We project onto the light front the pion's Poincar\'e-covariant Bethe-Salpeter wave function obtained using two different approximations to the kernels of quantum chromodynamics' Dyson-Schwinger equations. At an hadronic scale, both computed results are concave and significantly broader than the asymptotic distribution amplitude, φ_πᵃˢʸ(x)=6x(1-x); e.g., the integral of φ_π(x)/φ_πᵃˢʸ(x) is 1.8 using the simplest kernel and 1.5 with the more sophisticated kernel. Independent of the kernels, the emergent phenomenon of dynamical chiral-symmetry breaking is responsible for hardening the amplitude.
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Chang et al. (2013) studied this question.
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