Towards massive field-theory amplitudes from the cohomology of pure spinor superspace

By analogy with the formula for the massless string disk amplitudes, we define massive field-theory tree amplitudes and conjecture that the BRST cohomology structure of pure spinor superspace fixes their form. We give evidence by deriving the pure spinor superspace expression of the massive field-theory n-point tree amplitude with one first-level massive and n − 1 massless states in two ways: 1) from BRST cohomology arguments in pure spinor superspace and 2) from the α′² correction to the massless string amplitudes by inverting the unitarity constraint in superspace.