Reconstructing generalized parton distributions from the lattice off-forward Compton amplitude
A. Hannaford-Gunn, Kadir Utku Can, J. A. Crawford, R. Horsley, P. E. L. Rakow, G. Schierholz, H. Stüben, R. D. Young, J. M. Zanotti
Abstract
We present a determination of the structure functions of the off-forward Compton amplitude <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi mathvariant="script">H</a:mi><a:mn>1</a:mn></a:msub></a:math> and <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:msub><d:mi mathvariant="script">E</d:mi><d:mn>1</d:mn></d:msub></d:math> from the Feynman-Hellmann method in lattice QCD. At leading twist, these structure functions give access to the generalized parton distributions (GPDs) <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>H</g:mi></g:math> and <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>E</i:mi></i:math>, respectively. This calculation is performed for an unphysical pion mass of <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msub><k:mi>m</k:mi><k:mi>π</k:mi></k:msub><k:mo>=</k:mo><k:mn>412</k:mn><k:mtext> </k:mtext><k:mtext> </k:mtext><k:mi>MeV</k:mi></k:math> and four values of the soft momentum transfer, <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>t</m:mi><m:mo>≈</m:mo><m:mn>0</m:mn><m:mo>,</m:mo><m:mo>−</m:mo><m:mn>0.3</m:mn><m:mo>,</m:mo><m:mo>−</m:mo><m:mn>0.6</m:mn><m:mo>,</m:mo><m:mo>−</m:mo><m:mn>1.1</m:mn><m:mtext> </m:mtext><m:mtext> </m:mtext><m:msup><m:mi>GeV</m:mi><m:mn>2</m:mn></m:msup></m:math>, all at a hard momentum scale of <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:msup><o:mover accent="true"><o:mi>Q</o:mi><o:mo stretchy="false">¯</o:mo></o:mover><o:mn>2</o:mn></o:msup><o:mo>≈</o:mo><o:mn>5</o:mn><o:mtext> </o:mtext><o:mtext> </o:mtext><o:msup><o:mi>GeV</o:mi><o:mn>2</o:mn></o:msup></o:math>. Using these results, we test various methods to determine properties of the real-time scattering amplitudes and GPDs: (1) we fit their Mellin moments, and (2) we use a simple GPD ansatz to reconstruct the entire distribution. Our final results show promising agreement with phenomenology and other lattice results and highlight specific systematics in need of control. Published by the American Physical Society 2024