Small-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>x</mml:mi></mml:math> gluon GPD constrained from deeply virtual <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>J</mml:mi><mml:m

We phenomenologically constrain the small-<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>x</a:mi></a:math> and small-<c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>ξ</c:mi></c:math> gluon generalized parton distributions (GPDs) with the deeply virtual <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>J</e:mi><e:mo>/</e:mo><e:mi>ψ</e:mi></e:math> production (<g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mrow><g:mi>DV</g:mi><g:mi>J</g:mi><g:mo>/</g:mo><g:mi>ψ</g:mi><g:mi mathvariant="normal">P</g:mi></g:mrow></g:math>) in the framework of GPDs through universal moment parameterization (GUMP). We use a hybrid cross-section formula combining collinear factorization to the next-to-leading order (NLO) accuracy of the strong coupling <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:msub><j:mi>α</j:mi><j:mi>s</j:mi></j:msub></j:math>, with corrections from nonrelativistic QCD to account for the power corrections due to the heavy <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:mi>J</l:mi><l:mo>/</l:mo><l:mi>ψ</l:mi></l:math> mass. We reach reasonable fit to the measured differential cross sections of <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:mrow><n:mi>DV</n:mi><n:mi>J</n:mi><n:mo>/</n:mo><n:mi>ψ</n:mi><n:mi mathvariant="normal">P</n:mi></n:mrow></n:math> by H1 at the Hadron-Electron Ring Accelerator as well as forward gluon parton distribution functions (PDFs) from JAM22 global analysis. We find that both NLO and nonrelativistic corrections are significant for heavy vector meson productions. Of course, the gluon GPD we obtain still contains considerable freedom in need of inputs from other constraints, particularly in the distribution-amplitude-like region.