| The standard model(SM) of elementary particle describes strong and electroweak interactions. The mechanism of electroweak symmetry breaking(EWSB) remains an open question in current physics despite the SM which has been extensively tested by the high energy experimental data during the past 40 years. Furthermore, in the SM, elementary Higgs field is assumed to be responsible to the EWSB, the scalar sector suffers from the problem of triviality and unnaturalness, etc . Therefore SM isn't perfect theory, it can only be effective field theory below some high energy scale characteristic of underlying non-trivial physics. There must have new physics beyond the SM. So people provided some new physics models. For example, the supersymmetry(SUSY) theory, topcolor assisted technicolor(TC2) model and so on. Now TC2 model is very prevail.TC2 model predict the essence of neutral top-pion πt0. In this paper, we first study the contributions of the πt0 to the lepton flavor violating(LFV) processes li→ljγ, li→ljlkll , t →clilj and Z→lilj in the context of the TC2 model. Taking into account the constraints of the present experimental bound on μ→eγ, we obtain the branching ratio Br(τ→ eγ) is approximately equal to Br(τ→ μγ), the value is at least four orders below the present experimental bound on τ→ lγ, which is far from the reach of present or next generation experiments; Br(μ→ 3e) is approximately equal to 2.87 ×10-14, which might be observable in the planned experiments of the next generation; Br(τ→ 3e)(?) Br(τ→ 2eμ) and Br(τ→ 3u) (?) Br(τ→ 2μe) are far below the experimental bound and can't be observable in the next generation experiments. For the rare top decays t → clilj, Br(t →cee) and Br(t → cμμ) are smaller than Br(t→ cττ). The value of Br(t→cττ) can reach 7.1×10-7. Thus, if we would like to detect the possible signals of the neutral top-pion πt0 at the future high energy experiments via the rare top decays t→clilj , we should first consider the process t→cττ.Secondly, we study the LFV Z decays process Z→lilj which via the FC scalar couplings πt0τli. We obtained 8.7×10-15 ≤ Br(Z →τl) ≤ 3.6 ×10-14; 5×10-16≤ Br(Z→μe)≤ 8.3×10-15, which may be observable in the next generation experiments.Finally, we calculate the contributions of the neutral top-pion πt0 to tγ and tZ production via the processes ep→γc→tγ and ep→ γc → tZ at the HERA and THERA colliders. Our results show that the cross section σtr(s) and σtZ(s) are very small at the HERA collider, it can't be observed at the HERA collider. However, it can generate several hundred tγ or tZ events at the THERA collider, so it might be observed at the THERA collider. |
