Second Moment of the Pion Light-cone Distribution Amplitude from Lattice QCD

Abstract

We present the results of a lattice study of the second moment of the light-cone pion distribution amplitude using two flavors of dynamical (clover) fermions on lattices of different volumes and pion masses down to $m_\pi\sim 150 \, \mathrm {MeV}$. At lattice spacings between $0.06 \, \mathrm {fm}$ and $0.08 \, \mathrm {fm}$ we find for the second Gegenbauer moment the value $a_2 = 0.1364(154)(145)$ at the scale $\mu=2 \, \mathrm {GeV}$ in the $\overline{\mathrm{MS}}$ scheme, where the first error is statistical including the uncertainty of the chiral extrapolation, and the second error is the estimated uncertainty coming from the nonperturbatively determined renormalization factors.