Modeling the TMD shape function in J/ψ electroproduction

A bstract The next-to-leading order hard function for quarkonium electroproduction is calculated within the framework of transverse-momentum-dependent (TMD) factorization in the low-transverse-momentum regime. The structure of the TMD shape function in quarkonium leptoproduction is analyzed through its operator-level definition. Particular attention is given to the convolution of the unpolarized TMD gluon distribution with the TMD shape function, thereby illustrating the latter’s phenomenological role. Building on this framework, we provide predictions for the unpolarized differential cross-section of J/ψ electroproduction at the future Electron-Ion Collider in the region of small transverse momentum.