Time-dependent CP asymmetries in charm decays

The CKM paradigm has been tested thoroughly over the last 40 years in both the neutral $K$ and $B$ systems. The recent discovery of neutral charm meson mixing has prompted the search for CP violation in $D$ decays. We discuss the prospects of performing time-dependent CP asymmetry measurements at facilities either taking data or under construction. Such measurements can (i) provide precision determinations of the charm mixing phase, and (ii) be used to probe for possible new physics effects (and perhaps ultimately constrain the CKM paradigm). We propose the use of the time-dependent asymmetry measurement of $D^0 \to K^+K^-$ decays to measure the phase of charm mixing, where existing experiments that are either under construction or taking data should be able to reach a precision of $<1.5^\circ$, and to use the phase difference between $D^0 \to K^+K^-$ and $D^0 \to \pi^+\pi^-$ decays to constrain the angle $\beta_c$ of the $cu$ unitarity triangle up to theoretical uncertainties from long distance and loop contributions. A large phase difference measured between these modes would indicate new physics.