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In the Type II superstring the 4-point function for massless NS-NS bosons atone-loop is well known [1][14]. The overall constant factor in this amplitudeis very important because it needs to satisfy the unitarity and S-dualityconditions [14]. This coefficient has not been computed in the pure spinorformalism due to the difficulty to solve the integrals on the pure spinorsspace. In this paper we compute it by using the non-minimal pure spinorformalism and we will show that the answer is in perfect agreement with the onegiven in [14].

One-loop Superstring Amplitude From Integrals on Pure Spinors Space