Unitarity Triangle through Time

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1995
2001
2004
2006
2009

1995

This first date is set at the time the top quark existence was established by the CDF and D0 experiments. These first measurements of the top quark mass allow B−Bbar mixing to be used as a constraint on the CKM matrix; prior to this time, a consistent constraint on the CKM matrix was only feasible by means of additional assumptions. Also, this date roughly coincides with the first significant measurements of the CKM matrix element |Vcb| at LEP, as well as the first evidences on exclusive b → u decays by ARGUS and CLEO, yielding reliable estimations of the CKM matrix element |Vub|. Also around this date, a first lower bound on Bs mixing is obtained by ALEPH.

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2001

Results available by summer 2001: CP violation on the B system is established following the first measurements of the CKM parameter sin2β by BABAR and Belle. Combining results from LEP with those from CLEO, the uncertainty on the Bd mixing parameter Δmd is reduced by a factor of two. Further studies of Bs mixing tighten the lower bound on the Δms parameter. Precision on the CKM matrix elements |Vcb| and |Vub| reaches around ∼ 5% and ∼ 15%, respectively. The constraints from εK and Δmd and Δms benefit from significant improvements in the estimations of bag parameters and decay constants through Lattice QCD computations. Finally, the precision on the CKM matrix element |Vus| is further improved by results from KTEV and NA48.

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2004

Improved measurements of sin2β are complemented by the first constraints on the CKM angle α. First “unquenched” determinations of decay and bag parameters drive a significant revisiting of uncertainties on inputs from Lattice QCD, and improvements in OPE calculations provide a more reliable extraction of the CKM matrix elements |Vcb| and |Vub|.

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2006

This date marks the first decisive contributions from experiments at TeVatron; first D0 provided a two-sided constraint at 95% CL on Bs mixing, soon followed by the first measurement of the Δms parameter by CDF. These results translate into a novel stringent constraint on the CKM matrix. Concerning B factories, both BABAR and Belle contribute with several new results: constraints on cos2β allow for a partial lift of the ambiguity on the extraction of the CKM angle β; first constraints on the CKM angle γ appear, exidence for the leptonic B → τ ν is obtained, and combined inclusive and exclusive measurements of the CKM parameters |Vcb| and |Vub| reach new levels of accuracy. The constraint from the CP violation parameter εK benefits from improved estimations of the bag parameter BK from lattice QCD.

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2009

With the conclusion of the data-taking period for BABAR, and the final running of Belle at the Υ(4S), this last date sets the status of the CKM matrix prior to the new decade, with an increasing set of final results from both experiments, based on their complete datasets. For instance, the extraction of the CKM angle α reaches a precision beyond expectations. Using all available information, the numerical value of the Jarlskog determinant is now constrained with an accuracy close to 5%. Finally, improved constraints on the B → τ ν decay rate, slightly in discrepancy with the global CKM fit, and results from CDF and D0 on the Bs mixing parameters βs and ΔΓs on marginal agreement with the CKM prediction, emerge as possible hints for the search of New Physics beyond the Standard Model in the flavor sector.

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