Color-singlet quark-pair transmutation: Helicity amplitudes and partial-wave analysis.

Abstract

Quark-pair transmutation via two gluons is the lowest-order, color-singlet process. In this paper the helicity amplitudes for this process are evaluated and a partial-wave analysis performed. The amplitudes for these annihilations are infrared divergent and this divergence is removed by giving the gluons a confinement mass. The results are generally dependent on this mass. Many of the features are similar to those of quark-pair annihilation into two gluons. Somewhat surprisingly, there is a large proportion of a ${1}^{+}$ partial wave. Threshold effects are understood in terms of threshold effects in pair annihilation into two gluons. However, there is a ``competition'' effect that depends on the ratio of masses of the initial- and final-quark pairs. For similar masses, singlet production dominates as expected, but for very dissimilar masses, singlet annihilation of the heavier pair competes with triplet production of the lighter pair. Some comments about the possible applications and extensions of this work are made. Obvious applications are to the Okubo-Zweig-Iizuka-rule-suppressed decays of quarkonia. Other applications include development of a quark-pair-creation model that differs from the usual $^{3}\mathrm{P}_{0}$ and $^{3}\mathrm{S}_{1}$ models.