  Background: A nonperturbative charm production contribution, known as
intrinsic charm, has long been speculated but has never been satisfactorily
proven. The SeaQuest experiment at FNAL is in an ideal kinematic region to
provide evidence of $J/\psi$ production by intrinsic charm. Purpose: $J/\psi$
production in the SeaQuest kinematics is calculated with a combination of
perturbative QCD and intrinsic charm to see whether the SeaQuest data can put
limits on an intrinsic charm contribution. Methods: $J/\psi$ production in
perturbative QCD is calculated to next-to-leading order in the cross section.
Cold nuclear matter effects include nuclear modification of the parton
densities, absorption by nucleons, and $p_T$ broadening by multiple scattering.
The $J/\psi$ contribution from intrinsic charm is calculated assuming
production from a $|uud c \overline c \rangle$ Fock state. Results: The nuclear
modification factor, $R_{pA}$, is calculated as a function of $x_F$ and $p_T$
for $p+$C, $p+$Fe, and $p+$W interactions relative to $p+$d. Conclusions: The
SeaQuest kinematic acceptance is ideal for testing the limits on intrinsic
charm in the proton.
