Four-loop vacuum energy beta function in O(N) symmetric scalar theory.

The {beta} function of the vacuum energy density is computed at the four-loop level in massive O({ital N}) symmetric {phi}{sup 4} theory. Dimensional regularization is used in conjunction with the MS scheme and all calculations are in momentum space in the massive theory. The result is {beta}{sub {ital v}}=({ital N}/4){ital g}+[{ital N}({ital N}+2)/96]{ital g}{sup 3}+{l_brace}{ital N}({ital N}+2)({ital N}+8)[12{zeta}(3){minus}25]/1296{r_brace}{ital g}{sup 4}+{ital O}({ital g}{sup 5}). {copyright} {ital 1996 The American Physical Society.}