The matrix of unitarity triangle angles for quarks

Abstract

In the context of quark (as for lepton) mixing, we introduce the concept of the matrix of unitarity triangle angles Φ, emphasising that it carries equivalent information to the complex mixing matrix V itself. The angle matrix Φ has the added advantage, with respect to V, of being both basis- and phase-convention independent and consequently observable (indeed several Φ-matrix entries, e.g., Φcs=α, Φus=β, etc. are already long-studied as directly measurable/measured in B-physics experiments). We give complete translation formulae between the mixing-matrix and angle-matrix representations. We go on to consider briefly the present state of the experimental data on the full angle matrix and some of the prospects for the future, with reference to both the quark and lepton cases.