Double-mixing CP violation in B decays

Abstract

Abstract We study a long-overlooked CP violation observable, termed double-mixing CP violation, which arises from the interference between two neutral meson oscillating paths involved in a decay chain. The double-mixing CP violation is beneficial for the precise test of the Standard Model CKM mechanism, as it offers the potential to extract weak phases without pollution from strong dynamics. To provide a comprehensive understanding of the double-mixing CP violation, we perform phenomenological analyses on the cascade decays of the $$B^0_d$$ B d 0 and $$B^0_s$$ B s 0 mesons. Our results show that the double-mixing CP violation can be very significant in certain decay channels, such as $$B^0_d \rightarrow J/\psi K \rightarrow J/\psi (\pi ^+\ell ^-{\bar{\nu }}_\ell )$$ B d 0 → J / ψ K → J / ψ ( π + ℓ - ν ¯ ℓ ) , where the total CP violation arises almost entirely from the double-mixing CP violation. In addition, we employ the decay process $$B^0_d \rightarrow D^0 K \rightarrow (K^-\pi ^+)(\pi \ell \nu )$$ B d 0 → D 0 K → ( K - π + ) ( π ℓ ν ) to demonstrate that the involved strong and weak phases can be directly determined from the experimental data without any theoretical inputs. Specifically, the overall weak phase of this process is $$2\beta +\gamma $$ 2 β + γ , which is of significant importance for extracting the CKM phase angles. We also use $$B^0_s \rightarrow \rho ^0 K \rightarrow \rho ^0(\pi ^-\ell ^+\nu _\ell )$$ B s 0 → ρ 0 K → ρ 0 ( π - ℓ + ν ℓ ) to illustrate and discuss the significant importance of $$K^0_S - K^0_L$$ K S 0 - K L 0 interference.