Evolution Equations And Higher Order Calculations In Small-x Physics

In high energy limit or small values of Bjorken x,the density of partons inside nucleus grows rapidly leading to the saturation of partonic distribution.In small-x physics,due to high energy density,the non-perturbative effects can be dealt with the appropriate perturbative technique,which is known as the Color Glass Condensate(CGC).In the thesis,we systematically study the dynamics and evolution equations in small-x limit.The main contents are listed:In the first chapter,we introduce briefly the basic of Quantum chromodynamics(QCD).In the second chapter,we start from cross section and structure function in dynamics of deep inelastic scattering(DIS),and introduce the partonic saturation formalism and evolution equations in small-x physics.Finally,we study the dipole picture of DIS and Muller's dipole model.In the third chapter,in small-x physics,we calculate the non-forward scattering amplitude which have a dependence of impact parameter.Because of this,we get a dipole-nuclear model which has angular dependent between dipole size and impact parameter.We study the Balitsky-Kovchegov nonlinear evolution equation and its approximate analytical solutions-travelling wave function.Furthermore,we discuss the conformal symmetry in the BK equation,and derive the conformal version of BK equation.In the fourth chapter,before calculating the expressional form of dipole,quadrupole,sextupole and octupole,we outline the main aspects of the McLerran-Venugopalan(MV)model.As a result,we proceed to conjecture the analytical form of 2n-piont correlator.In the fifth chapter,after introducing the formalism for the inclusive forward hadron production at pA collisions in the leading order and next-to-leading order we discuss divergences of rapidity and collinear at NLO.After removing the divergences,the NLO subtractions are convergence.In the limit of k12>>these results coin-cides with calculation of collinear factorization when we use exact kinematics.After discussing the problem of the negativity of the NLO cross section at high transverse momenta,we try to introduce the threshold resummation formalism to deal with this problem.We leave the complete derivation of the NLO results with threshold resummation for a future work.In the last chapter,we make a summarize and discuss some future studies.