Figure 3

Fitting the unitarity triangle International groups of theorists and experimentalists such as UTFit and CKMFitter are putting the measurements of the angles and sides of the unitarity triangle together to determine whether or not the triangle really is a triangle. In this figure from the CKMFitter collaboration, the experimental measurements and their uncertainties are represented as bands on the complex plane in which the unitarity triangle is drawn (black). If the measurements are consistent, then one choice for the apex of the triangle will fit all the constraints – graphically speaking, the coloured bands will all overlap at a single point. The precise measurements of sin2β from BaBar and Belle are shown by the narrow blue wedge, while the less precisely measured α and γ are shown by the blue crescents and light-green wedge, respectively. As for the sides of the triangle, the constraint on the length of the left-hand side from the rate of up to bottom-quark transitions is shown by the green ring; while the constraint on the right-hand side from B-meson oscillations is the yellow ring (recently narrowed to the orange ring by the measurements of B⁰_s oscillations at Fermilab). Earlier measurements of CP violation from kaons are represented by the green hyperbola. All the measurements are consistent with the apex of the unitarity triangle lying within the small red band, a great triumph for the Standard Model explanation of CP violation.

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