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 $\mathrm{\Psi }(x,k_{\perp }^2)$ 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.

Figure 1

Quasidistribution amplitude $Q_{\pi }^{\mathrm{CZ}}(y,P)$ for $P/\mathrm{\Lambda }=1$, 3, 5, 10 in the Gaussian (left) and slow models (right).

Figure 2

Quasidistribution amplitudes $Q_{\pi }(y,P)$ in the slow model for $P=\mathrm{\Lambda }$ (left) and $P=3\mathrm{\Lambda }$ (right) evolving to CZ, flat and asymptotic DAs.

Figure 3

Quasidistribution amplitudes $Q_{\pi }(y,P)$ in the slow model for $P=5\mathrm{\Lambda }$ (left) and $P=10\mathrm{\Lambda }$ (right) evolving to CZ, flat and asymptotic DAs.