  Using the exact formula for the A-twisted correlation functions of the two
dimensional $\mathcal{N}=(2,2)$ gauged linear sigma model, we reconsider the
computation of the B-model Yukawa couplings of the local toric Calabi-Yau
varieties. Our analysis is based on an exact result that has been evaluated
from the supersymmetric localization technique and careful treatment of its
application. We provide a detailed description of a procedure to investigate
the local B-model Yukawa couplings and also test our prescription by comparing
the results with known expressions evaluated from the local mirror symmetry
approach. In particular, we find that the ambiguities of classical intersection
numbers of a certain class of local toric Calabi-Yau varieties discovered
previously can be interpreted as degrees of freedom of the twisted mass
deformations.
