Parity violation on longitudinal single-spin asymmetries at the EicC

We explore two longitudinal single-spin asymmetries induced from parity violation in neutral-current deep inelastic scattering at the proposed electron-ion collider in China (EicC): <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msubsup><a:mi>A</a:mi><a:mi>PV</a:mi><a:mrow><a:mi>e</a:mi><a:mo stretchy="false">(</a:mo><a:mi>p</a:mi><a:mo stretchy="false">)</a:mo></a:mrow></a:msubsup></a:math> from longitudinally polarized (unpolarized) electrons scattering off unpolarized (longitudinally polarized) protons. We find <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msubsup><e:mi>A</e:mi><e:mi>PV</e:mi><e:mi>e</e:mi></e:msubsup></e:math>, of <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi mathvariant="script">O</g:mi><g:mo stretchy="false">(</g:mo><g:msup><g:mn>10</g:mn><g:mrow><g:mo>−</g:mo><g:mn>4</g:mn></g:mrow></g:msup><g:mo stretchy="false">)</g:mo></g:math>, is generically 1 to 3 orders of magnitude larger than <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:msubsup><l:mi>A</l:mi><l:mi>PV</l:mi><l:mi>p</l:mi></l:msubsup></l:math>. We further estimate different uncertainty sources including statistics, parton distribution functions, and beam polarization, for both asymmetries, and then identify individually their dominance in different regimes of the Bjorken-<n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:mi>x</n:mi></n:math>. Based on these results, we then advocate utilizing <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:msubsup><p:mi>A</p:mi><p:mi>PV</p:mi><p:mi>p</p:mi></p:msubsup></p:math> for the extraction of the weak mixing angle at two representative momentum transfer scales unexplored before, and we find a relative precision below 10% can be achieved at the EicC with an effective one-year operation time.