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The next-to-leading order QCD corrections to the Standard Model process of single top production, bg → tW − , for the CERN Large Hadron Collider with √ s = 14 TeV have been calculated. For renormalization and factorization scales µ = µ 0 (µ 0 = m t + m W ), the NLO hadronic cross section is ∼ 37 pb, while ∼ 25 pb for tree level. The NLO QCD corrections can enhance the cross section by a factor from 1.33 to 1.66 for µ 0 2 < µ < 2µ 0

We study the possible origin of Friedberg-Lee symmetry. First, we propose the generalized Friedberg-Lee symmetry in the potential by including the scalar fields in the field transformations, which can be broken down to the FL symmetry spontaneously. We show that the generalized Friedberg-Lee symmetry allows a typical form of Yukawa couplings, and the realistic neutrino masses and mixings can be generated via see-saw mechanism. If the right-handed neutrinos transform nontrivially under the generalized Friedberg-Lee symmetry, we can have the testable TeV scale see-saw mechanism. Second, we present two models with the SO(3)×U (1) global flavour symmetry in the lepton sector. After the flavour symmetry breaking, we can obtain the charged lepton masses, and explain the neutrino masses and mixings via see-saw mechanism. Interestingly, the complete neutrino mass matrices are similar to those of the above models with generalized Friedberg-Lee symmetry. So the Friedberg-Lee symmetry is the residual symmetry in the neutrino mass matrix after the SO(3) × U (1) flavour symmetry breaking.

We proposed a mechanism in which the lightness of Higgs boson and the smallness of charge parity (CP) violation are correlated based on the Lee model, namely, the spontaneous CP-violation two-Higgsdoublet model. In this model, the mass of the lightest Higgs boson m h as well as the quantities K and J are ∝ t β s ξ in the limit t β s ξ → 0 (see text for definitions of t β and ξ), namely, the CP conservation limit. Here, K and J are the measures for CP-violation effects in scalar and Yukawa sectors, respectively. It is a new way to understand why the Higgs boson discovered at the LHC is light. We investigated the important constraints from both high energy LHC data and numerous low energy experiments, especially the measurements of electric dipole moments of electron and neutron as well as the quantities of B meson and kaon. Confronting all data, we found that this model is still viable. It should be emphasized that there is no standard-model limit for this scenario; thus it is always testable for future experiments. In order to pin down the Lee model, it is important to discover the extra neutral and charged Higgs bosons and measure their CP properties and the flavor-changing decays. At the LHC with ffiffi ffi s p ¼ 14 TeV, this scenario is favored if there is significant suppression in the bb decay channel or any vector boson fusion, V þ H production channels. On the contrary, it will be disfavored if the signal strengths are standard-model-like more and more. It can be easily excluded at ð3-5Þσ level with several fb −1 at future e þ e − colliders, via accurately measuring the Higgs boson production cross sections.