The -violating phase originates from the interference between the mixing and direct decay of mesons to eigenstates. Ignoring subleading penguin contributions, the phase within the Standard Model (SM) is predicted to be where . An indirect determination of rad is obtained using a global fit to experimental data . Any deviation from this prediction would be a clear sign, so-called New Physics effects, strongly motivating the need for precise experimental measurements of this quantity . The measurement of -violating phase has been independently performed using , and decay modes. All measurements shown in the proceedings use 3 fb of data collected by the LHCb experiment  in collisions during 2011 and 2012.
2. Measurements of the -violating phase
A tagged time-dependent angular fit to candidates is applied to extract the -violating phase . The final state of the decay is an admixture of -even states, for and -odd states, for . It is decomposed into four amplitudes: three P-waves, , , and one S-wave, accounting for the nonresonant configuration. The phase is determined by where and . In the absence of violation in decay, . The complex parameters and describe the relation between flavour and mass eigenstates: and .
The candidates are reconstructed as the decay combined with a pair of oppositely charged kaons. After applying a full offline and trigger selection, signal candidates of the are obtained . The decay time and angular acceptances, decay time resolution as well as flavour tagging efficiency are taken into account in the fitting procedure. The decay time resolution is estimated using a large sample of prompt combinations produced directly in the interactions and is found to be 46 fs. Using a prescaled unbiased trigger sample and a tag and probe technique the decay time acceptance is determined from data. The angular acceptance is determined using simulated events that a subjected to the same trigger and selection criteria as the data. The flavour of the produced candidate is identified using two independent tagging algorithms: same side and opposite side. The flavour tagging algorithms are optimised on simulations and calibrated on data using flavour specific control channels. The combined effective tagging power is .
A weighted unbinned maximum likelihood fit is performed using a signal-only Probability Density Function (PDF), as described in Ref. . The signal weights are extracted using the sPlot technique . The data set is divided into six independent invariant mass bins that allows the measurement of the small S-wave amplitude in each bin and minimizes correction factors in the interference terms of the PDF . The projections of the decay time and angular distributions are shown in Fig. 1. The final results are rad, ps and ps where the first uncertainty is statistical and the second is systematic . The dominant contribution to the systematic uncertainty is contributed by the decay time and angular efficiency and background subtraction.
The analysis of decays has been also performed by the LHCb collaboration . The decay is similar to the one with a noticeable simplification: the final state being -odd, there is no need for the angular analysis. Fig. 2 shows the five interfering states dominated by component. After trigger and selection chain signal candidates are reconstructed (Fig. 2). With the time-dependent amplitude analysis, the measured value of the phase is rad. The dominant systematic uncertainty is coming from knowledge about resonance model. The combination of the and fit results gives rad .
Another decay mode with transition that has been exploited by the LHCb collaboration to measure is . The formalism used for this analysis is very close to that of decay  where the meson is replaced with . The number of signal candidates selected from a fit to the data sample is (Fig. 3). The decay time acceptance is determined using a control decay mode. Fig. 3 shows the decay time acceptance, which is defined as the product of the acceptance of the control channel and the ratio of acceptances of the simulated signal and control mode after full trigger and selection chain. The first measurement of the -violating parameters in a final state containing the resonance is rad, ps and ps . The fit result is consistent with measurement and the SM predictions. The systematic uncertainty is less than 20 of the statistical uncertainty, except for where it is close to 60 .
from in high range
The first measurement of the phase has been performed in the decay with invariant mass larger than 1050 MeV/c  that is above the resonance region. This decay has been studied using an analysis method very similar to that used for the decay mode reported in Ref. . The important difference between both decay analyses is that modelling of the distribution is included to distinguish different resonant and nonresonant contributions. The decay time acceptance is determined with the same method as described in Ref.  by using a control channel . The mass spectrum is fitted by considering the different contributions found in the time-dependent amplitude analysis as shown in Fig. 4. The final fit has been performed allowing eight independent sets of -violating parameters: three corresponding to transversity states, S-wave, , , and the combination of the two high-mass and states. The -violating parameters measurement of in high region is rad, ps and ps . The largest contribution to systematic uncertainty results from the resonance fit model. The combination with the decay fit results in the region gives rad, ps and ps that improves a precision of the measurement by more than 9 .
The -violating phase and lifetime parameters have been measured by several experiments, namely four analysis using the final state from CDF , D0 , ATLAS  and CMS  collaborations and five analysis using different final states performed by the LHCb collaboration, four of which discussed here. The world average result of and measurements from the Heavy Flavour Averaging Group  is shown in Fig. 5. They find rad and ps that is dominated by the measurements from LHCb collaboration and is consistent with the SM predictions.
The most precise measurement of -violating phase and lifetime parameters in the system has been performed using data collected by the LHCb experiment during Run I. So far all results are compatible with the Standard Model predictions. In order to reach an uncertainty of the measurement comparable or even better than the theoretical uncertainty of the SM prediction aside from improvements in available luminosity for the channels, inclusion of new decay modes have been investigated. For example, the channel not only could bring about 10 of the mode statistics, but it will be also an important verification of the as kinematics for both channels are expected to be identical. The statistical sensitivity to measurement after the LHCb upgrade, with an integrated luminosity of 46 fb , is expected 0.01 rad that will be close to the present theoretical uncertainty . As the measurement precision improves, the penguin polluion contributions to the meson decays have to been kept under control [18,19].
The work has been supported by the Polish National Science Centre (NCN) with Preludium grant UMO-2015/17/N/ST2/04056. I would like to thanks the organizers of the ICPPA'2017 conference for the invitation to present this work and my LHCb colleagues who helped in the preparation of this talk.