $B^{-}\to D^{\ast }{K}^{-}$ Decays
• Impact of D0-D0bar mixing on the experimental determination of gamma
• Search for D0D0bar Mixing and a Measurement of the Doubly Cabibbo-suppressed Decay Rate in D0 -> K pi Decays
• Limits on D0-D0bar Mixing and CP Violation from the Ratio of Lifetimes for Decay to K-pi+, K-K+, and pi-pi+
• Measuring the Weak Phase gamma in Color Allowed B->DKpi Decays
• Using untagged B^0 -> D K_S to determine gamma
• Exploring CP Violation with B_d -> D K_s Decays
• New CP-violating parameters in cascade decays
• Detecting new physics contributions to the D0-D0bar mixing through their effects on B decays
• Search for D0-D0bar Mixing Using Semileptonic Decay Modes
• Search for D^0-D^0bar mixing in D^0 -> K+pi- decays and measurement of the doubly-Cabibbo-suppressed decay rate
• Discrete Ambiguities in the Measurement of the Weak Phase Gamma
• Determining gamma using B->D^**K
• Pathways to a clean gamma (phi3): From B to Super B-factories
• Getting beta-alpha without penguins

Cited by in corpus (46)

• Averages of $b$-hadron, $c$-hadron, and $\tau$-lepton properties as of summer 2016
• Averages of $b$-hadron, $c$-hadron, and $\tau$-lepton properties as of 2018
• Averages of $b$-hadron, $c$-hadron, and $\tau$-lepton properties as of 2021
• Implications of LHCb measurements and future prospects
• Two body B decays with isosinglet final states in SCET
• Model-independent determination of the strong-phase difference between D^0 and D^0-bar-> K^0_S,L h^+ h^- (h=pi,K) and its impact on the measurement of the CKM angle gamma/phi_3
• Evidence for direct CP violation in the decay B->D(*)K, D->KsPi+Pi- and measurement of the CKM phase phi3
• B, D and K decays
• Improved measurement of the CKM angle gamma in B^-+ -> D^(*) K^(*)-+ decays with a Dalitz plot analysis of D decays to K_S^0 pi^+ pi^- and K_S^0 K^+ K^-
• Feasibility study of model-independent approach to phi_3 measurement using Dalitz plot analysis
• The use of quantum-correlated D^0 decays for phi3 measurement
• Evidence for direct CP violation in the measurement of the Cabibbo-Kobayashi-Maskawa angle gamma with B-+ --> D(*) K(*)-+ decays
• New Physics at a Super Flavor Factory
• Time-Independent Measurements of D0-D0bar Mixing and Relative Strong Phases Using Quantum Correlations
• New physics effects in tree-level decays
• Measurement of the CKM angle gamma from a combination of B->Dh analyses
• Model-independent determination of the relative strong-phase difference between $D^0$ and ${\bar{D}}^0\to K_{S,L}^0{\pi }^{+}{\pi }^{-}$ and its impact on the measurement of the CKM angle $\gamma /{\varphi }_3$
• Charm mixing in the model-independent analysis of correlated D0-D0bar decays
• Observation of direct CP violation in the measurement of the Cabibbo-Kobayashi-Maskawa angle gamma with B+- --> D(*)K(*)+- decays
• Improved method for CKM constraints in charmless three-body B and B_s decays
• Measurement of ${CP}\xspace$ Violation Parameters with a Dalitz Plot Analysis of $B^{\pm }\to D_{{\pi }^{+}{\pi }^{-}{\pi }^0}{K}^{\pm }$
• Measurement of CP observables in B+- --> D_CP K+- decays and constraints on the CKM angle gamma
• First model-independent determination of the relative strong phase between D0 and D0B --> K0Spi+pi- and its impact on the CKM Angle gamma/phi3 measurement
• Effect of D-Dbar mixing in the extraction of gamma with B- -> D0 K- and B- -> D0 pi- decays
• Measurements of branching fraction ratios and CP asymmetries in B+/- ->D_CP K+/- decays in hadron collisions
• CP violation in the B system
• Measurements of branching fraction ratios and CP-asymmetries in suppressed B^- -> D(-> K^+ pi^-)K^- and B^- -> D(-> K^+ pi^-)pi^- decays
• Enhanced effects on extracting γfrom untagged B^0 and B_s decays
• CP violation effects on the measurement of $\gamma$ from $B\to DK$
• Measurement of CP violation observables and parameters for the decays $B^{\pm }\to D{K}^{\ast \pm }$
• Effect of direct CP violation in charm on gamma extraction from B->DK, D->K0Spi+pi- Dalitz plot analysis
• Measurement of Ratios of Branching Fractions and CP-Violating Asymmetries of B -> D*K Decays
• Measurement of CP Observables for the Decays B+/- --> D0_CP K*+/-
• Measurements of the branching fractions and CP-asymmetries of B- --> D0_(CP) K- decays
• Improved measurement of CP observables in B- --> D0_{CP} K- decays
• B^\pm -> D K^\pm with direct CP violation in charm
• Determining the CKM angle gamma with B_c decays
• First model-independent Dalitz analysis of $B^0\to D{K}^{\ast 0}$, $D\to K_S^0{\pi }^{+}{\pi }^{-}$ decay
• Electroweak effects in the extraction of the CKM angle $\gamma$ from $B\to D\pi$ decays
• Search for b--> u transitions in B- -> [K+pi-pi0]_D K-
• Study of CKM angle $\gamma$ sensitivity using flavor untagged $B_s^0\to {\tilde{D}}^{(\ast )0}\varphi$ decays
• CP violation in beauty decays
• Novel correlated $D^0\overline{D}{}^0$ systems for $c/b$ physics and tests of $T/CPT$
• Weak Phases and CP Violation
• Supersymmetric contributions to B -> D K and the determination of angle γ
• CP-violation parameters from decay rates of $B^{\pm }\to D{K}^{\pm }$, $D\to$ multibody final states