Abstract
Linear constraint relations among loop-order five-point color-ordered amplitudes in SO(N) and Sp(2N) gauge theories are derived with the group-theoretic method. These constrains are derived up to four-loop order. It is found that in both theories, there are n=6,22,34,44,50 linear constraint relations at L=0,1,2,3,4 loop orders. Then the numbers of independent color-ordered five-point amplitudes under group-theoretic constraints are respectively nind.=6,12,22,34,50. We find that the number of independent color-ordered amplitudes begins to diverge from SU(N) at four-loop order. This provides an evidence on the argument that group-theoretic constraint relations depend on properties of group algebras. Some comments are given on future study along this direction.
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