The angle of the CKM triangle can be measured comparing and mediated transitions in decays. The decays proceed through the following diagrams:
These diagrams are practically free from the New Physics contribution.

There are three methods to extract relevant information, each of them deals with its own decay:

• a singly Cabibbo-suppressed CP eigenstate, like for Gronau-London-Wyler (GLW) method;
• a doubly Cabibbo-suppressed flavor eigenstate, like for Atwood-Dunietz-Soni (ADS) method;
• a Cabibbo-allowed self-conjugate 3-body state, like for Giri-Grossman-Soffer-Zupan (GGSZ) method.
Generally, the observables of the methods also depend on the amplitude ratio and the relative conserving phase between the two amplitudes. These parameters depend on the decay under investigation.

Gronau London Wyler method:

The Gronau-London-Wyler (GLW) method (M. Gronau D. Wyler Phys.Lett. B265 (1991) 172; M. Gronau, D. London, Phys.Lett. B253 (1991) 483) is based on the reconstruction of the decay to , where and decay to -even or -odd eigenstates. The modes normally used are:
• : , ;
• : , , , , and .
For the normalization, , with is also reconstructed.

The four observables for this method are formed in the following way:

This set can provide an information on , , and with an 8-fold ambiguity for the phases.

Atwood Dunitz Soni Method:

In the ADS method, D. Atwood, I. Dunietz and A. Soni, Phys. Rev. Lett. 78, 3257 (1997), is measured from the study of decays, where mesons decay into non eigenstate final states. The suppression of transition with respect to the one is partly overcome by the study of decays of the meson in final states which can proceed in two ways: either through a favored decay followed by a doubly-Cabibbo-suppressed decay, or through a suppressed decay followed by a Cabibbo-favored decay.

Neglecting -mixing effects, which in the SM give very small corrections to \g\ and do not affect the measurement, the measured ratios and are related to the and mesons' decay parameters through the following relations:

with:

In case of the analysis with we use the following ratios:

The used observables are connected to the "classical" and set by simple relations: and .

The values of and are taken from our study of charm mixing or the CLEO-c collaboration results. The ratio has been measured in different experiments and we take the average value from PDG.

Giri Grossman Soffer Zupan (GGSZ) method:

The Giri Grossman Soffer Zupan (GGSZ), also called Dalitz method (A. Giri, Y. Grossman, A. Soffer and J. Zupan, Phys. Rev. D 68, 054018 (2003)) is based on the reconstruction of the decay to , where and decay ;

The four observables for this method are formed in the following way: