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Basing on the systems of linear partial differential equations derived from Mellin-Barnes representations and Miller's transformation, we obtain GKZ-hypergeometric systems of one-loop self energy, one-loop triangle, two-loop vacuum, and two-loop sunset diagrams, respectively. The codimension of derived GKZ-hypergeometric system equals the number of independent dimensionless ratios among the external momentum squared and virtual mass squared. Taking GKZ-hypergeometric systems of one-loop self energy, massless one-loop triangle, and two-loop vacuum diagrams as examples, we present in detail how to perform triangulation and how to construct canonical series solutions in the corresponding convergent regions. The series solutions constructed for these hypergeometric systems recover the well known results in literature., Comment: 32 pages, 1 figure

The hypergeometric function method naturally provides the analytic expressions of scalar integrals from concerned Feynman diagrams in some connected regions of independent kinematic variables, also presents the systems of homogeneous linear partial differential equations satisfied by the corresponding scalar integrals. Taking examples of the one-loop $B_{_0}$ and massless $C_{_0}$ functions, as well as the scalar integrals of two-loop vacuum and sunset diagrams, we verify our expressions coinciding with the well-known results of literatures. Based on the multiple hypergeometric functions of independent kinematic variables, the systems of homogeneous linear partial differential equations satisfied by the mentioned scalar integrals are established. Using the calculus of variations, one recognizes the system of linear partial differential equations as stationary conditions of a functional under some given restrictions, which is the cornerstone to perform the continuation of the scalar integrals to whole kinematic domains numerically with the finite element methods. In principle this method can be used to evaluate the scalar integrals of any Feynman diagrams., Comment: 39 pages, including 2 ps figures

The complete QCD corrections to the scalar top quark pair production via $\gamma \gamma$ fusion in parent $e^{+}e^{-}$ collider are calculated in the Supersymmetric Model. The various origins of corrections are discussed. We find that the correction due to gluino exchange is smaller than that due to conventional gluonic contribution, and the contribution due to squark quartic interactions is much smaller. Moreover, the dependences of the corrections on the masses and the mixing angle of the supersymmetric particles are also investigated., Comment: 25 Pages, LaTex, 10 eps figures.