A process-dependent soft-gluon term in the J/psi TMD shape function is needed to keep the matched cross-section and cos(2phi) asymmetry predictions physical at the EIC, which supports the analytic result of Boer et al. and suggests a node-based test for the gluon TMD sign.
Connections between collinear and transverse-momentum-dependent polarized observables within the Collins-Soper-Sterman formalism
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abstract
We extend the improved Collins-Soper-Sterman (iCSS) $W+Y$ construction recently presented in~\cite{Collins:2016hqq} to the case of polarized observables, where we focus in particular on the Sivers effect in semi-inclusive deep-inelastic scattering. We further show how one recovers the expected leading-order collinear twist-3 result from a (weighted) $q_T$-integral of the differential cross section. We are also able to demonstrate the validity of the well-known relation between the (TMD) Sivers function and the (collinear twist-3) Qiu-Sterman function within the iCSS framework. This relation allows for their interpretation as functions yielding the average transverse momentum of unpolarized quarks in a transversely polarized spin-$\frac{1}{2}$ target. We further outline how this study can be generalized to other polarized quantities.
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The impact of the TMD shape function on matching the transverse momentum spectrum in $J/\psi$ production at the EIC
A process-dependent soft-gluon term in the J/psi TMD shape function is needed to keep the matched cross-section and cos(2phi) asymmetry predictions physical at the EIC, which supports the analytic result of Boer et al. and suggests a node-based test for the gluon TMD sign.