ACP[D(s)0,+→Vγ] from a large O8 contribution

Abstract

$CP$ violation in $\mathrm{\ensuremath{\Delta}}{A}_{\mathrm{CP}}=\ensuremath{-}0.154(29)$, in the ${D}^{0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}/{K}^{+}{K}^{\ensuremath{-}}$ system, is established, and its central value is 1 order of magnitude above the naive Standard Model (SM) estimate. It remains unclear whether this is due to currently incalculable strong interaction matrix elements or genuine new physics, such as a shift in ${\mathcal{O}}_{8}$ with a weak phase. We show that interference of the long-distance (LD) terms with the ${\mathcal{O}}_{8}$ matrix element can give rise to ${A}_{CP}^{D\ensuremath{\rightarrow}V\ensuremath{\gamma}}=\mathrm{few}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ (for reference values $\mathrm{Im}[{C}_{8}^{\mathrm{NP}}]\ensuremath{\approx}{10}^{\ensuremath{-}3}$). In addition, it is pointed out that the ratio of left- to right-handed (photon polarization) LD amplitudes is measurable in time-dependent $CP$ asymmetries. We argue that both theory and experimental consideration favor weak annihilation (WA) as the dominant LD contribution. More definite progress could be achieved by either computing the radiative corrections to WA or the measurement of the charged modes ${D}_{(d,s)}^{+}\ensuremath{\rightarrow}(\ensuremath{\rho},{K}^{*}{)}^{+}\ensuremath{\gamma}$ and ${D}_{s}\ensuremath{\rightarrow}{\ensuremath{\rho}}^{+}\ensuremath{\gamma}$.