Reconstructing generalized parton distributions from the lattice off-forward Compton amplitude

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.