  In this Snowmass White Paper, we discuss physics opportunities involving
heavy quarkonia at the intensity and energy frontiers of high energy physics.
We focus primarily on two specific aspects of quarkonium physics for which
significant advances can be expected from experiments at both frontiers. The
first aspect is the spectroscopy of charmonium and bottomonium states above the
open-heavy-flavor thresholds. Experiments at e^+ e^- colliders and at hadron
colliders have discovered many new, unexpected quarkonium states in the last 10
years. Many of these states are surprisingly narrow, and some have electric
charge. The observations of these charged quarkonium states are the first
definitive discoveries of manifestly exotic hadrons. These results challenge
our understanding of the QCD spectrum. The second aspect is the production of
heavy quarkonium states with large transverse momentum. Experiments at the LHC
are measuring quarkonium production with high statistics at unprecedented
values of p_T. Recent theoretical developments may provide a rigorous
theoretical framework for inclusive production of quarkonia at large p_T.
Experiments at the energy frontier will provide definitive tests of this
framework. Experiments at the intensity frontier also provide an opportunity to
understand the exclusive production of quarkonium states.
