Parton physics from a heavy-quark operator product expansion: Lattice QCD calculation of the fourth moment of the pion distribution amplitude

The pion light-cone distribution amplitude (LCDA) is an essential nonperturbative input for a range of high-energy exclusive processes in quantum chromodynamics. Building on our previous work, the continuum limit of the fourth Mellin moment of the pion LCDA is determined in quenched QCD using quark masses which correspond to a pion mass of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msub> <a:mi>m</a:mi> <a:mi>π</a:mi> </a:msub> <a:mo>=</a:mo> <a:mn>550</a:mn> <a:mtext> </a:mtext> <a:mtext> </a:mtext> <a:mi>MeV</a:mi> </a:math> . This calculation finds <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mrow> <c:mo stretchy="false">⟨</c:mo> <c:msup> <c:mrow> <c:mi>ξ</c:mi> </c:mrow> <c:mrow> <c:mn>2</c:mn> </c:mrow> </c:msup> <c:mo stretchy="false">⟩</c:mo> <c:mo>=</c:mo> <c:mn>0.202</c:mn> <c:mo stretchy="false">(</c:mo> <c:mn>8</c:mn> <c:mo stretchy="false">)</c:mo> <c:mo stretchy="false">(</c:mo> <c:mn>9</c:mn> <c:mo stretchy="false">)</c:mo> </c:mrow> </c:math> and <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mrow> <k:mo stretchy="false">⟨</k:mo> <k:msup> <k:mrow> <k:mi>ξ</k:mi> </k:mrow> <k:mrow> <k:mn>4</k:mn> </k:mrow> </k:msup> <k:mo stretchy="false">⟩</k:mo> <k:mo>=</k:mo> <k:mn>0.039</k:mn> <k:mo stretchy="false">(</k:mo> <k:mn>28</k:mn> <k:mo stretchy="false">)</k:mo> <k:mo stretchy="false">(</k:mo> <k:mn>11</k:mn> <k:mo stretchy="false">)</k:mo> </k:mrow> </k:math> where the first error indicates the combined statistical and systematic uncertainty from the analysis and the second indicates the uncertainty from working with Wilson coefficients computed to next-to-leading order. These results are presented in the <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:mover accent="true"> <s:mrow> <s:mi>MS</s:mi> </s:mrow> <s:mo stretchy="true">¯</s:mo> </s:mover> </s:math> scheme at a renormalization scale of <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"> <w:mrow> <w:mi>μ</w:mi> <w:mo>=</w:mo> <w:mn>2</w:mn> <w:mtext> </w:mtext> <w:mtext> </w:mtext> <w:mi>GeV</w:mi> </w:mrow> </w:math> .