Determining the Phases α and γ from Direct CP Violation in B u , B d and B s Decays to Two Vectors

A method for clean determination of the unitarity angles α and γ is proposed that uses only direct CP violation and does not require any time dependent measurements. The method takes advantage of helicity amplitudes for Bu, Bd and Bs decay to two vector mesons and can be used, at any B-facility, in conjunction with a large number of modes. It also allows for experimental tests of theoretical approximations involved. Considerable progress has recently been made in experimental determination of the angle β of the unitarity triangle and improved measurements are expected in the near future [1, 2, 3]. However, even with increased precision in the extraction of β, the ability to test the CKM [4] description of CP violation in the Standard Model (SM) will be limited as the existing tests rely on theoretical calculation of hadronic matrix elements which still have considerable uncertainties [5]. Therefore clean determinations of all three angles (α, β, γ) of the unitarity triangle is important to facilitate precision tests of the SM and search for new CP-odd phase(s) due to physics beyond the SM. Currently the asymmetric B-factories are performing remarkably well and in the future hadronic B-machines may produce 1-3 orders of magnitude more B-mesons. Thus, it is very important to devise methods for clean extraction of the angles that can be used at all B-facilities. Furthermore, since time dependent measurements involving Bs mesons are extremely challenging due to the high frequency of Bs−B̄s oscillations, it would also be helpful if methods could be devised that do not require such time dependent information. email: [email protected] email: [email protected]