Distribution amplitudes of radially-excited pi- and K-mesons
  A symmetry-preserving truncation of the two-body bound-state problem in relativistic quantum field theory is used to compute the leading-twist parton distribution amplitudes (PDAs) for the first radial excitations of the $\pi$- and $K$-mesons. In common with ground states in these channels, the PDAs are found to be dilated with respect to the relevant conformal-limit form and skewed toward the heavier valence-quark in asymmetric systems. In addition, the PDAs of radially-excited pseudoscalar mesons are not positive definite, owing to the fact that dynamical chiral symmetry breaking (DCSB) forces the leptonic decay constant of such states to vanish in the chiral limit. These results highlight that DCSB is expressed visibly in every pseudoscalar meson constituted from light-quarks. Hence, so long as its impact is empirically evident in the pseudoscalar members of a given spectrum level, it is unlikely that chiral symmetry is restored in any of the hadrons that populate this level. 
Bo-Lin Li, Lei Chang, Fei Gao, Craig D. Roberts, Sebastian M. Schmidt,   Hong-Shi Zong
nucl-th hep-lat hep-ph nucl-ex