Enhanced Standard Model bound on charm CP violation from QCD penguins

Abstract

We investigate the impact of QCD penguin operators on direct CP violation in singly Cabibbo-suppressed $D^0$ decays within the framework of light-cone sum rules (LCSR) using pion and kaon light-cone distribution amplitudes. We determine, for the first time, the hadronic matrix elements of the QCD penguin operators for $D^0\to K^+K^-$ and $D^0\toπ^+π^-$ at leading order in $α_s$, employing a three-point correlation function with an artificial momentum to avoid unphysical parasitic cuts. We also compute the matrix elements of the current-current operators using the same framework and compare them with previous LCSR results. We find that the scalar penguin operators $Q_5$ and $Q_6$ can have substantially enhanced matrix elements. We identify two sources of enhancement: quark-condensate contributions, which arise already at tree level and are therefore enhanced by a relative factor of $16 π^2$ compared to the remaining, loop-induced terms in the sum rule; and an annihilation-type contribution from the $\bar u u$ component of these operators, which enters already through twist-three light-cone distribution amplitudes and is of comparable magnitude. While the impact of QCD penguin operators on the branching ratios is negligible, they can enhance the magnitude of the ``penguin-to-tree'' amplitude ratios relevant for direct CP violation. The relevant strong phases, however, remain largely unconstrained within the accuracy of our framework. Assuming maximal relative strong phases, we find that the corresponding upper bound on the Standard Model contribution to charm CP violation can be enhanced compared to estimates based on the current-current operators alone, reducing the gap with the experimental measurement.