Factorization in exclusive quarkonium production

We present factorization theorems for two exclusive heavy-quarkonium production processes: production of two quarkonia in e⁺e^- annihilation and production of a quarkonium and a light meson in B-meson decays. We describe the general proofs of factorization and supplement them with explicit one-loop analyses, which illustrate some of the features of the soft-gluon cancellations. We find that violations of factorization are generally suppressed relative to the factorized contributions by a factor v2mc/Q for each S-wave charmonium and a factor mc/Q for each L-wave charmonium with L>0. Here, v is the velocity of the heavy quark or antiquark in the quarkonium rest frame, Q=√s for e⁺e^- annihilation, Q=mB for B-meson decays, √s is the e⁺e^- center-of-momentum energy, mc is the charm-quark mass, and mB is the B-meson mass. There are modifications to the suppression factors if quantum-number restrictions apply for the specific process.