Color-octet nonrelativistic QCD matrix elements for heavy quarkonium decays in the refined Gribov-Zwanziger theory

We determine color-octet nonrelativistic QCD matrix elements for quarkonium decays from moments of the two-point correlation function of the QCD field-strength tensor computed in the refined Gribov-Zwanziger theory. We find that a tree-level calculation in the refined Gribov-Zwanziger theory can give a suitable description of the QCD field-strength correlation function at both short and long distances, which leads to moments that are infrared finite and can be properly renormalized. By using the color-octet matrix elements we obtain, we quantitatively improve the nonrelativistic effective field theory description of quarkonium decay rates, especially for the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>χ</a:mi><a:mrow><a:mi>Q</a:mi><a:mi>J</a:mi></a:mrow></a:msub></a:math> and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>η</c:mi><c:mi>Q</c:mi></c:msub></c:math> states, where <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>Q</e:mi><e:mo>=</e:mo><e:mi>c</e:mi></e:math> or <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>b</g:mi></g:math>.