Is the CKM matrix going to crack?

During the last decade the Standard Model description of flavor transitions has been put to multiple tests, especially in the B-meson sector. The overall agreement between theory and experiment is excellent, much better than what we should expect assuming exotic particles lurking just behind the corner. Here and there, however, one finds a few glitches - most likely experimental flukes or underestimated theory errors but intriguing enough to keep a flicker of hope alive. This year there has been a lot of commotion about the D0 observation of the same sign di-muon asymmetry, since the Standard Model predicts this effect should be well below the current experimental precision. If the D0 result is confirmed, it would be a clear indication of new physics contribution to CP violation in the mixing of neutral B-mesons. Another, less publicized 3-sigma blip is the tension between:

• the CP asymmetry in the Bd meson decay into J/ψ + kaon,
• the branching fraction of the decay of a charged B meson into a tau lepton and a tau neutrino.

This tension has been around for a while, but below I'll follow a more recent presentation by Lunghi and Soni who put a slightly different twist to it.

All this fuzz is about measuring the entries of the CKM matrix - a 3x3 unitary matrix that is the source of all flavor violation in the Standard Model. See the usual parametrization pasted on the right. The parameters λ and A are well measured in several different ways that yield consistent results. Therefore one is more interested in constraints on the remaining two parameters called ρ and η. The 2 processes mentioned in the previous paragraph are sensitive to slightly different combinations of these parameters. The B → τν decay proceeds at tree-level via an off-shell W-boson, so the branching fraction is proportional to the Vub, that is the (13) element. Thus, the measurement of this branching fraction carves out a circle in the ρ,η plane. On the other hand, the CP asymmetry Bd → J/ψ K is due to an interference of tree-level decays and one-loop B-meson mixing, and the final result depends on Sin(2β) where β ∼ Arg[Vtb Vtd/Vcs Vcb ] is one of the angles in the unitarity triangle. This measurement appears as a diagonal line in the ρ,η plane. Now let us see how these two processes combine with several other measurements of ρ and η:
The point is that one can reconcile either of the two measurements with the other constraints on ρ,η but accommodating both is difficult. For example, in the upper plot B → τν is included in the fit to ρ and η. That best fit value uniquely predicts Sin(2β), but the result is off from the experimental value by more than 3 sigma. Conversely, if one uses Bd → J/ψ K in the fit, then B → τν is off by almost 3 sigma. The authors prefer the former interpretation because it provides a better overall consistency of the fit. This interpretation is also more plausible from the new physics point of view, since in general it is easier for new physics to compete with Standard Model loop processes than with tree-level processes. Moreover, this way it may go along better with the D0 di-muon anomaly as the latter is also related to B-meson mixing...

Now, how large is the tension clearly depends on the choice of observables going into the fit,
as well as on your personal beliefs in the errors quoted by various theoretical, experimental and lattice groups whose results enter the fit. For example, in the similar plots presented by the CKMfitter collaboration the errors are more conservative and the tension is not apparent. Clearly, on tabloid blogs such as Resonaances the aggressive approach is promoted, but one should remember that the cautious approach to flavor anomalies is usually right, at least historically. Asymptotically in the future, the new generation of B-factories (who should go online in late two-thousand-teens) will shrink the errors and swipe the floor. In a shorter time perspective, updates from Tevatron may clarify or further blur the situation. And then we're dying to see LHCb joining in the game, some time next year. But the last one is a perfect subject for a separate post...