Abstract
We calculate the $cos~2 \phi$ asymmetry in $J/\psi$ production in electron-proton collision for the kinematics of the planned electron-ion collider (EIC). This directly probes the Weisz\"acker-Williams (WW) type linearly polarized gluon distribution. Assuming generalized factorization, we calculate the asymmetry at next-to-leading-order (NLO) when the energy fraction of the $J/\psi$ satisfies $z<1$ and the dominating subprocess is $\gamma^* +g \rightarrow c + {\bar c}+g$. We use non-relativistic QCD based color singlet model for $J/\psi$ production. We investigate the small $x$ region which will be accessible at the EIC. We present the upper bound of the asymmetry, as well as estimate it using a (i) Gaussian type parametrization for the TMDs and (ii) McLerran-Venugopalan model at small $x$. We find small but sizable asymmetry in all the three cases.
Highlights
J=ψ electroproduction is a direct probe of gluon transverse momentum dependent parton distributions (TMDs), as the leading process is the virtual photon-gluon fusion
We have calculated the cos 2φ asymmetry in electroproduction of J=ψ at electron-ion collider (EIC), which probes the linearly polarized gluon distribution in the unpolarized proton
We calculated the asymmetry in the kinematical region z < 1, where the NLO subprocess γà þ g → J=ψ þ g gives the leading contribution
Summary
J=ψ electroproduction is a direct probe of gluon transverse momentum dependent parton distributions (TMDs), as the leading process is the virtual photon-gluon fusion. In [42] the J=ψ production rate for unpolarized pp collision at RHIC assuming a generalized TMD factorization was calculated in the CS model, and it was found that the theoretical estimate reasonably explains the data for low values of pT, where pT is the transverse momentum of J=ψ. As we are interested in the small x region, we consider the process γà þ g → J=ψ þ g, as gluon distributions are dominant at small x This process probes the WW-type gluon TMDs. In order to estimate the cos 2φ asymmetry, we use three different models for the TMDs. First, we use a Gaussian parametrization [30,31,32] for both the linearly polarized gluon distribution and the unpolarized TMD.
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