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Register a new userMeasurement of $cos{2beta}$ in $B^{0} to D^{(*)} h^{0}$ with $D to K_{S}^{0} pi^{+} pi^{-}$ decays by a combined time-dependent Dalitz plot analysis of BaBar and Belle data
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We report measurements of $sin{2beta}$ and $cos{2beta}$ 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 $772 times 10^{6}$ $Bbar{B}$ pairs collected at the $Upsilonleft(4Sright)$ resonance at the asymmetric-energy B factories PEP-II at SLAC and KEKB at KEK, respectively. We measure $sin{2beta} = 0.80 pm 0.14 ,(rm{stat.}) pm 0.06 ,(rm{syst.}) pm 0.03 ,(rm{model})$ and $cos{2beta} = 0.91 pm 0.22 ,(rm{stat.}) pm 0.09 ,(rm{syst.}) pm 0.07 ,(rm{model})$. 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 $e^{+}e^{-} to cbar{c}$ data sample as part of this analysis. We find the first evidence for $cos2beta>0$ 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.
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We present first evidence that the cosine of the CP-violating weak phase $2beta$ 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 $D to K_{S}^{0} pi^{+} pi^{-}$ decays, where $h^{0} in {pi^{0}, eta, omega }$ 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 $Upsilon(4S)$ resonance at the asymmetric-energy B factories PEP-II at SLAC and KEKB at KEK, respectively. The data samples contain $( 471 pm 3 )times 10^6, Bbar{B}$ pairs recorded by the BaBar detector and $( 772 pm 11 )times 10^6, Bbar{B}$ pairs recorded by the Belle detector. The results of the measurement are $sin{2beta} = 0.80 pm 0.14 ,(rm{stat.}) pm 0.06 ,(rm{syst.}) pm 0.03 ,(rm{model})$ and $cos{2beta} = 0.91 pm 0.22 ,(rm{stat.}) pm 0.09 ,(rm{syst.}) pm 0.07 ,(rm{model})$. The result for the direct measurement of the angle $beta$ of the CKM Unitarity Triangle is $beta = left( 22.5 pm 4.4 ,(rm{stat.}) pm 1.2 ,(rm{syst.}) pm 0.6 ,(rm{model}) right)^{circ}$. The quoted model uncertainties are due to the composition of the $D^{0} to K_{S}^{0} pi^{+} pi^{-}$ decay amplitude model, which is newly established by performing a Dalitz plot amplitude analysis using a high-statistics $e^{+}e^{-} to cbar{c}$ data sample. CP violation is observed in $B^{0} to D^{(*)} h^{0}$ decays at the level of $5.1$ standard deviations. The significance for $cos{2beta}>0$ is $3.7$ standard deviations. The trigonometric multifold solution $pi/2 - beta = (68.1 pm 0.7)^{circ}$ 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.
The resonant substructures of $B^0 to overline{D}^0 pi^+pi^-$ decays are studied with the Dalitz plot technique. In this study a data sample corresponding to an integrated luminosity of 3.0 fb$^{-1}$ of $pp$ collisions collected by the LHCb detector is used. The branching fraction of the $B^0 to overline{D}^0 pi^+pi^-$ decay in the region $m(overline{D}^0pi^{pm})>2.1$ GeV$/c^2$ is measured to be $(8.46 pm 0.14 pm 0.29 pm 0.40) times 10^{-4}$, where the first uncertainty is statistical, the second is systematic and the last arises from the normalisation channel $B^0 to D^*(2010)^-pi^+$. The $pi^+pi^-$ S-wave components are modelled with the Isobar and K-matrix formalisms. Results of the Dalitz plot analyses using both models are presented. A resonant structure at $m(overline{D}^0pi^-) approx 2.8$ GeV$/c^{2}$ is confirmed and its spin-parity is determined for the first time as $J^P = 3^-$. The branching fraction, mass and width of this structure are determined together with those of the $D^*_0(2400)^-$ and $D^*_2(2460)^-$ resonances. The branching fractions of other $B^0 to overline{D}^0 h^0$ decay components with $h^0 to pi^+pi^-$ are also reported. Many of these branching fraction measurements are the most precise to date. The first observation of the decays $B^0 to overline{D}^0 f_0(500)$, $B^0 to overline{D}^0 f_0(980)$, $B^0 to overline{D}^0 rho(1450)$, $B^0 to D_3^*(2760)^- pi^+$ and the first evidence of $B^0 to overline{D}^0 f_0(2020)$ are presented.
A binned Dalitz plot analysis of the decays $B^0 to D K^{ast 0}$, with $D to K_{S}^{0} pi^{+} pi^{-}$ and $K_{S}^{0} K^{+} K^{-}$, is performed to measure the observables $x_pm$ and $y_pm$, which are related to the CKM angle $gamma$ 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, the values of the $CP$ violation parameters are found to be $x_+ = 0.05 pm 0.35 pm 0.02$, $x_-=-0.31pm 0.20 pm 0.04$, $y_+=-0.81pm 0.28pm 0.06$ and $y_-=0.31pm 0.21 pm 0.05$, where the first uncertainties are statistical and the second systematic. These observables correspond to values $gamma$ = $(71 pm 20)^circ$, $r_{B^0} = 0.56pm 0.17$ and $delta_{B^0} = (204,^{+21}_{-20})^circ$. The parameters $r_{B^0}$ and $delta_{B^0}$ are the magnitude ratio and strong phase difference between the suppressed and favoured $B^0$ decay amplitudes, and have been measured in a region of $pm 50$ MeV/$c^2$ around the $K^{ast}(892)^{0}$ mass and with the magnitude of the cosine of the $K^{ast}(892)^{0}$ helicity angle larger than 0.4.
We report a measurement of the CP violation parameter $varphi_1$ obtained in a time-dependent analysis of $B^0tobar{D}{}^{(*)0}h^0$ decays followed by $bar{D}{}^0to K_S^0pi^+pi^-$ decay. A model-independent measurement is performed using the binned Dalitz plot technique. The measured value is $varphi_1 = 11.7^{circ}pm7.8^{circ}({rm stat.})pm 2.1^{circ}({rm syst.})$. Treating $sin{2varphi_1}$ and $cos{2varphi_1}$ as independent parameters, we obtain $sin{2varphi_1} = 0.43pm 0.27({rm stat.})pm 0.08({rm syst.})$ and $cos{2varphi_1} = 1.06pm 0.33({rm stat.})^{+0.21}_{-0.15}({rm syst.})$. The results are obtained with a full data sample of $772 times 10^6 Bbar{B}$ pairs collected near the $Upsilon(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^+e^-$ collider.
We report a measurement of the amplitude ratio $r_S$ of $B^0 to D^0K^{*0}$ and $B^0 to bar{D^0}K^{*0}$ decays with a model-independent Dalitz plot analysis using $Dto K_S^0pi^+pi^-$ decays. Using the full data sample of $772times10^6$ $Bbar{B}$ pairs collected at the $Upsilon(4S)$ resonance with the Belle detector at KEKB accelerator the upper limit is $r_S < 0.87$ at the 68 % confidence level. This result is the first measurement of $r_S$ with a model-independent Dalitz analysis, and is consistent with results from other analyses. The value of $r_S$ indicates the sensitivity of the decay to $phi_3$ because the statistical uncertainty is proportional to $1/r_S$. The $r_S$ result is obtained from observables ($x_pm$, $y_pm$) begin{eqnarray} x_- &=& +0.4 ^{+1.0 +0.0}_{-0.6 -0.1} pm0.0 y_- &=& -0.6 ^{+0.8 +0.1}_{-1.0 -0.0} pm0.1 x_+ &=& +0.1 ^{+0.7 +0.0}_{-0.4 -0.1} pm0.1 y_+ &=& +0.3 ^{+0.5 +0.0}_{-0.8 -0.1} pm0.1 , end{eqnarray} where $x_pm = r_S cos(delta_S pm phi_3)$, $y_pm = r_S sin(delta_S pm phi_3)$ and $phi_3 (delta_S)$ are the weak (strong) phase difference between $B^0 to D^0K^{*0}$ and $B^0 to bar{D^0}K^{*0}$. The first uncertainty is statistical, the second is the experimental systematic and the third is the systematic due to the uncertainties on $c_i$ and $s_i$ parameters measured by CLEO.
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