Completing the first saturation correction to single inclusive gluon production in high energy pA collisions

<!--HTML-->The leading order result of single inclusive gluon production in high energy pA collisions has been calculated by various approaches for more than two decades . The first saturation correction to the leading order result, terms that are enhanced by $\alpha_s^2 A^{1/3}$ with $\alpha_s$ the strong coupling constant and $A$ the atomic number of nucleus, was only analytically attempted recently through a diagrammatic approach despite many relevant numerical studies. In this talk, I will present our efforts in completing this calculation analytically. Our approach is to solve the classical Yang-Mills equations in the dilute-dense regime and use the LSZ reduction formula to calculate gluon production from classical gluon fields. Exact next-to-leading order solutions of the Yang-Mills equations in the dilute-dense regime will be presented. The systematic approach in completing the first saturation correction to single inclusive gluon production will be explained and final results will be presented.