Δf = 2 observables and B → X _qγ decays in the left-right model: Higgs particles striking back

We present a complete study of ΔS = 2 and ΔB = 2 processes in the leftright model (LRM) based on the weak gauge group SU(2) _L × SU(2) _R × U(1) _B-L. This includes ε _K, ΔM _K, ΔM _q, A _SL ^q, Δγ _q with q = d; s and the mixing induced CP asymmetries SΨK _S and SΨφ. Compared to the Standard Model (SM) these observables are affected by tree level contributions from heavy neutral Higgs particles (H ⁰) as well as new box diagrams with WR gauge boson and charged Higgs (H±) exchanges. We also analyse the B → X _s;dγ decays that receive important new contributions from the W _L - W _R mixing and H± exchanges. Compared to the existing literature the novel feature of our analysis is the search for correlations between various observables that could help us to distinguish this model from other extensions of the SM and to obtain an insight into the structure of the mixing matrix V ^R that governs right-handed currents. Moreover, we perform the full phenomenology including both gauge boson and Higgs boson contributions. We find that even for M _H ⁰ ≈ M _H± ∼ Ο(20)TeV, the tree level H ⁰ contributions to ΔF = 2 observables are by far dominant and the H± contributions to B → X _qγ can be very important, even dominant for certain parameters of the model. While in a large fraction of the parameter space this model has to struggle with the experimental constraint from ε _K, we demonstrate that there exist regions in parameter space which satisfy all existing ΔF = 2, B → X _s;dγ, tree level decays and electroweak precision constraints for scales M _WR ≃ 2 - 3TeV in the reach of the LHC. We also show that the SΨK _S - εK tension present in the SM can be removed in the LRM. Simultaneously Br(B → X _sγ) can be brought closer to the data. However, we point out that with the increased lower bound on M _WR, the LRM cannot help in explaining the difference between the inclusive and exclusive determinations of [V _ub], when all constraints are taken into account, unless allowing for large fine-tuning. Finally we present a rather complete list of Feynman rules involving quarks, gauge bosons and Higgs particles.