Patterns of flavour violation in the presence of a fourth generation of quarks and leptons

We calculate a number of observables related to particle-antiparticle mixing and the branching ratios for the most interesting rare and CP-violating K and B decays in the Standard Model (SM3) extended by a fourth generation of quarks and leptons (SM4). A model-independent parametrisation of these observables in terms of gauge-independent functions is adopted, which is useful for studying the breaking of the universality between K, B-d and B-s systems through non-minimal flavour violating interactions. We calculate first the mass differences Delta M-i in the neutral K and B systems, the mixing-induced CP asymmetries S-psi KS, S-psi phi, S-phi KS, S-eta'KS and epsilon(K). Subsequently, a detailed analysis of K+ -> pi(+)nu(nu) over bar, K-L -> pi(0)nu(nu) over bar, B-s,B-d -> mu(+)mu(-), B -> X-s,X-d nu(nu) over bar, K-L -> pi(0)l(+)l(-), B -> X-s gamma and B -> X(s,d)l(+)l(-) is presented, and also epsilon'/epsilon is considered. For some of these observables the departures from SM3 predictions can still be spectacular. We discuss how the new mixing parameters (3 angles, 2 CP phases) can be determined using the flavour observables in question. We identify the different hierarchical structures in the SM4 flavour mixing matrix, allowed by phenomenological and theoretical constraints, and define the corresponding generalised Wolfenstein expansion. Most importantly, we show how the characteristic patterns of correlations among the considered flavour observables allow to distinguish this New Physics scenario from supersymmetric flavour models, the Littlest Higgs model with T-parity and the Randall-Sundrum model with custodial protection. Of particular importance are the correlations involving S-psi phi, S-phi KS, Br(K+ -> pi(+)nu(nu) over bar), Br(K-L -> pi(0)nu(nu) over bar), Br(B-s,B-d -> mu(+)mu(-)), which could in principle rule out the SM4. Interestingly epsilon'/epsilon turns out to be suppressed below the data for large positive values of S-psi phi unless the relevant hadronic matrix elements differ strongly from the large N results. The important role of epsilon'/epsilon in bounding large enhancements of rare K decay branching ratios is reemphasised. We also show how the existing anomalies in the unitarity triangle fits as well as in S-psi phi and S-phi KS can be simultaneously explained in the SM4 scenario.