Revisiting the top-quark pair production at future e^(+)e^(−)colliders

In this study,we reanalyze the top-quark pair production at next-to-next-to-leading order(NNLO)in quantum chromodynamics(QCD)at future e^(+)e^(−)colliders using the Principle of Maximum Conformality(PMC)method.The PMC renormalization scales inαs are determined by absorbing the non-conformalβterms by recursively using the Renormalization Group Equation(RGE).Unlike the conventional scale-setting method of fixing the scale at the center-of-mass energyμ_(r)=√s,the determined PMC scale Q_(⋆)is far smaller than the √sand increases with the √s,yielding the correct physical behavior for the top-quark pair production process.Moreover,the convergence of the pQCD series for the top-quark pair production is greatly improved owing to the elimination of the renormalon divergence.For a typical collision energy of √s=500 GeV,the PMC scale is Q_(⋆)=107 GeV;the QCD correction factor K for conventional results is K∼1+0.1244+0.0102+0.0012−0.0087−0.0011+0.0184−0.0086+0.0002+0.0061−0.0003,where the first error is caused by varying the scaleμr∈[√s/2,2√s]and the second error is from the top-quark massΔm_(t)=±0.7 GeV.After applying the PMC,the renormalization scale uncertainty is eliminated,and the QCD correction factor K is improved to K∼1+0.1507_(−0.0015)^(+0.0015)−0.0057_(−0.0000)^(+0.0001),where the error is from the top-quark massΔm_(t)=±0.7 GeV.The PMC improved predictions for the top-quark pair production are helpful for detailed studies of the properties of the top-quark at future e^(+)e^(−)colliders.

New method of applying conformal group to quantum fields

Most of previous work on applying the conformal group to quantum fields has emphasized its invariant aspects, whereas in this paper we find that the conformal group can give us running quantum fields, with some constants, vertex and Green functions running, compatible with the scaling properties of renormalization group method （RGM）. We start with the renormalization group equation （RGE）, in which the differential operator happens to be a generator of the conformal group, named dilatation operator. In addition we link the operator/spatial representation and unitary/spinor representation of the conformal group by inquiring a conformal-invariant interaction vertex mimicking the similar process of Lorentz transformation applied to Dirac equation. By this kind of application, we find out that quite a few interaction vertices are separately invaxiant under certain transformations （generators） of the conformal group. The significance of these transformations and vertices is explained. Using a particular generator of the conformal group, we suggest a new equation analogous to RGE which may lead a system to evolve from asymptotic regime to nonperturbative regime, in contrast to the effect of the conventional RGE from nonperturbative regime to asymptotic regime.

Correlation of normal neutrino mass ordering with upper octant of θ_(23) and third quadrant of δ via RGE-induced μ-τ symmetry breaking

The recent global analysis of three-flavor neutrino oscillation data indicates that the normal neutrino mass ordering is favored over the inverted one at the 3σ level, and the best-fit values of the largest neutrino mixing angle 023 and the Dirac CP-violating phase δ are located in the higher octant and third quadrant, respectively. We show that all these important issues can be naturally explained by the μ-τ reflection symmetry breaking of massive neutrinos from a superhigh energy scale down to the electroweak scale owing to the one-loop renormalization-group equations （RGEs） in the minimal supersymmetric standard model （MSSM）. The complete parameter space is explored for the first time in both the Majorana and Dirac cases, by allowing the smallest neutrino mass m1 and the MSSM parameter tanβ to vary within their reasonable regions.

Meson polarized distribution function and mass dependence of the nucleon parton densities

The polarized distribution functions of mesons, including pion, kaon and eta, using the proton structure function, are calculated. We are looking for a relationship between the polarized distribution of mesons and the polarized structure of nucleons. We show that the meson polarized parton distributions leads to zero total spin for the concerned mesons, considering the orbital angular momentum of quarks and gluons inside the meson. Two separate Monte Carlo algorithms are applied to compute the polarized parton distributions of the kaon. Via the mass dependence of quark distributions, the distribution function of the eta meson is obtained. A new method by which the polarized sea quark distributions of protons are evolved separately which cannot be performed easily using the standard solution of DGLAP equations - is introduced. The mass dependence of these distributions is obtained, using the renormalization group equation which makes their evolutions more precise. Comparison between the evolved distributions and the available experimental data validates the suggested solutions for separated evolutions.