Analysis of $CP$ Violation in ${D}^{0}\to {K}^{+}{K}^{-}{\pi }^{0}$

Zheng, Bo  (School of Nuclear Science and Technology, University of South China, Hengyang, Hunan 421001, China) (Helmholtz Institute Mainz, Johann-Joachim-Becher-Weg 45, D-55099 Mainz, Germany) ; Zhang, Zhen-Hua  (School of Nuclear Science and Technology, University of South China, Hengyang, Hunan 421001, China) ; Zhou, Hang  (School of Nuclear Science and Technology, University of South China, Hengyang, Hunan 421001, China)

22 November 2018

Abstract: We study the $CP$ violation induced by the interference between two intermediate resonances ${K}^{⁎}\left(\mathrm{892}{\right)}^{+}$ and ${K}^{⁎}\left(\mathrm{892}{\right)}^{-}$ in the phase space of singly-Cabibbo-suppressed decay ${D}^{\mathrm{0}}\to {K}^{+}{K}^{-}{\pi }^{\mathrm{0}}$ . We adopt the factorization-assisted topological approach in dealing with the decay amplitudes of ${D}^{\mathrm{0}}\to {K}^{±}{K}^{⁎}\left(\mathrm{892}{\right)}^{\mp }$ . The $CP$ asymmetries of two-body decays are predicted to be very tiny, which are $\left(-\mathrm{1.27}±\mathrm{0.25}\right)×\mathrm{1}{\mathrm{0}}^{-\mathrm{5}}$ and $\left(\mathrm{3.86}±\mathrm{0.26}\right)×\mathrm{1}{\mathrm{0}}^{-\mathrm{5}}$ , respectively, for ${D}^{\mathrm{0}}\to {K}^{+}{K}^{⁎}\left(\mathrm{892}{\right)}^{-}$ and ${D}^{\mathrm{0}}\to {K}^{-}{K}^{⁎}\left(\mathrm{892}{\right)}^{+}$ , while the differential $CP$ asymmetry of ${D}^{\mathrm{0}}\to {K}^{+}{K}^{-}{\pi }^{\mathrm{0}}$ is enhanced because of the interference between the two intermediate resonances, which can reach as large as $\mathrm{3}×\mathrm{1}{\mathrm{0}}^{-\mathrm{4}}$ . For some NPs which have considerable impacts on the chromomagnetic dipole operator ${O}_{\mathrm{8}g}$ , the global $CP$ asymmetries of ${D}^{\mathrm{0}}\to {K}^{+}{K}^{⁎}\left(\mathrm{892}{\right)}^{-}$ and ${D}^{\mathrm{0}}\to {K}^{-}{K}^{⁎}\left(\mathrm{892}{\right)}^{+}$ can be then increased to $\left(\mathrm{0.56}±\mathrm{0.08}\right)×\mathrm{1}{\mathrm{0}}^{-\mathrm{3}}$ and $\left(-\mathrm{0.50}±\mathrm{0.04}\right)×\mathrm{1}{\mathrm{0}}^{-\mathrm{3}}$ , respectively. The regional $CP$ asymmetry in the overlapped region of the phase space can be as large as $\left(\mathrm{1.3}±\mathrm{0.3}\right)×\mathrm{1}{\mathrm{0}}^{-\mathrm{3}}$ .

Published in: Advances in High Energy Physics 2018 (2018) 7627308