Possible effects of noncommutative geometry on weakCPviolation and unitarity triangles

Abstract

The possible effects of noncommutative geometry on weak $\mathrm{CP}$ violation and unitarity triangles are discussed by taking into account a simple version of the momentum-dependent quark mixing matrix in the noncommutative standard model. In particular, we calculate nine rephasing invariants of $\mathrm{CP}$ violation and illustrate the noncommutative $\mathrm{CP}$-violating effect in a couple of charged D-meson decays. We also show how inner angles of the deformed unitarity triangles are related to $\mathrm{CP}$-violating asymmetries in some typical ${B}_{d}$ and ${B}_{s}$ transitions into $\mathrm{CP}$ eigenstates. B-meson factories are expected to help probe or constrain noncommutative geometry at low energies in the near future.