Searching for gluon saturation effects in the momentum transfer dependence of coherent charmonium electroproduction off nuclei

We study for the first time the transverse momentum transfer distributions <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>d</a:mi> <a:mi>σ</a:mi> <a:mo>/</a:mo> <a:mi>d</a:mi> <a:mi>t</a:mi> </a:math> in coherent production of charmonia in nuclear ultraperipheral and electron-ion collisions within the QCD color dipole approach based on a rigorous Green function formalism. This allows us to treat properly the color transparency effects, as well as the higher and leading-twist shadowing corrections associated with the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mo stretchy="false">|</c:mo> <c:mi>Q</c:mi> <c:mover accent="true"> <c:mi>Q</c:mi> <c:mo stretchy="false">¯</c:mo> </c:mover> <c:mo stretchy="false">⟩</c:mo> </c:math> and <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mo stretchy="false">|</i:mo> <i:mi>Q</i:mi> <i:mover accent="true"> <i:mi>Q</i:mi> <i:mo stretchy="false">¯</i:mo> </i:mover> <i:mi>n</i:mi> <i:mi>G</i:mi> <i:mo stretchy="false">⟩</i:mo> </i:math> Fock components of the photon. While the multigluon photon fluctuations represent the dominant source of nuclear shadowing at kinematic regions related to the recent LHC and its future upgrade to LHeC, the upcoming electron-ion collider at RHIC will additionally require the proper incorporation of reduced quark shadowing. The latter effect leads to a significant decrease in the differential cross sections <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:mi>d</o:mi> <o:mi>σ</o:mi> <o:mo>/</o:mo> <o:mi>d</o:mi> <o:mi>t</o:mi> </o:math> compared to standard calculations based on the eikonal form for the dipole-nucleus amplitude. The leading-twist shadowing corrections, corresponding to a nonlinear QCD evolution of a partial dipole-nucleus amplitude, reduce substantially charmonium <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:mi>t</q:mi> </q:math> -distributions in the LHeC energy range. We predict a nonmonotonic energy dependence of <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:mi>d</s:mi> <s:mi>σ</s:mi> <s:mo>/</s:mo> <s:mi>d</s:mi> <s:mi>t</s:mi> </s:math> suggesting so possible gluon saturation effects with increased onset at larger <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:mi>t</u:mi> </u:math> -values. In addition to shadowing corrections, we study how the color transparency effects affect the shape of <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"> <w:mi>t</w:mi> </w:math> -dependent nuclear modification factor.