Pion distribution amplitude and quasidistributions

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 $\mathrm{\ensuremath{\Psi}}(x,{k}_{\ensuremath{\perp}}^{2})$ and the pion quasidistribution amplitude (QDA) ${Q}_{\ensuremath{\pi}}(y,{p}_{3})$. 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.