Up to a few years ago, no significant measurement of the angle γ in the unitarity triangle of B-meson physics was expected to come out of the current B-factories. However, a recent proposal to measure γ in B → DK decays using a Dalitz plot analysis has revolutionized the field. Results are emerging from both the B-factories at KEK and at SLAC.

Determinations of the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements provide important checks on the consistency of the Standard Model and ways to search for new physics. The CKM matrix parameterizes the mixing of different quarks as seen by the weak interaction and provides the Standard Model interpretation for charge-parity (CP) violation.

The nine complex elements of the matrix are related by unitarity constraints to a series of equations. One such relationship of specific interest to B-physics can be represented by a triangle, referred to as the “unitarity triangle”. The angles of the unitarity triangle are referred to as α, β and γ (ϕ_{2}, ϕ_{1} and ϕ_{3} respectively in Japan). Although β has already been measured with an accuracy of a few degrees, it is more difficult to measure α and γ accurately.

.The new analysis uses three-body decay of the neutral D, D^{0} → K_{s}π^{+}π^{–} from the channels B^{±} → D^{0}K^{±}, B^{±} → D*K^{±} and B^{±} → DK*^{±}. In the Dalitz plot analysis on the three-body decay of the D the invariant mass of the K_{s}π^{+} system is plotted versus the K_{s}π^{–} system in two dimensions, helping a measurement of an asymmetry when looking at B^{+} compared with B^{–} decays. The method also utilizes more event information and is thus more sensitive compared with a 1D approach.

Using a data sample of 253 fb^{-1}, the Belle collaboration at KEK obtains 276 signal candidates for B^{±} → D^{0}K^{±}, 69 candidates for B^{±} → D*K^{±} and 56 candidates for B^{±} → DK*^{±} (Abe *et al.* 2004 and 2005). Combining the first two channels yields the result γ = 68° ± 14° ± 13° ± 11°. The first error is statistical, the second is experimental systematics and the third is model uncertainty. The statistical significance of CP violation is 98%. This is not quite enough to claim observation of direct CP violation just yet, but it is getting close.

The BaBar collaboration at SLAC is also working on a similar analysis and their preliminary result stands at γ = 70° ± 26° ± 10° ± 10° (Aubert *et al.* 2004). Such values of γ agree with what is expected by the Standard Model and global fits of other information; moreover, the Dalitz plot method is fast becoming an established tool for measuring γ.

### Further reading

K Abe *et al.* The Belle collaboration 2004 http://arxiv.org/abs/hep-ex/0411049

K Abe *et al.* The Belle collaboration 2005 http://arxiv.org/abs/hep-ex/0504013

B Aubert *et al.* The BaBar collaboration 2004 http://arxiv.org/abs/hep-ex/0408088