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 $D^0 \rightarrow K_S^0 K_S^0$ 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, $A_{CP}(D^0 \to K_S^0 K_S^0) = (1.86 \pm 0.23 \pm 0.11)\%$, 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 $λ_{ud} > λ_{us}$, can simultaneously account for the observed deviation from the U-spin sum rule in $D^0 \to K^+ K^-$ and $D^0 \to π^+ π^-$ 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.

Figures (2)

• Figure 1: Direct CP asymmetry $a_{CP}^{dir}$ in $D^0 \to K_S^0 K_S^0$ vs. diquark mass $M_\Phi$. The predictions for the color-sextet ($S_6$, solid blue) and color-triplet ($S_3$, dashed green) models are compared against the LHCb measurement. A suppression factor of $0.1$ is applied to the $S_3$ curve to account for the destructive interference arising from the relation $C_1^q = -C_2^q$.
• Figure 2: A comprehensive multi-channel comparison showing the absolute asymmetries for $D^0 \to K_S^0 K_S^0$, $D^0 \to K^+ K^-$, and $D^0 \to \pi^+ \pi^-$ under both the $S_6$ (left panel) and $S_3$ (right panel) scenarios.