Dispersive and absorptive CP violation in D0−D¯0 mixing

$CP$ violation (CPV) in ${D}^{0}\ensuremath{-}{\overline{D}}^{0}$ mixing is described in terms of the dispersive and absorptive ``weak phases'' ${\ensuremath{\phi}}_{f}^{M}$ and ${\ensuremath{\phi}}_{f}^{\mathrm{\ensuremath{\Gamma}}}$. They parametrize CPV originating from the interference of ${D}^{0}$ decays with and without dispersive mixing, and with and without absorptive mixing, respectively, for $CP$ conjugate hadronic final states $f$, $\overline{f}$. These are distinct and separately measurable effects. For $CP$ eigenstate final states, indirect CPV only depends on ${\ensuremath{\phi}}_{f}^{M}$ (dispersive CPV), whereas ${\ensuremath{\phi}}_{f}^{\mathrm{\ensuremath{\Gamma}}}$ (absorptive CPV) can only be probed with non-$CP$ eigenstate final states. Measurements of the final state dependent phases ${\ensuremath{\phi}}_{f}^{M}$, ${\ensuremath{\phi}}_{f}^{\mathrm{\ensuremath{\Gamma}}}$ determine the intrinsic dispersive and absorptive mixing phases ${\ensuremath{\phi}}_{2}^{M}$ and ${\ensuremath{\phi}}_{2}^{\mathrm{\ensuremath{\Gamma}}}$. The latter are the arguments of the dispersive and absorptive mixing amplitudes ${M}_{12}$ and ${\mathrm{\ensuremath{\Gamma}}}_{12}$, relative to their dominant ($\mathrm{\ensuremath{\Delta}}U=2$) $U$-spin components. The intrinsic phases are experimentally accessible due to approximate universality: in the SM, and in extensions with negligible new CPV phases in Cabibbo favored/doubly Cabibbo suppressed (CF/DCS) decays, the deviation of ${\ensuremath{\phi}}_{f}^{M,\mathrm{\ensuremath{\Gamma}}}$ from ${\ensuremath{\phi}}_{2}^{M,\mathrm{\ensuremath{\Gamma}}}$ is negligible in CF/DCS decays ${D}^{0}\ensuremath{\rightarrow}{K}^{\ifmmode\pm\else\textpm\fi{}}X$, and below 10% in CF/DCS decays ${D}^{0}\ensuremath{\rightarrow}{K}_{S,L}X$ (up to precisely known $O({\ensuremath{\epsilon}}_{K})$ corrections). In singly Cabibbo suppressed (SCS) decays, QCD pollution enters at $O(\ensuremath{\epsilon})$ in $U$-spin breaking and can be significant, but is $O({\ensuremath{\epsilon}}^{2})$ in the average over $f={K}^{+}{K}^{\ensuremath{-}}$, ${\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$. SM estimates yield ${\ensuremath{\phi}}_{2}^{M},{\ensuremath{\phi}}_{2}^{\mathrm{\ensuremath{\Gamma}}}=O(0.2%)$. A fit to current data allows $O(10)$ larger phases at $2\ensuremath{\sigma}$, from new physics. A fit based on naively extrapolated experimental precision suggests that sensitivity to ${\ensuremath{\phi}}_{2}^{M}$ and ${\ensuremath{\phi}}_{2}^{\mathrm{\ensuremath{\Gamma}}}$ in the SM may be achieved at the LHCb Phase II upgrade.