Kinematic power corrections to deeply virtual Compton scattering to twist-six accuracy

We calculate <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mo stretchy="false">(</a:mo><a:msqrt><a:mrow><a:mo>−</a:mo><a:mi>t</a:mi></a:mrow></a:msqrt><a:mo>/</a:mo><a:mi>Q</a:mi><a:msup><a:mo stretchy="false">)</a:mo><a:mi>k</a:mi></a:msup></a:math> and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mo stretchy="false">(</e:mo><e:mi>m</e:mi><e:mo>/</e:mo><e:mi>Q</e:mi><e:msup><e:mo stretchy="false">)</e:mo><e:mi>k</e:mi></e:msup></e:math> power corrections with <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>k</i:mi><i:mo>≤</i:mo><i:mn>4</i:mn></i:math>, where <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>m</k:mi></k:math> is the target mass and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>t</m:mi></m:math> is the momentum transfer, to several key observables in deeply virtual Compton scattering (DVCS). We find that the power expansion is well convergent up to <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mo stretchy="false">|</o:mo><o:mi>t</o:mi><o:mo stretchy="false">|</o:mo><o:mo>/</o:mo><o:msup><o:mi>Q</o:mi><o:mn>2</o:mn></o:msup><o:mo>≲</o:mo><o:mn>1</o:mn><o:mo>/</o:mo><o:mn>4</o:mn></o:math> for most of the observables, but is naturally organized in terms of <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mn>1</s:mn><s:mo>/</s:mo><s:mo stretchy="false">(</s:mo><s:msup><s:mi>Q</s:mi><s:mn>2</s:mn></s:msup><s:mo>+</s:mo><s:mi>t</s:mi><s:mo stretchy="false">)</s:mo></s:math> rather than the nominal hard scale <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mn>1</w:mn><w:mo>/</w:mo><w:msup><w:mi>Q</w:mi><w:mn>2</w:mn></w:msup></w:math>. We also argue that target mass corrections remain under control and do not endanger quantum chromodynamics (QCD) factorization for coherent DVCS on nuclei. These results remove an important source of uncertainties due to the frame dependence and violation of electromagnetic Ward identities in the QCD predictions for the DVCS amplitudes in the leading-twist approximation.