Polarized single top quark production at leptonic colliders from brokenRparity interactions incorporatingCPviolation

Abstract

The contribution from the $R$ parity violating interaction ${\ensuremath{\lambda}}_{\mathrm{ijk}}^{\ensuremath{'}}{L}_{i}{Q}_{j}{D}_{k}^{c}$ in the associated production of a top quark (antiquark) with a charm antiquark (quark) is examined for high energy leptonic colliders. We concentrate on the reaction ${l}^{\ensuremath{-}}{+l}^{+}\ensuremath{\rightarrow}(t\overline{c})+(c\overline{t})\ensuremath{\rightarrow}(b\overline{l}\ensuremath{\nu}\overline{c})+(\overline{b}l\overline{\ensuremath{\nu}}c)$ associated with the semileptonic top quark decay. A set of characteristic dynamical distributions for the signal events is evaluated and the results contrasted against those from the standard model $W\ensuremath{-}\mathrm{boson}$ pair production background. The sensitivity to parameters $(R$ parity violating coupling constants and down-squark mass) is studied at the energies of the CERN LEP-II collider and the future linear colliders. Next, we turn to a study of a $CP\ensuremath{-}\mathrm{odd}$ observable, associated with the top quark spin, which leads to an asymmetry in the energy distribution of the emitted charged leptons for the pair of $CP\ensuremath{-}\mathrm{conjugate}$ final states $b\overline{l}\ensuremath{\nu}\overline{c}$ and $\overline{b}l\overline{\ensuremath{\nu}}c.$ A nonvanishing asymmetry arises from a $CP\ensuremath{-}\mathrm{odd}$ phase, embedded in the $R$ parity violating coupling constants, through interference terms between the $R$ parity violating amplitudes at both the tree and loop levels. The one-loop amplitude is restricted to contributions from vertex corrections to the photon and $Z\ensuremath{-}\mathrm{boson}$ exchange diagram. We predict unpolarized and polarized rate asymmetries of order ${O(10}^{\ensuremath{-}3})--{O(10}^{\ensuremath{-}2}).$ An order of magnitude enhancement may be possible should the $R$ parity violating coupling constants ${\ensuremath{\lambda}}_{\mathrm{ijk}}^{\ensuremath{'}}$ exhibit a hierarchical structure in the quarks and leptons generation spaces.