  The scalar theory is ultraviolet (UV) quadratically divergent on ordinary
spacetime. On noncommutative (NC) spacetime, this divergence will generally
induce pole-like infrared (IR) singularities in external momenta through the
UV/IR mixing. In spontaneous symmetry breaking theory this would invalidate the
Goldstone theorem which is the basis for mass generation when symmetry is
gauged. We examine this issue at two loop level in the U(N) linear sigma model
which is known to be free of such IR singularities in the Goldstone
self-energies at one loop. We analyze the structures in the NC parameter
(\theta_{\mu\nu}) dependence in two loop integrands of Goldstone self-energies.
We find that their coefficients are effectively once subtracted at the external
momentum p=0 due to symmetry relations between 1PI and tadpole contributions,
leaving a final result proportional to a quadratic form in p. We then compute
the leading IR terms induced by NC to be of order p^2\ln(\theta_{\mu\nu})^2 and
p^2\ln\tilde{p}^2 (\tilde{p}_{\mu}=\theta_{\mu\nu}p^{\nu}) which are much
milder than naively expected without considering the above cancellation. The
Goldstone bosons thus keep massless and the theorem holds true at this level.
However, the limit of \theta\to 0 cannot be smooth any longer as it is in the
one loop Goldstone self-energies, and this nonsmooth behaviour is not
necessarily associated with the IR limit of the external momentum as we see in
the term of p^2\ln(\theta_{\mu\nu})^2.
