CP Violation in $D\to KK$ Decays: A Comparative Analysis of Triplet and Sextet Diquarks

Abstract

Recent measurements of the CP asymmetry in the decay $D^0\to K_S^0{K}_S^0$ by the CMS collaboration, $A_{CP}(K_S^0{K}_S^0)=(6.2\pm 3.0\pm 0.2\pm 0.8)\%$, and by LHCb, $A_{CP}(D^0\to K_S^0{K}_S^0)=(1.86\pm 1.04\pm 0.41)\%$, suggest possible deviations from Standard Model (SM) expectations, which predict asymmetries below the percent level. This singly Cabibbo-suppressed decay is particularly sensitive to new physics, as the leading amplitudes vanish in the exact U-spin symmetry limit and the process is dominated by W-exchange topologies. We investigate scalar diquark contributions to this decay, comparing color-sextet and color-triplet representations. We find that the color-sextet diquark, characterized by a symmetric color structure $(C_1^{\mathrm{NP}}=C_2^{\mathrm{NP}})$, avoids color suppression and can generate CP asymmetries in the range $0.5\%$--$1.5\%$ for a diquark mass of order 1~TeV. In contrast, the color-triplet contribution is strongly suppressed due to destructive interference from its antisymmetric color structure. We further show that a flavor hierarchy in the sextet couplings, with ${\lambda }_{ud}>{\lambda }_{us}$, can simultaneously account for the observed deviation from the U-spin sum rule in $D^0\to K^{+}{K}^{-}$ and $D^0\to {\pi }^{+}{\pi }^{-}$ and the measured CP asymmetry in $D^0\to K_S^0{K}_S^0$. These results identify color-sextet scalar diquarks as viable candidates for explaining enhanced CP violation in charm decays.

Comments: 12 pages, 2 figures, some misprints have been corrected and references added