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References
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If we adopt the definition:\(CP\left( {B^0 } \right) = \bar B^0 , CP\left( {\bar B^0 } \right) = \bar B^0 \), then in the approximations of (2.12) BH and BL areCP eigenstates, and (2.13) implies:CP(BL)=+BL,CP(BH)=−BH.
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Expression (8.12) is valid forCP(f)=+f. Iff isCP odd, λ should be multiplied by a factor (−1), as discussed in ref. [11].
In case of decays toCP eigenstates, the effects of α1 and α2 can be included in the definition of an effective value of Im (λ), simplifying the formalism used in the analysis. (And with some generalization, for small σ t values, α3 could also be included.) However, in the most general case, ∣ρ∣2 is affected differently by the oscillation reducing coefficients, and we prefer to use the most general notation.
In a different notation, λэexp [2iϕ], where the phase ϕ can be identified with one of the inner angles of the «unitarity triangle»; see for instanceJ. L. Rosner, A. I. Sanda andM. P. Schmidt:Proceedings of the Workshop on High Sensitivity Beauty Physics at Fermilab, 1987, edited byA. J. Slaughter, N. Lockyer andM. Schmidt (Fermilab, Batavia, 1985), p. 165;F. J. Gilman: SLAC Report, SLAC-PUB-5018 (1989).
We did not analyse the quark sub-processes with ∣ρ∣2=1800, and ∣ρ∣2=5.6·10−4 because of the small size of ∣Im(γ)∣/(1+∣ρ∣2) (see table II). The detection ofCP violation would result more difficult, despite the branching ratios are estimated to be typically larger in this case (see ref. [11] ).
Apart from the obvious symmetry operation (ξ, ϕ)→(ξ+2n·π, ϕ+2m·π) withn, m integer, the solutions are symmetric under the transformations: (ξ, ϕ)→(ξ+π, ϕ+π), (ξ, ϕ)→(π−ξ,−ϕ) (ξ, ϕ)→(π/2−ϕ, π/2−ξ). The last transformation is used in the example reported in the text.
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Biino, C., Palestini, S. Mixing andCP violation in the\(B^0 - \bar B^0 \) systemssystems. Riv. Nuovo Cim. 14, 1–23 (1991). https://doi.org/10.1007/BF02813497
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DOI: https://doi.org/10.1007/BF02813497