Constraints on the CKM angle gamma in B^0 --> barD^0 (D^0) K^*0 from a Dalitz analysis of D^0 --> K_S pi^+ pi^-

Exclusion of multifold solutions of the CKM Unitarity Triangle by a time-dependent Dalitz plot analysis of $\bar B^0 \to D^{(*)0} h^0$ with $D^0 \to K^0_S π^+ π^-$ decays combining BABAR and Belle data

We present results of a new analysis campaign, which combines the final data samples collected by the B factory experiments BABAR and Belle in single physics analyses to achieve a unique sensitivity in time-dependent \CP\ violation measurements. The data samples contain $(471 \pm 3) \times 10^6 ~B \bar B$ pairs recorded by the BABAR detector and $(772 \pm 11) \times 10^6 ~ B \bar B$ pairs recorded by the Belle detector in $e^+e^-$ collisions at the center-of-mass energies corresponding to the mass of the $Υ(4S)$ resonance at the asymmetric-energy $B$ factories PEP-II at SLAC and KEKB at KEK, r…

利用$B^0 \to D π^+ π^-$、$D \to K_S^0 π^+ π^-$衰变对CKM角$β$进行模型无关测量的Dalitz图分箱优化

Dalitz plot binning optimization for the model-independent measurement of the CKM angle $β$ with $B^0 \to D π^+ π^-$, $D \to K_S^0 π^+ π^-$ decays

本文针对$B^0 \to D π^+ π^-$、$D \to K_S^0 π^+ π^-$衰变的CKM角$β$模型无关测量，采用Fisher信息品质因子$Q^2$和模拟退火优化Dalitz图分箱，使$β$测量灵敏度提升约10%，且对多种实验效应具有鲁棒性。

Measurement of the CKM angle gammma with B-+ ->D^(*)[K0s pi- pi+]K^(*)-+ decays in BaBar

We report on the measurement of the Cabibbo-Kobayashi-Maskawa angle gamma through a Dalitz analysis of neutral D decays to K0s pi- pi+ in the processes B-+ -> D^(*) K-+ and B-+ -> D K^*-+, D^* -> D pi0, D gamma, with the Babar detector at the SLAC PEP-II e^+ e^- asymmetric-energy collider.

Measurements of CKM angle phi1 with charmless penguins at Belle

We present measurements of time-dependent CP violation parameters in B0 --> K0 PI0, B0 --> Ks Pi+ Pi- and B0 --> Ks K+ K- decays. The latter two are extracted using time-dependent Dalitz plot analyses. These results are obtained from a large data sample that contains 657 x 10^6 BBbar pairs collected at the Upsilon(4S) resonance with the Belle detector at the KEKB asymmetric-energy e+e- collider.

The CKM phase $α$ through $B \to a_0 π$

We propose the decay modes $B \to a_0 (\to ηπ) π$ to determine the CKM phase $α$. One can analyze these modes through (i) the $B \to a_0 π$ isospin pentagon, (ii) the time dependent Dalitz plot of $B^0(t) \to a_0^{\pm} π^{\mp} \to ηπ^+ π^-$, and (iii) the time dependence of $B^0(t) \to a_0^0 (\to ηπ^0) π^0$. We show that the $a_0 π$ modes have certain advantages as compared to the $ρπ$ modes, and strongly recommend the time dependent Dalitz plot analysis in the $a_0 π$ channel.

Measurement of the angle ϕ_3 with Dalitz analysis of three-body D^0 decay from B\to D^0 K process

A new method to measure the angle $ϕ_3$ of the CKM unitarity triangle using a Dalitz analysis of the three-body decay of the $D^0$ meson from the $B\to D^0 K$ process has been introduced recently. The method employs the interference between $D^0$ and $\bar{D^0}$ to extract both the weak and strong phases. We present a study of statistical and systematic errors of this method using Monte Carlo simulation. A fit of the $D^0$ Dalitz distribution has been performed based on a 140 fb$^{-1}$ sample collected by the Belle detector. We observe the indication of a CP asymmetry with the significance of …

Measurement of CP Asymmetry in a Time-Dependent Dalitz Analysis of B^0 \to (ρπ)^0 and a Constraint on the Quark Mixing Matrix Angle ϕ_2

We present a measurement of CP asymmetry using a time-dependent Dalitz plot analysis of B0 --> pi+pi-pi0 decays based on a 414/fb data sample containing 449M BB pairs. The data was collected on the $Υ$(4S) resonance with the Belle detector at the KEKB asymmetric energy e+e- collider. Combining our analysis with information on charged B decay modes, we perform a full Dalitz and isospin analysis and obtain a constraint on the CKM angle $ϕ_2$, 68 deg. < $ϕ_2$ < 95 deg. as the 68.3% confidence interval for the $ϕ_2$ solution consistent with the standard model (SM). A large SM-disfavored region als…

Extracting CKM $γ$ phase from $B^{\pm} \to K^{\pm} π^+ π^-$ and $B^0$, $\bar B^0 \to K_s π^+ π^-$

We discuss some aspects of the search for CP asymmetry in the three body B decays, revealed through the interference among neighbor resonances in the Dalitz plot. We propose a competitive method to extract the CKM $γ$ angle combining Dalitz plot amplitude analysis of $B^{\pm} \to K^{\pm} π^+ π^-$ and untagged $B^0$, $\bar B^0 \to K_s π^+ π^-$. The method also obtains the ratio and phase difference between the {\it tree} and {\it penguin} contributions from $B^0$ and $\bar B^0 \to K^{*\pm} π^{\mp} $ decays and the CP asymmetry between $B^0$ and $\bar{B^0}$. From Monte Carlo studies of 100K even…

Measurement of the CKM angles alpha and gamma at the BaBar experiment

We present recent measurements of the CKM angles alpha and gamma using data collected by the BaBar detector at the PEP-II asymmetric-energy e+ e- collider at the Stanford Linear Accelerator Center. In addition to constraints on alpha from the decays B0 -> pi+ pi-, B0 -> rho+ pi- and B0 -> rho+ rho-, we also report the first measurement of time-dependent CP asymmetries in the decay B0 -> a1+(1260) pi-. We present measurements of gamma in B+ -> D(*)0 K+ decays using a Dalitz analysis in the modes D^0 -> Ks pi+ pi- and D^0 -> pi+ pi- pi0.

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

We exploit the quantum coherence between pair-produced D0 and D0B in psi(3770) decays to make a first determination of the relative strong phase differences between D0--> K0Spi+pi- and D0B--> K0Spi+pi-, which are of great importance in determining the CKM angle gamma/phi3 in B- --> D0 (D0B) K- decays. Using 818 1/pb of e+e- collision data collected with the CLEO-c detector at Ecm = 3.77 GeV, we employ a binned Dalitz-plot analysis of K0S pi+pi- and K0Lpi+pi- decays recoiling against flavor-tagged, CP-tagged and K0Spi+pi- tagged events to determine these strong phase differences.

Double Dalitz Plot Analysis of the Decay B^0 -> D K+ Pi-, D -> Ks Pi+ Pi-

It is shown that it is possible to perform a model-independent extraction of the CKM Unitarity Triangle angle $γ$ using only the decays $B^0\to D K^+π^-$ with $D\to K^0_Sπ^+π^-$ and $B^0\to D K^+π^-$ with flavour-specific $D$ decays. The proposed method can also utilise the $B^0\to D K^+π^-$ data with CP-eigenstate decays of the D meson in a model-independent way.

A Method to Measure cos(2beta) Using Time-Dependent Dalitz Plot Analysis of B0 -> D_CP pi+ pi-

We present a feasibility study of a method to measure the cosine of twice the CKM Unitarity Triangle angle beta using a time-dependent Dalitz plot analysis of B0 -> D pi+ pi- decays, where the neutral D meson is reconstructed in decays to CP eigenstates. We show that this method can be used at the B factories to make a measurement of cos(2beta) that is competitive with, or more precise than, other techniques using different quark-level transitions, while sin(2beta) can be measured to an accuracy more precise than any existing measurement using b -> c ubar d transitions. Furthermore, this techn…

Optimising sensitivity to $γ$ with $B^0 \to DK^+π^-$, $D \to K_{\rm S}^0π^+π^-$ double Dalitz plot analysis

Two of the most powerful methods currently used to determine the angle $γ$ of the CKM Unitarity Triangle exploit $B^+ \to DK^+$, $D \to K_{\rm S}^0π^+π^-$ decays and $B^0 \to DK^+π^-$, $D \to K^+K^-$, $π^+π^-$ decays. It is possible to combine the strengths of both approaches in a "double Dalitz plot" analysis of $B^0 \to DK^+π^-$, $D \to K_{\rm S}^0π^+π^-$ decays. The potential sensitivity of such an analysis is investigated in the light of recently published experimental information on the $B^0 \to DK^+π^-$ decay. The formalism is also expanded, compared to previous discussions in the litera…

Evidence for direct CP violation in the decay B->D(*)K, D->KsPi+Pi- and measurement of the CKM phase phi3

We present a new measurement of the unitarity triangle angle phi3 using a Dalitz plot analysis of the KsPi+Pi- decay of the neutral D meson produced in B->D(*)K decays. The method exploits the interference between D0 and D0bar to extract the angle phi3, strong phase delta and the ratio r of suppressed and allowed amplitudes. We apply this method to a 605 fb-1 data sample collected by the Belle experiment. The analysis uses three decays: B->DK, and B->D*K with D*->DPi0 and D*->Dgamma, as well as the corresponding charge-conjugate modes. From a combined maximum likelihood fit to the three modes,…

The crucial role of CLEO-c in the measurement of gamma

The most sensitive method to measure the CKM angle gamma is to exploit interference in B(+/-)->DK(+/-) decays, with the D-meson decaying to a hadronic final state. The analysis of quantum-correlated decays of the psi(3770) at CLEO-c provides invaluable information on the strong-phase difference between the D0 and D0bar across the Dalitz plane. Results from analyses of the decays D->K0PiPi and D->K0KK will be presented.

LHCb strategies for gamma from B to DK

One of the most promising ways to determine the angle gamma of the CKM unitarity triangle is through measurement of the tree level processes B to DK. The LHCb collaboration has studied the potential of these decays employing the Atwood-Dunietz-Soni (ADS) and Dalitz methods, making use of a large sample of simulated data. For each method the expected sensitivities to the angle gamma are presented in this report.

Impact on $γϕ_3$ from CLEO-c Using CP-tagged $D\toK_{S,L}ππ$ Decays

Precision determination of the CKM angle $γ/ϕ_3$ depends upon constraints on charm mixing amplitudes, measurements of doubly-Cabibbo suppressed amplitudes and relative phases, and studies of charm Dalitz plots tagged by flavor or CP eigenstates. In this note we describe the technique used at CLEO-c to constrain the $K_{S,L}ππ$ model uncertainty, and its impact on $γ/ϕ_3$ measurements at B-factories presented at the Charm 2007 Workshop.

Measurement of the CKM angle $φ_1$ in $B^0\to\bar{D}{}^{(*)0}h^0$, $\bar{D}{}^0\to K_S^0π^+π^-$ decays with time-dependent binned Dalitz plot analysis

We report a measurement of the CP violation parameter $φ_1$ obtained in a time-dependent analysis of $B^0\to\bar{D}{}^{(*)0}h^0$ decays followed by $\bar{D}{}^0\to K_S^0π^+π^-$ decay. A model-independent measurement is performed using the binned Dalitz plot technique. The measured value is $φ_1 = 11.7^{\circ}\pm7.8^{\circ}({\rm stat.})\pm 2.1^{\circ}({\rm syst.})$. Treating $\sin{2φ_1}$ and $\cos{2φ_1}$ as independent parameters, we obtain $\sin{2φ_1} = 0.43\pm 0.27({\rm stat.})\pm 0.08({\rm syst.})$ and $\cos{2φ_1} = 1.06\pm 0.33({\rm stat.})^{+0.21}_{-0.15}({\rm syst.})$. The results are obt…

Charmless 2- and 3-body B decays and the angle alpha (phi2)

We present preliminary measurements of branching fractions and CP-asymmetry parameters in two- and three-body charmless hadronic B decays. The available data sample consists of 227 million Upsilon(4S) B decays collected with the BABAR detector at the PEP-II asymmetric-energy e+e- collider at SLAC. We establish the observation of the decays B --> pi0 pi0 and B0 --> K0K0bar and constrain the CKM angle alpha with a full SU(2) isospin analysis in the B --> pi pi system and with a B0 --> pi+ pi- pi0 time-dependent Dalitz plot analysis.

Measurement of γ from B->Dh decays at LHCb---including the effect of D0-D0bar mixing

I present a measurement of the CKM angle gamma from a combination of three LHCb measurements using the tree decays B -> DK and B -> Dpi. These measurements are based on a dataset corresponding to 1.0fb-1, collected in 2011. In contrast to what was presented at FPCP, these proceedings fully include the effect of D0--D0b mixing on the combination. I also report on the inclusion of new, preliminary results on the Dalitz analysis of B->DK, D->KShh, using a dataset corresponding to 3fb-1, collected in 2011--2012.

一种在 $B^{\pm} \to DK^{\pm}$ 衰变中以最优化精度测量 CKM 角 $\gamma$ 的新型非分箱模型无关方法

A novel unbinned model-independent method to measure the CKM angle $γ$ in $B^{\pm} \to DK^{\pm}$ decays with optimised precision

提出一种结合 $B^{\pm} \to DK^{\pm}$ 与 charm threshold 数据的非分箱模型无关方法，在 D 介子三体衰变下无偏测量 CKM 角 $\gamma$，避免了 Dalitz plot 积分，精度优于传统分箱方法且无模型失配偏差。

First evidence for $\cos 2β>0$ and resolution of the CKM Unitarity Triangle ambiguity by a time-dependent Dalitz plot analysis of $B^{0} \to D^{(*)} h^{0}$ with $D \to K_{S}^{0} π^{+} π^{-}$ decays

We present first evidence that the cosine of the CP-violating weak phase $2β$ is positive, and hence exclude trigonometric multifold solutions of the CKM Unitarity Triangle using a time-dependent Dalitz plot analysis of $B^{0} \to D^{(*)} h^{0}$ with $D \to K_{S}^{0} π^{+} π^{-}$ decays, where $h^{0} \in \{π^{0}, η, ω\}$ denotes a light unflavored and neutral hadron. The measurement is performed combining the final data sets of the BaBar and Belle experiments collected at the $Υ(4S)$ resonance at the asymmetric-energy B factories PEP-II at SLAC and KEKB at KEK, respectively. The data samples c…

Recent studies of CP violation in bottom meson decays at Belle

We present a summary of recent studies on $CP$ violation with the Belle experiment using the final data sample of $772 \times 10^{6}$ B\bar{B} pairs produced at the Ypsilon(4S) resonance at the KEK asymmetric e^+ e^- collider. We discuss preliminary measurements of the branching fraction, the polarization and the $CP$ asymmetries of the decay $B^0 \rightarrow ρ^{+} ρ^{-}$ and an updated constraint on the CKM angle $ϕ_2$ from the $B\toρρ$ system. Being also related to $ϕ_2$, we present a preliminary measurement of the branching fraction of $B^0\rightarrow π^0π^0$ decays. Last, a preliminary mod…

A model-independent Dalitz plot analysis of $B^\pm \to D K^\pm$ with $D \to K^0_{\rm S} h^+h^-$ ($h=π, K$) decays and constraints on the CKM angle $γ$

A binned Dalitz plot analysis of $B^\pm \to D K^\pm$ decays, with $D \to K^0_{\rm S} π^+π^-$ and $D \to K^0_{\rm S} K^+ K^-$, is performed to measure the CP-violating observables $x_{\pm}$ and $y_{\pm}$ which are sensitive to the CKM angle $γ$. The analysis exploits 1.0 $\rm fb^{-1}$ of data collected by the LHCb experiment. The study makes no model-based assumption on the variation of the strong phase of the D decay amplitude over the Dalitz plot, but uses measurements of this quantity from CLEO-c as input. The values of the parameters are found to be $x_- = (0.0 \pm 4.3 \pm 1.5 \pm 0.6) \tim…

Combined analysis of Belle and Belle II data to determine the CKM angle $ ϕ_{3} $ using $B^+ \to D(K_{S}^0 h^- h^+) h^+$ decays

We present a measurement of the Cabibbo-Kobayashi-Maskawa unitarity triangle angle $ ϕ_{3} $ (also known as~$γ$) using a model-independent Dalitz plot analysis of \linebreak $B^+\to D\left(K_{S}^{0}h^{+}h^{-}\right)h^+$, where $D$ is either a $D^0$ or $\bar{D}{}^0$ meson and $h$ is either a $π$ or $K$. This is the first measurement that simultaneously uses Belle and Belle~II data, combining samples corresponding to integrated luminosities of \SI{711}{fb^{-1}} and \SI{128}{fb^{-1}}, respectively. All data were accumulated from energy-asymmetric $e^+e^-$ collisions at a centre-of-mass energy cor…

Model-independent measurement of the CKM angle $γ$ using $B^0 \to D K^{\ast 0}$ decays with $D \to K_{S}^{0} π^{+} π^{-}$ and $K_{S}^{0} K^{+} K^{-}$

A binned Dalitz plot analysis of the decays $B^0 \to D K^{\ast 0}$, with $D \to K_{S}^{0} π^{+} π^{-}$ and $K_{S}^{0} K^{+} K^{-}$, is performed to measure the observables $x_\pm$ and $y_\pm$, which are related to the CKM angle $γ$ and the hadronic parameters of the decays. The $D$ decay strong phase variation over the Dalitz plot is taken from measurements performed at the CLEO-c experiment, making the analysis independent of the $D$ decay model. With a sample of proton-proton collision data, corresponding to an integrated luminosity of $3.0\,\rm{fb}^{-1}$, collected by the LHCb experiment, t…

Measurement of the CKM angle γusing B^\pm --> D K^\pm with D-->K_Sπ^+π^-, K_SK^+K^- decays

A binned Dalitz plot analysis of $B^\pm \to D K^\pm$ decays, with $D \to K_S π^+π^-$ and $D \to K_S K^+ K^-$, is performed to measure the \CP-violating observables $x_{\pm}$ and $y_{\pm}$, which are sensitive to the Cabibbo-Kobayashi-Maskawa angle $γ$. The analysis exploits a sample of proton-proton collision data corresponding to 3.0\invfb collected by the LHCb experiment. Measurements from CLEO-c of the variation of the strong-interaction phase of the $D$ decay over the Dalitz plot are used as inputs. The values of the parameters are found to be $x_+ = (-7.7 \pm 2.4 \pm 1.0 \pm 0.4)\times 10…

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

A binned Dalitz plot analysis of $B^\pm \to D K^\pm$ decays, with $D\to K_\text{S}^0π^+π^-$ 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 $γ$. 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…

利用 $B^{\rightarrow}DK^{\pm}$ 和 $B^{\pm}\rightarrow D\pi^{\pm}$ 衰变结合 $D\rightarrow K_{\rm S}^{0}\pi^{+}\pi^{-}$ 与 $D\rightarrow K_{\rm S}^{0}K^{+}K^{-}$ 对 $\gamma$ 的测量

Measurement of $γ$ using $B^{\pm}\rightarrow DK^{\pm}$ and $B^{\pm}\rightarrow Dπ^{\pm}$ decays with $D\rightarrow K_{\rm S}^{0}π^{+}π^{-}$ and $D\rightarrow K_{\rm S}^{0}K^{+}K^{-}$

该研究利用升级后的LHCb实验2024年采集的5.8 fb⁻¹数据，通过B⁺与B⁻介子的D衰变Dalitz图分布差异观测CP破坏，首次测量CKM角γ为(68.1±6.7)°。