Pion Distribution Amplitude from Lattice QCD

TL;DR

This paper computes the second moment of the pion distribution amplitude using lattice QCD with dynamical fermions, providing precise values for the Gegenbauer coefficient and width parameter at a specific scale.

Contribution

It presents the first lattice QCD calculation of the second Gegenbauer coefficient of the pion distribution amplitude with controlled uncertainties.

Findings

Second Gegenbauer coefficient a_2 = 0.1364(154)(145) at 2 GeV

Width parameter ⟨ξ²⟩ = 0.2361(41)(39) at 2 GeV

Results are obtained with physical pion masses and multiple lattice spacings

Abstract

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 $m_\pi\sim 150 \, \mathrm {MeV}$. Our result for the second Gegenbauer coefficient is $a_2 = 0.1364(154)(145)$ and for the width parameter $\langle \xi^2 \rangle = 0.2361(41)(39)$. Both numbers refer to the scale $\mu=2 \, \mathrm {GeV}$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.