  We consider the off-shell momentum space Green's functions in closed
superstring field theory. Recently in arXiv:1810.07197, the off-shell Green's
functions -- after explicitly removing contributions of massless states -- have
been shown to be analytic on a domain (to be called the LES domain) in complex
external momenta variables. Analyticity of off-shell Green's functions in local
QFTs without massless states in the primitive domain is a well-known result.
Using complex Lorentz transformations and Bochner's theorem allow to extend the
LES domain to a larger subset of the primitive domain. For the 2-, 3- and
4-point functions, the full primitive domain is recovered. For the 5-point
function, we are not able to obtain the full primitive domain analytically,
only a large part of it is recovered. While this problem arises also for
higher-point functions, it is expected to be only a technical issue.
