Pion Distribution Amplitude from Lattice QCD

We have calculated the second moment of the pion light-cone distribution amplitude using two flavors of dynamical (clover) fermions on lattices of different volumes, lattice spacings between $0.06 \, \mathrm {fm}$ and $0.08 \, \mathrm {fm}$ and pion masses down to $m_π\sim 150 \, \mathrm {MeV}$. Our result for the second Gegenbauer coefficient is $a_2 = 0.1364(154)(145)$ and for the width parameter $\langle ξ^2 \rangle = 0.2361(41)(39)$. Both numbers refer to the scale $μ=2 \, \mathrm {GeV}$in the $\overline{\text{MS}}$ scheme, 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.

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