The effects of the peculiar $CP$ conserving phases in unparticle propagators are explored. We find that the phases have a great impact on $CP$ violation. We adopt the decays $B_d\to {\pi }^{+}{\pi }^{-}$ and $B_d\to {\ell }^{-}{\ell }^{+}$ as the illustrators to demonstrate the influences of these phases on the direct $CP$ asymmetries. In particular, we emphasize that unparticle physics is the only model suggested to date that could give the direct $CP$ asymmetries in $B_d\to {\ell }^{-}{\ell }^{+}$ as large as 15%. We also point out that the unparticle phases could be probed in $B\to K^{*}{\ell }^{+}{\ell }^{-}$ decays by using T-odd correlations.

• Received 12 May 2007

DOI:https://doi.org/10.1103/PhysRevD.76.115003