R–parity violation, sneutrino mixing phenomena and CP-violation in p¯p → ˜ν → ℓ + ℓ − + X

The sneutrino resonance reactions p¯ p → ˜ ν → ℓ + ℓ − +X, for ℓ = e, µ, τ , in the MSSM without R–parity are considered. We perform a cross–section analysis and show that present limits on some products of R / P couplings in the sneutrino sector can be significantly improved in future upgraded Tevatron runs. Furthermore, we introduce CP–violating and CP–conserving τ –spin asymmetries which are generated already at the tree–level in the reaction p¯ p → ˜ ν → τ + τ − + X if there is˜ν µ − ¯ ˜ ν µ mixing and that vanish in the SM. We find, for example, that for muon–sneutrino masses in the range 150 GeV < ∼ m ˜ ν µ < ∼ 450 GeV, these spin asymmetries reach ∼ 20 − 30% and ∼ 10% for mass splitting between the muon–sneutrino CP–odd and CP–even states at the level of ∆m ∼ Γ and ∆m ∼ Γ/4, respectively, where Γ is the˜ν µ width. Both the CP–violating and the CP–conserving spin asymmetries should be detectable in future Tevatron runs even for a heavy sneutrino with a mass < ∼ 500 GeV. If detected, such asymmetries—being proportional to the mass splitting between the CP–even and CP–odd sneutrino states—may serve as strong indication for the existence of the sneutrino mixing phenomenon.