Preprint number: CP3-Origins-2012-23 and DIAS-2012-24
A large CP-asymmetry ∆ACP has been reported in the D0 → π+π−/K+K− system. At present it remains unclear whether this is due to incalculable strong interaction matrix elements or genuine new physics (NP). Amongst the latter a new weak phase in the chromomagnetic operator O8 has emerged as a promising candidate. Extending earlier ideas we show that the interference of long-distance (LD) terms with the O8 matrix element, which has a large strong phase, gives rise to direct CP-violation at the level of a few percent in D0 → (ρ0,ω) γ and D+(d,s) → (ρ+,K*+) γ for reference values Im[C8NP] ≅ 0.4 ·10−2. This is two orders of magnitude above a Standard Model (SM) estimate. The contribution of Im[C7NP], which is dependent on the model of NP, is governed by the LD strong phase which vanishes in the chiral limit at leading order. The question of whether this is significantly changed by radiative corrections is an open and interesting question that we discuss. Furthermore we point out that the relative size of left- and right-handed (photon polarisation)-LD amplitudes can be measured, in principle, through time-dependent CP (TDCP) asymmetries in the case where they are both sizeable which is supported by SM estimates. Thus determination of the latter provides interesting information on the LD-chirality independent of NP. We comment on the origin of the LD contribution, which we believe to be dominated by weak annihilation (WA), in the appendix.