We extend our analysis of quasidistributions onto the pion distribution amplitude. Using the formalism of parton virtuality distribution amplitudes, we establish a connection between the pion transverse momentum dependent distribution amplitude psi(x, k(perpendicular to)(2))and the pion quasidistribution amplitude (QDA) Q(pi)(y, p(3)). We build models for the QDAs from the virtuality-distribution-amplitude-based models for soft transverse momentum dependent distribution amplitudes, and analyze the p(3) dependence of the resulting QDAs. As there are many models claimed to describe the primordial shape of the pion distribution amplitude, we present the p(3)-evolution patterns for models producing some popular proposals: Chernyak-Zhitnitsky, flat, and asymptotic distribution amplitude. Our results may be used as a guide for future studies of the pion distribution amplitude on the lattice using the quasidistribution approach.
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