Dispersion relations of deeply virtual Compton scattering: Investigating twist-four kinematic power corrections

In this paper we include kinematic power corrections up to twist-four to the deeply virtual Compton scattering dispersion relation. We demonstrate that, both for (pseudo)scalar and spin- <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mn>1</a:mn> <a:mo>/</a:mo> <a:mn>2</a:mn> </a:math> targets, the formal expression of the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>n</c:mi> </c:math> -subtracted leading-twist dispersion relations is preserved. However, the expression of the subtracted constants modified by the kinematic powers. Importantly, the minimal-subtracted dispersion relation for the helicity-conserving amplitude, previously thought to depend only on the Polyakov-Weiss <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>D</e:mi> </e:math> -term, now also depends on the double distributions <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>F</g:mi> </g:math> and <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mi>K</i:mi> </i:math> . These results are consistent with the ones obtained previously in the literature. Such a mixing may be critical for the Jefferson Lab kinematic range, as it is not suppressed for typical values of <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mi>t</k:mi> </k:math> and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:msup> <m:mi>Q</m:mi> <m:mn>2</m:mn> </m:msup> </m:math> in the valence region. We therefore expect a strong impact on the attempts to extract pressure forces from deeply virtual Compton scattering data.