Based on lattice simulations with two flavors of dynamical, $\mathcal{O}(a)$-improved Wilson fermions we present results for the first two moments of the distribution amplitudes of pseudoscalar mesons at several values of the valence quark masses. By extrapolating our results to the physical masses of up/down and strange quarks, we find the first two moments of the $K^{+}$ distribution amplitude and the second moment of the ${\pi }^{+}$ distribution amplitude. We use nonperturbatively determined renormalization coefficients to obtain results in the $\overline{\mathrm{MS}}$ scheme. At a scale of $4{\mathrm{GeV}}^2$ we find $a_2^{\pi }=0.201(114)$ for the second Gegenbauer moment of the pion’s distribution amplitude, while for the kaon, $a_1^K=0.0453(9)(29)$ and $a_2^K=0.175(18)(47)$.

• Received 28 June 2006

DOI:https://doi.org/10.1103/PhysRevD.74.074501