  A refinement of the stable pair invariants of Pandharipande and Thomas for
non-compact Calabi-Yau spaces is introduced based on a virtual
Bialynicki-Birula decomposition with respect to a C* action on the stable pair
moduli space, or alternatively the equivariant index of Nekrasov and Okounkov.
This effectively calculates the refined index for M-theory reduced on these
Calabi-Yau geometries. Based on physical expectations we propose a product
formula for the refined invariants extending the motivic product formula of
Morrison, Mozgovoy, Nagao, and Szendroi for local P^1. We explicitly compute
refined invariants in low degree for local P^2 and local P^1 x P^1 and check
that they agree with the predictions of the direct integration of the
generalized holomorphic anomaly and with the product formula. The modularity of
the expressions obtained in the direct integration approach allows us to relate
the generating function of refined PT invariants on appropriate geometries to
Nekrasov's partition function and a refinement of Chern-Simons theory on a lens
space. We also relate our product formula to wallcrossing.
