Ratios of observables for B mesons

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Abstract
One might expect to learn that the Cabibbo-Kobayashi-Maskawa matrix possessed a complex phase simply by measuring the magnitudes of enough of its elements. Indeed, for a 3*3 matrix, specification of the magnitudes suffices to specify the matrix, aside from some discrete ambiguities. One should be able to learn, for example, that the elements Vub and Vtd had a nontrivial relative phase with respect to one another by measuring the magnitude of each and taking account of the unitarity constraint Vub*+Vtd approximately=-Vcb*Vcb approximately=VusVcd approximately=0.01. This constraint will be referred to as the unitarity triangle. The authors examine the practical implementation of this suggestion. They find that extreme precision is needed to establish the presence of such a nontrivial phase. On the other hand, the measurement of the ratio mod Vub/Vtd mod can probably be accomplished with sufficient accuracy to resolve an ambiguity in CKM matrix parameters that arises in present analyses.

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