Dalitz Plot Analysis Research Articles

Amplitude analysis of the {D}_s^{+} → π−π+π+ decay

A Dalitz plot analysis of the {D}_s^{+} → π−π+π+ decay is presented. The analysis is based on proton-proton collision data recorded by the LHCb experiment at a centre-of-mass energy of 8 TeV and corresponding to an integrated luminosity of 1.5 fb−1. The resonant structure of the decay is obtained using a quasi-model-independent partial-wave analysis, in which the π+π− S-wave amplitude is parameterised as a generic complex function determined by a fit to the data. The S-wave component is found to be dominant, followed by the contribution from spin-2 resonances and a small contribution from spin-1 resonances. The latter includes the first observation of the {D}_s^{+} → ω(782)π+ channel in the {D}_s^{+} → π−π+π+ decay. The resonant structures of the {D}_s^{+} → π−π+π+ and D+→ π−π+π+ decays are compared, providing information about the mechanisms for the hadron formation in these decays.

Analysis of rescattering effects in 3pi final states

Decays into three particles are often described in terms of two-body resonances and a non-interacting spectator particle. To go beyond this simplest isobar model, crossed-channel rescattering effects need to be accounted for. We quantify the importance of these rescattering effects in three-pion systems for different decay masses and angular-momentum quantum numbers. We provide amplitude decompositions for four decay processes with total J^{PC} = 0^{--}, 1^{--}, 1^{-+}, and 2^{++}, all of which decay predominantly as rho pi states. Two-pion rescattering is described in terms of an Omnès function, which incorporates the rho resonance. Inclusion of crossed-channel effects is achieved by solving the Khuri–Treiman integral equations. The unbinned log-likelihood estimator is used to determine the significance of the rescattering effects beyond two-body resonances; we compute the minimum number of events necessary to unambiguously find these in future Dalitz-plot analyses. Kinematic effects that enhance or dilute the rescattering are identified for the selected set of quantum numbers and various masses.

New reaction approach to reflect exotic structure of hadronic molecular state

With the accumulation of experimental data, more and more exotic hadrons are observed. Among the interpretations of these exotic hadrons, molecular state and compact multiquark are two of the most popular pictures. However, it is still difficult to determine the structure of an exotic hadron. In this work, we propose a possible way to detect the internal structure of an exotic state. When a molecular state composed of two consistent hadrons is attacked by another particle, one of the constituents should be kicked out while another quasifree constituent stays almost unaffected. It is different from a compact multiquark which has no obvious subcluster. In this work, taking the $X(3872)$ as an example, we perform a Dalitz plot analysis of such reaction to find the effect of the different internal structures. Under the assumption of the $X(3872)$ as a molecular state or a compact tetraquark state, with the help of the effective Lagrangians, the Dalitz plot and the invariant mass spectrum are estimated with different total invariant mass of three final particles, and the effect of different binding energies is also discussed. Obvious event concentration can be observed as strips in the Dalitz plot and sharp peaks in the invariant mass spectrum for the $X(3872)$ with a small binding energy under the molecular state picture, while such concentration cannot be observed under the compact tetraquark picture. Such phenomenon can be applied to identify the internal structure of a new hadron state.

Analysis of CKM-favored quasi-two-body B rightarrow D (Rrightarrow ) K pi decays in PQCD approach

LHCb Collaboration studied the resonant structure of B_srightarrow overline{D}^0K^-pi ^+ decays using the Dalitz plot analysis technique, based on a data sample corresponding to an integrated luminosity of 3.0textrm{fb}^{-1} of pp collision. The K^-pi ^+ components have been analyzed in the amplitude model, where the decay amplitude is modeled to be the resonant contributions with respect to the intermediate resonances K^*(892), K_0^*(1430) and K_2^*(1430). Motivated by the experimental results, we investigate the CKM-favored quasi-two-body B rightarrow overline{D}^0Kpi decays in the framework of the perturbative QCD (PQCD) approach. We calculate the the branching fractions by introducing the appropriate wave functions of Kpi pair. Our results are in agreement well the available data, and others can be tested in LHCb and Belle-II experiments. Using the narrow-width-approximation, we also extract the branching fractions of the corresponding two-body Brightarrow {overline{D}} R decays, which agree to the previous theoretical calculations and the experimental data within the errors. There are no CP asymmetries in these decays in the standard model, because these decays are all governed by only the tree operators.

ηc three-body decays at BaBar

We study the processes γγ→ηc→η′K+K−, η′π+π−, and ηπ+π− using a data sample of 519 fb−1 recorded with the BaBar detector operating at the SLAC PEP-II asymmetric-energy e+e− collider at center-of-mass energies at and near the ϒ(nS) (n=2,3,4) resonances. A Dalitz plot analysis is performed of ηc decays to η′K+K−, η′π+π−, and ηπ+π−. We compare ηc decays to η and η′ final states in association with scalar mesons as they relate to the identification of the scalar glueball.

Exotic resonance of Zc(4100)− in B0 → ηcK+π− decay

The B0→ηcK+π− decay rate is calculated using the factorization approach, the Dalitz plot analysis technique is used to describe this process. One of the decay mechanisms involves an interesting exotic Zc(4100)− meson, besides, the non-resonant contribution and the contribution from neutral excited kaons K⁎0(892), K⁎0(1410), and K⁎0(1680) are taken into account. The overall branching fraction is obtained to be B(B0→ηcK+π−)=(5.58±1.19)×10−4. The dominant contribution to this result is the non-resonant one.

Combined analysis of Belle and Belle II data to determine the CKM angle ϕ3 using B+ → D( {K}_S^0 h+h−)h+ decays

We present a measurement of the Cabibbo-Kobayashi-Maskawa unitarity triangle angle ϕ3 (also known as γ) using a model-independent Dalitz plot analysis of B+ → D ( {K}_S^0 h+h−)h+, where D is either a D0 or overline{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 711 fb−1 and 128 fb−1, respectively. All data were accumulated from energy-asymmetric e+e− collisions at a centre-of-mass energy corresponding to the mass of the Υ(4S) resonance. We measure ϕ3 = (78.4 ± 11.4 ± 0.5 ± 1.0)°, where the first uncertainty is statistical, the second is the experimental systematic uncertainty and the third is from the uncertainties on external measurements of the D-decay strong-phase parameters.

Production of charmed baryon Λc(2860) via low energy antiproton-proton interaction

In the present work, we study the production problem of the charmed baryon $\Lambda_c(2860)^+$ at $\overline{\mbox{P}}$ANDA. With the $J^P=\frac{3}{2}^+$ assignment to $\Lambda_c(2860)^+$, an effective Lagrangian approach is adopted to calculate the cross section of $p\bar{p} \to \Lambda_c^-\Lambda_c(2860)^+$. The Dalitz plot analysis and the $D^0p$ invariant mass spectrum distribution are also given for the $p\bar{p} \to \Lambda_c^-\Lambda_c(2860)^+ \to \Lambda_c^-pD^0$ process. The numerical results show that the total cross section may reach up to about 10 $ \mu $b. With the designed luminosity of $\overline{\mbox{P}}$ANDA ($2\times10^{32}~\mbox{cm}^{-2}\mbox{s}^{-1}$), about $ 10^8 $ $\Lambda_c(2860)$ events can be expected per day by reconstructing the final $ pD^0 $.

CP violation in quasi-two-body D→VP decays and three-body D decays mediated by vector resonances

We reexamine direct $CP$ violation in the quasi-two-body $D\ensuremath{\rightarrow}VP$ decays and study $CP$ asymmetries in three-body $D$ decays proceeding through intermediate vector resonances within the framework of the topological amplitude approach for tree amplitudes and the QCD factorization approach for penguin amplitudes. Using the same mechanism of incorporating long-distance penguin-exchange amplitude induced from final-state rescattering that nicely accounts for the $CP$ asymmetry difference between ${D}^{0}\ensuremath{\rightarrow}{K}^{+}{K}^{\ensuremath{-}}$ and ${\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ modes, we find that $CP$ asymmetry can also occur at the per mille level in many of the $D\ensuremath{\rightarrow}VP$ channels or otherwise be negligibly small. We point out six golden modes which have sufficiently large branching fractions and direct $CP$ violation of order ${10}^{\ensuremath{-}3}$. In particular, the direct $CP$ asymmetry difference $\mathrm{\ensuremath{\Delta}}{a}_{CP}^{VP}$ between ${D}^{0}\ensuremath{\rightarrow}{K}^{+}{K}^{*\ensuremath{-}}$ and ${\ensuremath{\pi}}^{+}{\ensuremath{\rho}}^{\ensuremath{-}}$ is predicted to be $(\ensuremath{-}1.61\ifmmode\pm\else\textpm\fi{}0.33)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$, very similar to the counterpart in the $PP$ sector. Besides, we find a positive and large $CP$ asymmetry of order ${10}^{\ensuremath{-}3}$ in ${D}^{0}\ensuremath{\rightarrow}{K}_{S}{K}^{*0}$, an example of the asymmetry induced at tree level. We take into account the flavor-singlet QCD-penguin contributions to calculate their effects on the modes such as $D\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\phi}$ and $D\ensuremath{\rightarrow}\ensuremath{\eta}\ensuremath{\phi}$. We compare our results with the other approach in detail. For three-body $D$ decays, we perform the Dalitz plot analysis of those decays mediated by several vector resonances with the same mass but different electric charges. Local $CP$ asymmetry varies in magnitude and sign from region to region and can reach the percent level in certain local regions of phase space due to interference.

Light meson spectroscopy from Dalitz plot analyses of ηc decays to η′K+K− , η′π+π− , and ηπ+π− produced in two-photon interactions

We study the processes $\gamma \gamma \to \eta_c \to \eta' K^+ K^-$, $\eta' \pi^+ \pi^-$, and $\eta \pi^+ \pi^-$ using a data sample of 519 $fb^{-1}$ recorded with the BaBar detector operating at the SLAC PEP-II asymmetric-energy $e^+e^-$ collider at center-of-mass energies at and near the $\Upsilon(nS)$ ($n = 2,3,4$) resonances. This is the first observation of the decay $\eta_c \to \eta' K^+ K^-$ and we measure the branching fraction $\Gamma(\eta_c \to \eta' K^+ K^-)/(\Gamma(\eta_c \to \eta' \pi^+ \pi^-)=0.644\pm 0.039_{\rm stat}\pm 0.032_{\rm sys}$. Significant interference is observed between $\gamma \gamma \to \eta_c\to \eta \pi^+ \pi^-$ and the non-resonant two-photon process $\gamma \gamma \to \eta \pi^+ \pi^-$. A Dalitz plot analysis is performed of $\eta_c$ decays to $\eta' K^+ K^-$, $\eta' \pi^+ \pi^-$, and $\eta \pi^+ \pi^-$. Combined with our previous analysis of $\eta_c \to K \bar K \pi$, we measure the $K^*_0(1430)$ parameters and the ratio between its $\eta' K$ and $\pi K$ couplings. The decay $\eta_c \to \eta' \pi^+ \pi^-$ is dominated by the $f_0(2100)$ resonance, also observed in $J/\psi$ radiative decays. A new $a_0(1700) \to \eta \pi$ resonance is observed in the $\eta_c \to \eta \pi^+ \pi^-$ channel. We also compare $\eta_c$ decays to $\eta$ and $\eta'$ final states in association with scalar mesons as they relate to the identification of the scalar glueball.

Probing the \u2206U = 0 rule in three body charm decays

CP violation in charm decay was observed in the decays D0→ P±P∓ of a D0 meson to two pseudoscalars. When interpreted within the SM, the results imply that the ratio of the relevant rescattering amplitudes has a magnitude and phase that are both of O(1). We discuss ways to probe similar ratios in D0→ V±P∓ decays, where V is a vector that decays to two pseudoscalars, from the Dalitz-plot analysis of time-integrated three-body decays. Compared to two-body decays, three-body decays have the advantage that the complete system can be solved without the need for time-dependent CP violation measurements or use of correlated {D}^0-{overline{D}}^0 production. We discuss the decays D0→ π+π−π0 and D0→ K+K−π0 as examples by considering a toy model of only two overlapping charged resonances, treating the underlying pseudo two-body decays in full generality.

Measurement of the relative branching fractions of B+→h+h′+h′− decays

The relative branching fractions of $B^+ \to h^+h^{\prime +}h^{\prime -}$ decays, where $h^{(\prime)}$ is a pion or kaon, are measured. The analysis is performed with a data sample, collected with the LHCb detector, corresponding to an integrated luminosity of $3.0 {\rm fb}^{-1}$ of $pp$ collisions. The results obtained improve significantly on previous measurements of these quantities, and are important for the interpretation of Dalitz plot analyses of three-body charmless hadronic decays of $B^+$ mesons.

Dalitz analysis of D0→K−π+η decays at Belle

We present the results of the first Dalitz plot analysis of the decay $D^{0}\to K^{-}\pi^{+}\eta$. The analysis is performed on a data set corresponding to an integrated luminosity of 953 $\rm{fb}^{-1}$ collected by the Belle detector at the asymmetric-energy $e^{+}e^{-}$ KEKB collider. The Dalitz plot is well described by a combination of the six resonant decay channels $\bar{K}^{*}(892)^0\eta$, $K^{-}a_0(980)^+$, $K^{-}a_2(1320)^+$, $\bar{K}^{*}(1410)^0\eta$, $K^{*}(1680)^-\pi^{+}$ and $K_2^{*}(1980)^-\pi^{+}$, together with $K\pi$ and $K\eta$ S-wave components. The decays $K^{*}(1680)^{-}\to K^{-}\eta$ and $K_{2}^{*}(1980)^{-}\to K^{-}\eta$ are observed for the first time. We measure ratio of the branching fractions, $\frac{\mathcal{B}(D^{0}\to K^{-}\pi^{+}\eta)}{\mathcal{B}(D^{0}\to K^{-}\pi^{+})}=0.500\pm0.002{\rm(stat)}\pm0.020{\rm(syst)}\pm0.003{\rm (\mathcal{B}_{PDG})}$. Using the Dalitz fit result, the ratio $\frac{\mathcal{B}(K^{*}(1680)\to K\eta)}{\mathcal{B}(K^{*}(1680)\to K\pi)}$ is measured to be $0.11\pm0.02{\rm(stat)}^{+0.06}_{-0.04}{\rm(syst)}\pm0.04{\rm(\mathcal{B}_{\text{PDG}})}$; this is much lower than the theoretical expectations ($\approx1$) made under the assumption that $K^{*}(1680)$ is a pure $1^{3}D_1$ state. The product branching fraction $\mathcal{B}(D^0\to [K_2^{*}(1980)^-\to K^{-}\eta]\pi^{+})=(2.2^{+1.7}_{-1.9})\times10^{-4}$ is determined. In addition, the $\pi\eta^{\prime}$ contribution to the $a_0(980)^{\pm}$ resonance shape is confirmed with 10.1$\sigma$ statistical significance using the three-channel Flatt\'{e} model. We also measure $\mathcal{B}(D^0\to\bar{K}^{*}(892)^0\eta)=(1.41^{+0.13}_{-0.12})\%$. This is consistent with, and more precise than, the current world average $(1.02\pm0.30)\%$, deviates with a significance of more than $3\sigma$ from the theoretical predictions of (0.51-0.92)%.

Recent results of the hadronic cross section measurements with the CMD-3 detector at e+e− collider VEPP-2000

A brief review of the recent results on the hadronic cross section measurements with the CMD-3 detector at the e+e− collider VEPP-2000 is given. Focus is made on the processes with charged kaons in multihadron events, which have a strong impact on strange meson spectroscopy and form factors that are important ingredients in the Dalitz plot analysis. Experimental data relevant to the topic are presented from the broad energy range covered by VEPP-2000 and compared to earlier measurements by the different collaborations. The analysis is based on the integrated luminosity of about 100 pb−1 collected in 2011, 2012 and 2017.

Measurement of cos2β in B0→D(*)h0 with D→KS0π+π− decays by a combined time-dependent Dalitz plot analysis of BaBar and Belle data

We report measurements of $\sin{2\beta}$ and $\cos{2\beta}$ from a time-dependent Dalitz plot analysis of $B^{0} \to D^{(*)} h^{0}$ with $D \to K_{S}^{0} \pi^{+} \pi^{-}$ decays, where the light unflavored and neutral hadron $h^{0}$ is a $\pi^{0}$, $\eta$, or $\omega$ meson. The analysis is performed with a combination of the final data sets of the \babar\ and Belle experiments containing $471 \times 10^{6}$ and $772 \times 10^{6}$ $B\bar{B}$ pairs collected at the $\Upsilon\left(4S\right)$ resonance at the asymmetric-energy B factories PEP-II at SLAC and KEKB at KEK, respectively. We measure $\sin{2\beta} = 0.80 \pm 0.14 \,(\rm{stat.}) \pm 0.06 \,(\rm{syst.}) \pm 0.03 \,(\rm{model})$ and $\cos{2\beta} = 0.91 \pm 0.22 \,(\rm{stat.}) \pm 0.09 \,(\rm{syst.}) \pm 0.07 \,(\rm{model})$. The result for the direct measurement of the angle is $\beta = \left( 22.5 \pm 4.4 \,(\rm{stat.}) \pm 1.2 \,(\rm{syst.}) \pm 0.6 \,(\rm{model}) \right)^{\circ}$. The last quoted uncertainties are due to the composition of the $D^{0} \to K_{S}^{0} \pi^{+} \pi^{-}$ decay amplitude model, which is newly established by a Dalitz plot amplitude analysis of a high-statistics $e^{+}e^{-} \to c\bar{c}$ data sample as part of this analysis. We find the first evidence for $\cos2\beta>0$ at the level of $3.7$ standard deviations. The measurement excludes the trigonometric multifold solution $\pi/2 - \beta = (68.1 \pm 0.7)^{\circ}$ at the level of $7.3$ standard deviations and therefore resolves an ambiguity in the determination of the apex of the CKM Unitarity Triangle. The hypothesis of $\beta = 0^{\circ}$ is ruled out at the level of $5.1$ standard deviations, and thus CP violation is observed in $B^{0} \to D^{(*)} h^{0}$ decays.

First Evidence for cos2β>0 and Resolution of the Cabibbo-Kobayashi-Maskawa Quark-Mixing Unitarity Triangle Ambiguity.

We present first evidence that the cosine of the CP-violating weak phase 2β is positive, and hence exclude trigonometric multifold solutions of the Cabibbo-Kobayashi-Maskawa (CKM) Unitarity Triangle using a time-dependent Dalitz plot analysis of B^{0}→D^{(*)}h^{0} with D→K_{S}^{0}π^{+}π^{-} decays, where h^{0}∈{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 contain (471±3)×10^{6}BB[over ¯] pairs recorded by the BABAR detector and (772±11)×10^{6}BB[over ¯] pairs recorded by the Belle detector. The results of the measurement are sin2β=0.80±0.14(stat)±0.06(syst)±0.03(model) and cos2β=0.91±0.22(stat)±0.09(syst)±0.07(model). The result for the direct measurement of the angle β of the CKM Unitarity Triangle is β=[22.5±4.4(stat)±1.2(syst)±0.6(model)]°. The measurement assumes no direct CP violation in B^{0}→D^{(*)}h^{0} decays. The quoted model uncertainties are due to the composition of the D^{0}→K_{S}^{0}π^{+}π^{-} decay amplitude model, which is newly established by performing a Dalitz plot amplitude analysis using a high-statistics e^{+}e^{-}→cc[over ¯] data sample. CP violation is observed in B^{0}→D^{(*)}h^{0} decays at the level of 5.1 standard deviations. The significance for cos2β>0 is 3.7 standard deviations. The trigonometric multifold solution π/2-β=(68.1±0.7)° is excluded at the level of 7.3 standard deviations. The measurement resolves an ambiguity in the determination of the apex of the CKM Unitarity Triangle.

Dalitz plot analysis of the decay ω→π+π−π0

Using a low-background sample of $2.6\times 10^5$ $J/\psi\rightarrow\omega\eta(\omega\rightarrow\pi^{+}\pi^{-}\pi^{0},\eta\rightarrow\gamma\gamma)$ events, about 5 times larger statistics than previous experiments, we present a Dalitz plot analysis of the decay $\omega\rightarrow\pi^{+}\pi^{-}\pi^{0}$. It is found that the Dalitz plot distribution differs from the pure $P$-wave phase space with a statistical significance of $18.9\sigma$. The parameters from the fit to data are in reasonable agreement with those without the cross-channel effect within the dispersive framework, which indicates that the cross-channel effect in $\omega\rightarrow\pi^+\pi^-\pi^0$ is not significant.

Ξ(1690)− production in the K−p→K+K−Λ reaction process near threshold

We investigate $\Xi(1690)^-$ production from the $K^-p\to K^+K^-\Lambda$ reaction within the effective Lagrangian approach at the tree-level Born approximation. We consider the $s$- and $u$-channel $\Sigma/\Lambda$ ground states and resonances for the $\Xi$-pole contributions, in addition to the $s$-channel $\Lambda$, $u$-channel nucleon pole, and $t$-channel $K^-$-exchange for the $\phi$-pole contributions. The $\Xi$-pole includes $\Xi(1320)$, $\Xi(1535)$, $\Xi(1690)(J^p=1/2^-)$,and $\Xi(1820)(J^p=3/2^-)$. We calculate the Dalitz plot density of $(d^2\sigma/dM_{K^+K^-}dM_{K^-\Lambda}$ at 4.2 GeV$/c$) and the total cross sections for the $K^-p\to K^+K^-\Lambda$ reaction near the threshold. The calculation results are in good agreement with previously acquired experimental data. Using the parameters from the fit, we present the total and differential cross sections for the two-body $K^-p\to K^+\Xi(1690)^-$ reaction near the threshold. In our calculation, a strong enhancement at backward $K^+$ angles is predicted because of the dominant $u$-channel contribution. We also demonstrate that the Dalitz plot analysis for $p_{K^-}=1.915 -- 2.065$ GeV/c enables us to access direct information regarding $\Xi(1690)^-$ production, which can be tested by future $K^-$ beam experiments. The possible spin-parity states of $\Xi(1690)^-$ are briefly discussed as well.

Evidence for an eta _c(1S) pi ^- resonance in B^0 rightarrow eta _c(1S) K^+pi ^- decays

A Dalitz plot analysis of {{B} ^0} !rightarrow eta _c(1S) {{K} ^+} {{pi } ^-} decays is performed using data samples of pp collisions collected with the text{ LHCb } detector at centre-of-mass energies of {sqrt{s}} =7,~8 and 13{,mathrm {Te}mathrm {V}} , corresponding to a total integrated luminosity of 4.7 ,text{ fb }^{-1} . A satisfactory description of the data is obtained when including a contribution representing an exotic eta _c(1S) pi ^- resonant state. The significance of this exotic resonance is more than three standard deviations, while its mass and width are 4096 pm 20~^{+18}_{-22} ,mathrm {Me}mathrm {V} and 152 pm 58~^{+60}_{-35} ,mathrm {Me}mathrm {V} , respectively. The spin-parity assignments J^P=0^+ and J^{P}=1^- are both consistent with the data. In addition, the first measurement of the {{B} ^0} !rightarrow eta _c(1S) {{K} ^+} {{pi } ^-} branching fraction is performed and gives B(B0→ηc(1S)K+π-)=(5.73±0.24±0.13±0.66)×10-4,\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document}$$\\begin{aligned} \\displaystyle \\mathcal {B}({{B} ^0} \\!\\rightarrow \\eta _c(1S) {{K} ^+} {{\\pi } ^-} ) = (5.73 \\pm 0.24 \\pm 0.13 \\pm 0.66) \\times 10^{-4}, \\end{aligned}$$\\end{document}where the first uncertainty is statistical, the second systematic, and the third is due to limited knowledge of external branching fractions.

Recent results on CP violation at B factories

We review recent results of the Beauty Factories BaBar and Belle on CP violation in the quark sector and constraints on the CKM unitarity triangle. We first present the recent measurement, using BaBar and Belle data, of cos(2β) = cos(2ϕ1) in B0 → D(∗)h0 with $D \rightarrow {K^{0}_{S}} \pi ^{+} \pi ^{-}$ decays, using a combined time-dependent Dalitz plot analysis. The BaBar Dalitz plot analysis of the $B^{+} \rightarrow {K^{0}_{S}} \pi ^{+} \pi ^{0}$ decay is also presented, and shows an evidence for direct CP violation in B+ → K∗(892)π0. A recently published BaBar measurement of the |V ub| CKM matrix element allows to contrain one side of the unitarity triangle. These analyses use the data sets of the BaBar and Belle experiments containing 471 × 106 and 772 × 106 $B\overline {B}$ pairs collected at the Υ(4S) resonance at the asymmetric-energy B factories PEP-II at SLAC and KEKB at KEK, respectively.