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.

Comments: 14 Pages, 13 figures. PACS numbers: 12.38Gc, 13.60Le, 14.40Be