Pion Distribution Amplitudes from Functional QCD

We present the first functional QCD calculation of the pion distribution amplitude (DA) using the large-momentum effective theory within the functional renormalisation group (fRG) approach. With only the strong coupling and current quark masses as inputs, we compute the quasi-DA from first-principles QCD correlation functions. By pushing the pion momentum up to $P_z=4.5\mathrm{G}\mathrm{e}\mathrm{V}$, the quasi-DA becomes fully saturated, rendering the extrapolation errors to the light-cone limit negligible. The resulting second-order moment $⟨{\xi }^2{⟩}_{\pi }=0.267$ is significantly smaller than existing lattice-LaMET determinations and lies in a range consistent with other nonperturbative approaches.