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88 Section 2: CDF Physics Analysis 2.4.7 B Mixing and CP Violation (Prof. Huth, Dr. Maksimovic & Mr. Bailey) In the next few years several experiments will come online with the intention of detecting and measuring CP violation with B mesons in several decay modes. These include dedicated B factory experiments such as Belle and BaBar as well as hadronic experiments such as CDF. CDF has already demonstrated its potential to measure B sector CP violation with the recent measurement of the CP violating parameter sin(2) =0:790:390:16 [24] using the decay mode B 0 ! J= K s in the Run I data. This analysis used a B 0 avor tagging algorithm developed by Maksimovic for his thesis. CDF II should be able to signicantly improve this measurement as well as measure other CP violating parameters with other decay modes. The Harvard group will be involved with these studies, especially those involving B s mesons. The group has interest in CP violation studies using B s ! Ds K and B s ! J= as well as the requisite measurements of B s mixing and avor tagging. Contributions have already been made in the area of a signal to background study, avor tagging algorithms, and a feasibility study for B s ! Ds K . These B physics interests are directly related to our work on the Silicon Readout Controller (SRC) for the Silicon Vertex Detector data acquisition system (SVX DAQ). The SVX DAQ is designed to process a 40 kHz level 1 accept rate and trigger on B events at level 2. This ability is unique to CDF and is crucial to acquiring a large and pure B sample for performing these B physics studies. The Unitarity Triangle In the Standard Model, CP violation arises from a single complex phase in the V CKM mixing matrix which relates the quark mass and weak eigenstates. By treating the elements of the unitarity relation V ud V ub + V cd V cb + V td V tb =0 as vectors in the complex plane, one may form the \unitarity triangle" which neatly summarizes the relevant parameters in B meson CP violation studies. Dierent decay modes of B mesons produce CP violating eects proportional to the sine of various combinations of these angles.
Section 2: B Mixing and CP Violation 89 6 (; ) V ud V ub V cd V cb V td V tb V cd V cb arg , V tdV tb b bbbbbbbbbb b (1; 0) - V ud V ub arg , V cdV cb V td V tb arg , V udV ub V cd V cb Many new physics scenarios (e.g. SUSY) predict alternate forms of CP violation which would aect these measurements [25]. One possibility is that the new physics would introduce new phases such that the measured + + would not equal 180 . These new phases would also aect B 0 decays dierently than B s decays and thus the same angle measured with two dierent decays could produce dierent results. Another possibility is that no new phases would be introduced but that the magnitudes of B 0 and B s mixing would be increased such that the measured sides of the unitarity triangle would not be consistent with the measured angles. Thus measuring CP violation with a variety of B decays provides a rigorous test of the Standard Model's explanation of CP violation as well as a sensitive probe for new physics. Mixing Induced CP Violation The form of CP violation which is most useful for constraining the Standard Model is due to mixing between B 0 and B 0 , or B s and B s . For nal states to which both particle and anti-particle can decay, interference can arise due to phase dierences between the two decay channels. Considering the decay B s ( B s ) ! D s , K + for example, the V CKM elements for B s ! D s , K + are approximately real as are the elements for the B s ! B s mixing. But the V CKM phase of B s ! D s , K + is approximately the angle of the unitarity triangle. The time dependence of the B s mixing produces a time dependent CP violating parameter of magnitude sin . real - B s D , H K+ s HHHHHj * real B s
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