Classical color field modified minijet model for for pp and p ̅p total cross section

We present a formalism for gluon-gluon elastic scattering in the presence of the classical color field of the protons in high energy collision. The classical field is obtained by solving the classical YangMills equation in the covariant gauge and treated as a prescribed background for the quantum gluons involved in the scattering process. The interaction between the classical field and the quantum gluon modifies the gluon propagator, and, in turn, the gg → gg amplitude. The modified gluon propagator is derived to the first non-zero order of the classical field using the Gaussian approximation in Color Glass Condensate and shown to satisfy the generalized Slavnov-Taylor identity. This formalism is the theoretical basis for our recently proposed classical color field modified minijet model where we show that the pp and ¯pp cross section data from √s = 5 GeV to 30 TeV can be satisfactorily fitted and the model predicts a (ln s)² behavior for large s, which saturates the asymptotic behaviour of Froissart bound.