Abstract: The CP violation observables S and C in the decay channel B-0 -> D+D- are determined from a sample of proton-proton collisions at center-of-mass energies of 7 and 8 TeV, collected by the LHCb experiment and corresponding to an integrated luminosity of 3 fb(-1). The observable S describes CP violation in the interference between mixing and the decay amplitude, and C parametrizes direct CP violation in the decay. The following values are obtained from a flavor-tagged, decay-time-dependent analysis: S = -0.54(-0.16)(+0.17) (stat) +/- 0.05(syst) ,C=0.26(-0.17)(+0.18) (stat) +/- 0.02(syst). These values provide evidence for CP violation at a significance level of 4.0 standard deviations. The phase shift due to higher-order standard model corrections is constrained to a small value of Delta phi = -0.16(-0.21)(+0.19) rad.

Abstract: We present first evidence that the cosine of the CP-violating weak phase 2 beta 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)pi(+)pi(-) decays, where h(0) is an element of {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 (sic)(4S) resonance at the asymmetric-energy B factories PEP-II at SLAC and KEKB at KEK, respectively. The data samples contain (471 +/- 3) x 10(6) B (B) over bar pairs recorded by the BABAR detector and (772 +/- 11) x 10(6) B (B) over bar pairs recorded by the Belle detector. The results of the measurement are sin 2 beta = 0.80 +/- 0.14 (stat) +/- 0.06 (syst) +/- 0.03 (model) and cos 2 beta = 0.91 +/- 0.22(stat) +/- 0.09 (syst) +/- 0.07(model). The result for the direct measurement of the angle beta of the CKM Unitarity Triangle is beta = [22.5 +/- 4.4 (stat) +/- 1.2 (syst) +/- 0.6(model)]degrees. 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)pi(+)pi(-) decay amplitude model, which is newly established by performing a Dalitz plot amplitude analysis using a high-statistics e(+)e(-) -> c (c) over bar data sample. CP violation is observed in B-0 -> D-(*) h(0) decays at the level of 5.1 standard deviations. The significance for cos 2 beta > 0 is 3.7 standard deviations. The trigonometric multifold solution pi/2 – beta = (68.1 +/- 0.7)degrees 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.

Abstract: We derive lower bounds on the variance of estimators in quantum metrology by choosing test observables that define constraints on the unbiasedness of the estimator. The quantum bounds are obtained by analytical optimization over all possible quantum measurements and estimators that satisfy the given constraints. We obtain hierarchies of increasingly tight bounds that include the quantum Cramer-Rao bound at the lowest order. In the opposite limit, the quantum Barankin bound is the variance of the locally best unbiased estimator in quantum metrology. Our results reveal generalizations of the quantum Fisher information that are able to avoid regularity conditions and identify threshold behavior in quantum measurements with mixed states, caused by finite data.