Skewness-dependent moments of the pion GPD from nonlocal quark-bilinear correlators

We present lattice QCD calculations of the odd Mellin moments of pion valence-quark generalized parton distribution up to fifth order <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mo stretchy="false">⟨</a:mo> <a:msup> <a:mi>x</a:mi> <a:mn>4</a:mn> </a:msup> <a:mo stretchy="false">⟩</a:mo> </a:math> and for the skewness range <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mo stretchy="false">[</e:mo> <e:mo>−</e:mo> <e:mn>0.33</e:mn> <e:mo>,</e:mo> <e:mn>0</e:mn> <e:mo stretchy="false">]</e:mo> </e:math> using operator product expansion of bilocal quark-bilinear operators. The calculations are performed on an ensemble with lattice spacing <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mi>a</i:mi> <i:mo>=</i:mo> <i:mn>0.04</i:mn> <i:mtext> </i:mtext> <i:mtext> </i:mtext> <i:mi>fm</i:mi> </i:math> and valence pion mass 300 MeV, employing boosted pion states with momenta up to 2.428 GeV and momentum transfers reaching <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mn>2.748</k:mn> <k:mtext> </k:mtext> <k:mtext> </k:mtext> <k:msup> <k:mi>GeV</k:mi> <k:mn>2</k:mn> </k:msup> </k:math> . We employ ratio-scheme renormalization and next-to-leading logarithmic resummed perturbative matching. At zero skewness, our results are consistent with previous lattice studies. By combining matrix elements at multiple values of skewness and momentum transfer, skewness-dependent moments are obtained through simultaneous polynomiality-constrained fits.