BrokenRparity contributions to flavor changing rates andCPasymmetries in fermion pair production at leptonic colliders

Abstract

We examine the effects of the R parity odd renormalizable interactions on flavor changing rates and $\mathrm{CP}$ asymmetries in the production of fermion-antifermion pairs at leptonic (electron and muon) colliders. In the reactions ${l}^{\ensuremath{-}}{+l}^{+}\ensuremath{\rightarrow}{f}_{J}+{f}_{{J}^{\ensuremath{'}}} (l=e,$ \ensuremath{\mu}; $J\ensuremath{\ne}{J}^{\ensuremath{'}})$ the produced fermions may be leptons, down quarks, or up quarks, and the center of mass energies may range from the Z-boson pole up to $1000$ GeV. Off the Z-boson pole, the flavor changing rates are controlled by tree level amplitudes and the $\mathrm{CP}$ asymmetries by interference terms between tree and loop level amplitudes. At the Z-boson pole, both observables involve loop amplitudes. The lepton number violating interactions, associated with the coupling constants ${\ensuremath{\lambda}}_{\mathrm{ijk}},$ ${\ensuremath{\lambda}}_{\mathrm{ijk}}^{\ensuremath{'}},$ are only taken into account. The consideration of loop amplitudes is restricted to the photon and Z-boson vertex corrections. We briefly review flavor violation physics at colliders. We present numerical results using a single, species and family independent, mass parameter $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{m}$ for all the scalar superpartners and considering simple assumptions for the family dependence of the R parity odd coupling constants. Finite nondiagonal rates $(CP$ asymmetries) entail nonvanishing products of two (four) different coupling constants in different family configurations. For lepton pair production, the Z-boson decays branching ratios ${B}_{{\mathrm{JJ}}^{\ensuremath{'}}}=B(\stackrel{\ensuremath{\rightarrow}}{Z}{l}_{J}^{\ensuremath{-}}{+l}_{{J}^{\ensuremath{'}}}^{+})$ scale in order of magnitude as ${B}_{{\mathrm{JJ}}^{\ensuremath{'}}}\ensuremath{\approx}(\ensuremath{\lambda}{/0.1)}^{4}(100\mathrm{GeV}/\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{m}{)}^{2.5}{10}^{\ensuremath{-}9},$ with coupling constants $\ensuremath{\lambda}={\ensuremath{\lambda}}_{\mathrm{ijk}}$ or ${\ensuremath{\lambda}}_{\mathrm{ijk}}^{\ensuremath{'}}$ in appropriate family configurations. The corresponding results for d- and u quarks are larger, due to an extra color factor ${N}_{c}=3.$ The flavor nondiagonal rates, at energies well above the Z-boson pole, slowly decrease with the center of mass energy and scale with the mass parameter approximately as ${\ensuremath{\sigma}}_{{\mathrm{JJ}}^{\ensuremath{'}}}\ensuremath{\approx}(\ensuremath{\lambda}{/0.1)}^{4}(100\mathrm{GeV}/\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{m}{)}^{2\ensuremath{-}3}(1\ensuremath{-}10)\mathrm{fbarn}.$ Including the contributions from an sneutrino s-channel exchange could raise the rates for leptons or d quarks by one order of magnitude. The $\mathrm{CP}$-odd asymmetries at the Z-boson pole, ${\mathcal{A}}_{{\mathrm{JJ}}^{\ensuremath{'}}}{=(B}_{{\mathrm{JJ}}^{\ensuremath{'}}}\ensuremath{-}{B}_{{J}^{\ensuremath{'}}J}{)/(B}_{{\mathrm{JJ}}^{\ensuremath{'}}}{+B}_{{J}^{\ensuremath{'}}J}),$ vary inside the range ${(10}^{\ensuremath{-}1}\ensuremath{-}{10}^{\ensuremath{-}3})\mathrm{sin}\ensuremath{\psi},$ where $\ensuremath{\psi}$ is the $\mathrm{CP}$-odd phase. At energies higher than the Z-boson pole, $\mathrm{CP}$-odd asymmetries for leptons, d-quark and u-quark pair production lie approximately at ${(10}^{\ensuremath{-}2}\ensuremath{-}{10}^{\ensuremath{-}3})\mathrm{sin}\ensuremath{\psi},$ irrespective of whether one deals with light or heavy flavors.