Two-loop superstring five-point amplitudes. Part III. Construction via the RNS formulation: even spin structures

A bstract The contribution from even spin structures to the genus-two amplitude for five massless external NS states in Type II and Heterotic superstrings is evaluated first principles RNS formulation. Using chiral splitting with help of loop momenta this problem reduces evaluation corresponding amplitude, which carried out using same techniques that were used four states. results agree parity-even components a construction pure spinors given earlier companion papers [29] [33].