Measurement of asymmetries in decays
The latest measurements of the individual time-integrated asymmetry in the Cabibbo-suppressed decays decays are presented. The results are based on collision data, corresponding to an integrated luminosity of 3, collected with the LHCb detector at centre-of-mass energies of 7 and 8. A combination of the asymmetries using both prompt and secondary charm decays is presented
These are the most precise measurements from a single experiment. The result for is the most precise determination of a time-integrated asymmetry in the charm sector to date, and neither measurement shows evidence of asymmetry.
Charge-parity () violation in weak decays is described by the Standard Model (SM) and is governed by a single complex phase in the Cabibbo-Kobayashi-Maskawa (CKM) matrix. The charmed meson system is suitable for probing the violation in the up-type quark sector. Recent studies of violation in weak decays of mesons have not found evidence of violation, while the phenomenon is well established in decays of - and -meson systems [1, 2, 3, 4, 5].
To distinguish the two -conjugate decays, the flavour of the at production must be known. At LHCb, two different techniques are employed. The flavour of the can be tagged by the charge of the soft pion, , in the strong decay for prompt decays , or by the charge of the muon in the semileptonic decay for secondary charm decays . The time-integrated asymmetry in the decay rates of the singly Cabibbo-supressed process
was measured recently at LHCb . This observable cannot be accessed directly due to the presence of production asymmetry of the and mesons at collider, and due to the presence of detection asymmetries. The latter can origin from an asymmetric interaction of the charged particles with the material of the detector. One example for this is the different cross-section for interaction with matter of and . Any asymmetry in the detector e.g. some inefficient regions, faulty electronics, etc could also contribute to the detection asymmetry. The effect of such asymmetries can cancel to first order with the regular swap of the magnetic field of the dipole magnet at LHCb.
The measured raw asymmetry in the number of background-subtracted number of signal decays \linenomath
is related to the observable of interest, , via \linenomath
To cancel the effect of the nuisance detection and production asymmetry, a set of Cabibbo-favoured decays, , in which no violation is expected, is used. For example, by exploiting the prompt channel, one can cancel the production asymmetry, and the soft pion detection asymmetry. However, a new detection asymmetry is present due to the asymmetric final state . The effect of this asymmetry is mitigated using the other two calibration channels leading to \linenomath
The results are obtained using a data sample of proton-proton () collisions at centre-of-mass energies of 7 and 8 collected by the LHCb detector in 2011 and 2012, corresponding to approximately 3 of integrated luminosity.
The LHCb detector [10, 11] is a single-arm forward spectrometer covering the pseudorapidity range , designed for the study of particles containing b or c quarks. The detector elements that are particularly relevant to this analysis are: a silicon-strip vertex detector surrounding the pp interaction region that allows c- and b-hadrons to be identified from their characteristically long flight distance; a tracking system that provides a measurement of momentum, , of charged particles; and two ring-imaging Cherenkov detectors that are able to discriminate between different species of charged hadrons.
The production and detection asymmetries depend on the kinematics of the particles involved. If the kinematic distributions are very different, this may lead to an imperfect cancellation of the nuisance asymmetries in . This effect is alleviated by equalising the corresponding kinematical distributions by assigning weights to each candidate .
The raw asymmetries and the signal yields are determined from binned likelihood fits to the , distributions in the decay modes, and to the invariant mass distributions in the channels (see Fig. 1). The yields of the decay modes, before and after the weighting procedure, are listed in Table 1.
|Channel||Before weighting||After weighting|
The non-adequateness of the fit model, and the presence of peaking background can cause biases in the determination of individual raw asymmetries, and their effects are studied using pseudoexperiments, and simulated events. Possible presence of large local asymmetries can spoil the measurement since Eq. 3 is valid only for small asymmetries. This systematic uncertainty is accounted for by excluding additional regions of the detector acceptance, and comparing the result to the nominal one.
The non-cancellation of detection and production asymmetries is accounted for by modifying the configuration of the procedure. Another way to asses this systematic contribution is by modelling the kinematic dependancies of the raw asymmetries, and combining them with per-event weights from data. Presence of secondary charm decays can bias the measurement due to the different asymmetries related to the production of secondary decays. The uncertainty was calculated by measuring the fraction of secondary decays, and using the measured production asymmetries at LHCb as an input. A systematic uncertainty on the calculation of the neutral kaon detection asymmetry is also taken into account. All other investigated sources are found to be negligible.
A summary of the systematic uncertainties considered can be found in Table 2 and added in quadrature to obtain the overall systematic uncertainty.
|Determination of raw asymmetries:|
|Cancellation of nuisance asymmetries:|
|Additional fiducial cuts|
|Secondary charm meson|
|Neutral kaon asymmetry|
The time-integrated asymmetry in decays measured using prompt charm decays is determined to be \linenomath
This result can be combined with previous LHCb measurements of the same and related observables. A combination with measured using secondary charm decays  yields
Since the same decay channels are employed for the cancellation of detection asymmetries, the result is partially correlated with . The statistical correlation coefficient is . The difference in asymmetries between and decays, , is measured at LHCb using prompt charm decays . A combination of the measurement of with yields a value for \linenomath
The statistical correlation coefficient of the two measurements is .
A combination with the measurement using secondary charm results in \linenomath
Fig. 2 shows the LHCb measurements of asymmetry using both prompt and secondary and decays. Additionally, the latest combined values of the Heavy Flavour Averaging Group  for these quantities are presented.
In conclusion, no evidence of violation is found in the Cabibbo-suppressed decays and . These results are obtained assuming that there is no violation in – mixing and no direct violation in the Cabibbo-favoured , and decay modes. The combined LHCb results are the most precise measurements of the individual time-integrated asymmetries and from a single experiment to date.
10 \mciteSetBstSublistModen \mciteSetBstMaxWidthFormsubitem) \mciteSetBstSublistLabelBeginEnd\mcitemaxwidthsubitemform
-  J. H. Christenson, J. W. Cronin, V. L. Fitch, and R. Turlay, Evidence for the decay of the meson, Phys. Rev. Lett. 13 (1964) 138\mciteBstWouldAddEndPuncttrue\mciteSetBstMidEndSepPunct\mcitedefaultmidpunct \mcitedefaultendpunct\mcitedefaultseppunct\EndOfBibitem
-  BaBar collaboration, B. Aubert et al., Observation of CP violation in the meson system, Phys. Rev. Lett. 87 (2001) 091801, arXiv:hep-ex/0107013\mciteBstWouldAddEndPuncttrue\mciteSetBstMidEndSepPunct\mcitedefaultmidpunct \mcitedefaultendpunct\mcitedefaultseppunct\EndOfBibitem
-  Belle collaboration, K. Abe et al., Observation of large CP violation in the neutral meson system, Phys. Rev. Lett. 87 (2001) 091802, arXiv:hep-ex/0107061\mciteBstWouldAddEndPuncttrue\mciteSetBstMidEndSepPunct\mcitedefaultmidpunct \mcitedefaultendpunct\mcitedefaultseppunct\EndOfBibitem
-  LHCb collaboration, R. Aaij et al., First observation of violation in the decays of mesons, Phys. Rev. Lett. 110 (2013) 221601, arXiv:1304.6173\mciteBstWouldAddEndPuncttrue\mciteSetBstMidEndSepPunct\mcitedefaultmidpunct \mcitedefaultendpunct\mcitedefaultseppunct\EndOfBibitem
-  LHCb collaboration, R. Aaij et al., Observation of violation in decays, Phys. Lett. B712 (2012) 203, Erratum ibid. B713 (2012) 351, arXiv:1203.3662\mciteBstWouldAddEndPuncttrue\mciteSetBstMidEndSepPunct\mcitedefaultmidpunct \mcitedefaultendpunct\mcitedefaultseppunct\EndOfBibitem
-  LHCb collaboration, R. Aaij et al., Measurement of the difference of time-integrated asymmetries in and decays, Phys. Rev. Lett. 116 (2016) 191601, arXiv:1602.03160\mciteBstWouldAddEndPuncttrue\mciteSetBstMidEndSepPunct\mcitedefaultmidpunct \mcitedefaultendpunct\mcitedefaultseppunct\EndOfBibitem
-  LHCb collaboration, R. Aaij et al., Measurement of asymmetry in and decays, JHEP 07 (2014) 041, arXiv:1405.2797\mciteBstWouldAddEndPuncttrue\mciteSetBstMidEndSepPunct\mcitedefaultmidpunct \mcitedefaultendpunct\mcitedefaultseppunct\EndOfBibitem
-  LHCb, R. Aaij et al., Measurement of asymmetry in decays, arXiv:1610.09476\mciteBstWouldAddEndPuncttrue\mciteSetBstMidEndSepPunct\mcitedefaultmidpunct \mcitedefaultendpunct\mcitedefaultseppunct\EndOfBibitem
-  LHCb collaboration, R. Aaij et al., Search for direct violation in modes using semileptonic decays, Phys. Lett. B723 (2013) 33, arXiv:1303.2614\mciteBstWouldAddEndPuncttrue\mciteSetBstMidEndSepPunct\mcitedefaultmidpunct \mcitedefaultendpunct\mcitedefaultseppunct\EndOfBibitem
-  LHCb collaboration, A. A. Alves Jr. et al., The LHCb detector at the LHC, JINST 3 (2008) S08005\mciteBstWouldAddEndPuncttrue\mciteSetBstMidEndSepPunct\mcitedefaultmidpunct \mcitedefaultendpunct\mcitedefaultseppunct\EndOfBibitem
-  LHCb collaboration, R. Aaij et al., LHCb detector performance, Int. J. Mod. Phys. A30 (2015) 1530022, arXiv:1412.6352\mciteBstWouldAddEndPuncttrue\mciteSetBstMidEndSepPunct\mcitedefaultmidpunct \mcitedefaultendpunct\mcitedefaultseppunct\EndOfBibitem
-  CDF collaboration, T. Aaltonen et al., Measurement of the difference in CP–violating asymmetries in and decays at CDF, Phys. Rev. Lett. 109 (2012) 111801, arXiv:1207.2158\mciteBstWouldAddEndPuncttrue\mciteSetBstMidEndSepPunct\mcitedefaultmidpunct \mcitedefaultendpunct\mcitedefaultseppunct\EndOfBibitem
-  Heavy Flavor Averaging Group, Y. Amhis et al., Averages of -hadron, -hadron, and -lepton properties as of summer 2014, arXiv:1412.7515, updated results and plots available at http://www.slac.stanford.edu/xorg/hfag/\mciteBstWouldAddEndPuncttrue\mciteSetBstMidEndSepPunct\mcitedefaultmidpunct \mcitedefaultendpunct\mcitedefaultseppunct\EndOfBibitem
-  LHCb collaboration, A search for time-integrated violation in and decays, LHCb-CONF-2013-003\mciteBstWouldAddEndPuncttrue\mciteSetBstMidEndSepPunct\mcitedefaultmidpunct \mcitedefaultendpunct\mcitedefaultseppunct\EndOfBibitem