How large can the SM contribution to CP violation in $D^0-\bar D^0$ mixing be?

Abstract

We investigate the maximum size of CP violating effects in $D$-mixing within the Standard Model (SM), using Heavy Quark Expansion (HQE) as theoretical working tool. For this purpose we determine the leading HQE contributions and also $\alpha_s$ corrections as well as subleading $1/m_c$ corrections to the absorptive part of the mixing amplitude of neutral $D$ mesons. It turns out that these contributions to $\Gamma_{12}$ do not vanish in the exact SU$(3)_\mathrm{F}$ limit. Moreover, while the leading HQE terms give a result for $\Gamma_{12}$ orders of magnitude lower than the current experimental value, we do find a sizeable phase. In the literature it was suggested that higher order terms in the HQE might be much less affected by the severe GIM cancellations of the leading terms; it is even not excluded that these higher order terms can reproduce the experimental value of $y$. If such an enhancement is realized in nature, the phase discovered in the leading HQE terms can have a sizeable effect. Therefore, we think that statements like: {\it "CP violating effects in $D$-mixing of the order of $10^{-3}$ to $10^{-2}$ are an unambigous sign of new physics"}--given our limited knowlegde of the SM prediction--are premature. Finally, we give an example of a new physics model that can enhance the leading HQE terms to $\Gamma_{12}$ by one to two orders of magnitude.