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We show that a recently conjectured expression for the superstringthree-point amplitude, in the framework of the Cacciatori, Dalla Piazza, vanGeemen - Grushevsky ansatz for the chiral measure, fails to vanish atthree-loop, in contrast with expectations from non-renormalization theorems.Based on analogous two-loop computations, we discuss the possibility of anon-trivial correction to the amplitude and propose a natural candidate forsuch a contribution. Thanks to a new remarkable identity, it is reasonable toexpect that the corrected three-point amplitude vanishes at three-loop,recovering the agreement with non-renormalization theorems.

Superstring measure and non-renormalization of the three-point amplitude