Physics case for quarkonium studies at the Electron Ion Collider

 Physics case for quarkonium studies at the Electron Ion Collider

The physics case for quarkonium studies at the Electron–Ion Collider (EIC) is anchored in the unique capacity of heavy quark–antiquark bound states to serve as clean, well-understood probes of the gluonic structure and dynamics of protons and nuclei, enabling transformative insights into quantum chromodynamics (QCD) that are inaccessible through light‐quark observables alone. 

 By virtue of their large masses, charmonium and bottomonium states are produced predominantly via gluon‐initiated subprocesses, so measurements of differential cross sections, polarization observables, and nuclear modification factors for $J/\psi$, $\psi(2S)$, $\Upsilon(nS)$, and related states in both exclusive and inclusive channels provide direct sensitivity to gluon generalized parton distributions (GPDs), transverse momentum‐dependent distributions (TMDs), and nuclear parton distribution functions (nPDFs). 

 In exclusive electroproduction, the squared four‐momentum transfer $t$ dependence of vector quarkonium production can be Fourier‐transformed to map the transverse spatial distribution of gluons in the proton or nucleus, yielding the first true “gluonic tomography” of hadrons and revealing how gluon densities vary as a function of impact parameter. 

 Simultaneously, the Bjorken-$x$ and photon virtuality $Q^2$ dependence of quarkonium yields probes the onset of gluon saturation and the possible formation of a Color Glass Condensate, since nonlinear recombination effects at small $x$ can be quantified through deviations from linear QCD evolution when comparing rates in electron–proton versus electron–nucleus collisions across a range of energies and atomic mass numbers. 

 Beyond exclusive channels, semi-inclusive quarkonium production in conjunction with identified hadrons or jets enables access to gluon TMDs, unraveling the intrinsic transverse momentum and spin–momentum correlations of gluons inside the nucleon and thereby expanding our three-dimensional momentum–space picture of hadronic matter. 

 Moreover, the EIC’s capability to collide polarized electrons with polarized protons and light ions opens the door to spin‐dependent quarkonium measurements—single‐spin and double‐spin asymmetries in electroproduction provide leverage on the gluon helicity distribution $\Delta g(x)$ and gluon transversity, inching us closer to resolving the enduring “proton spin puzzle” by disentangling the contributions of gluon spin and orbital angular momentum to the proton’s total spin. 

 In the nuclear arena, precision comparisons of quarkonium production in $e+A$ versus $e+p$ collisions isolate cold‐nuclear matter effects such as shadowing, energy loss, and final‐state absorption: by systematically varying nuclear targets from deuterium to heavy nuclei like gold, one can chart how pre-hadronization interactions of a nascent heavy quark pair with the nuclear medium modify both yields and transverse momentum distributions, thereby testing theoretical frameworks of multiple scattering, parton energy loss, and hadronization in cold QCD matter. 

 These measurements carry profound implications for interpreting quarkonium suppression patterns in relativistic heavy‐ion collisions at RHIC and the LHC, where hot‐medium effects complicate the extraction of fundamental QCD parameters. Theoretical advances in lattice QCD can be directly benchmarked by high‐precision moments of gluon GPDs extracted from exclusive quarkonium data, while effective field theories such as nonrelativistic QCD (NRQCD) will be refined through global analyses that incorporate polarized and unpolarized quarkonium yields over wide kinematic ranges.

 Furthermore, the application of modern machine‐learning techniques to multidimensional unfolding and parameter extraction promises to enhance the fidelity of parton distribution reconstructions from complex experimental observables. Realizing the full potential of these physics opportunities imposes stringent requirements on detector performance—high‐resolution vertex tracking to separate prompt quarkonium from feed‐down sources, excellent lepton identification over a broad momentum spectrum to reconstruct decay channels, and forward proton or neutron tagging to ensure exclusivity—while the EIC’s adjustable center‐of‐mass energies and beam species flexibility will allow comprehensive scans of $x$, $Q^2$, and nuclear size. 

 In sum, quarkonium studies at the EIC represent a cornerstone of its scientific program, offering an unparalleled window into gluon spatial and momentum structure, non‐linear QCD dynamics, spin phenomena, and cold‐nuclear matter effects, and thereby promising to revolutionize our understanding of the strong force and the complex internal landscape of hadrons.

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