The impact of a 4th generation on mixing and CP violation in the charm system

Abstract

We study \( {D^0} - {\overline D^0} \) mixing in the presence of a fourth generation of quarks. In particular, we calculate the size of the allowed CP violation which is found at the observable level well beyond anything possible with CKM dynamics. We calculate the semileptonic asymmetry a SL(D) and the mixing induced CP asymmetry η f S f (D) which are correlated with each other. We also investigate the correlation of η f S f (D) with a number of prominent observables in other mesonic systems like ε′/ε, Br(K L → π0 \( \nu \overline \nu \)), Br(K + → π+ \( \nu \overline \nu \)), Br(B s → μ+μ-), Br(B d → μ+μ-) and finally S ψϕ(B s ) in the Bs system. We identify a clear pattern of flavour and CP violation predicted by the SM4 model: While simultaneous large 4G effects in the K and D systems are possible, accompanying large NP effects in the B d system are disfavoured. However this behaviour is not as pronounced as found for the LHT and RSc models. In contrast to this, sizeable CP violating effects in the B s system are possible unless extreme effects in η f S f (D) are found, and Br(B s → μ+μ-) can be strongly enhanced regardless of the situation in the D system. We find that, on the other hand, S ψϕ(B s ) > 0.2 combined with the measured ε′/ε significantly diminishes 4G effects within the D system.