Transverse momentum broadening of vector boson production in high energy nuclear collisions

We calculate in perturbative QCD the transverse momentum broadening of vector boson production in high energy nuclear collisions. We evaluate the effect of initial-state parton multiple scattering for the production of the Drell-Yan virtual photon and $W/Z$ bosons. We calculate both the initial- and final-state multiple scattering effect for the production of heavy quarkonia and their transverse momentum broadening in both NRQCD and Color Evaporation model of quarkonium formation. We find that J/$\psi$ and $\Upsilon$ broadening in hadron-nucleus collision is close to $2C_A/C_F$ times the corresponding Drell-Yan broadening, which gives a good description of existing Fermilab data. Our calculations are also consistent with RHIC data on J/$\psi$ broadening in relativistic heavy ion collisions. We predict the transverse momentum broadening of vector boson (J/$\psi$, $\Upsilon$, and $W/Z$) production in relativistic heavy ion collisions at the LHC, and discuss the role of the vector boson broadening in diagnosing medium properties.