New Regularization in Extra Dimensional Model and Renormalization Group Flow of the Cosmological Constant

Casimir energy is calculated for 5D scalar theory in the {\it warped} geometry. A new regularization, called {\it sphere lattice regularization}, is taken. The regularized configuration is {\it closed-string like}. We numerically evaluate $\text{La}$(4D UV-cutoff), $\text{om}$(5D bulk curvature, warp parameter) and $T$(extra space IR parameter) dependence of Casimir energy. 5D Casimir energy is {\it finitely} obtained after the {\it proper renormalization procedure.} The {\it warp parameter} $\text{om}$ suffers from the {\it renormalization effect}. We examine the cosmological constant problem.