HadronicJψproduction calculated in the NRQCD factorization formalism

The NRQCD factorization formalism of Bodwin, Braaten, and Lepage prescribes how to write quarkonium production rates as a sum of products of short-distance coefficients times nonperturbative long-distance NRQCD matrix elements. We present a calculation of the inclusive cross section for hadronic $\psi$ production within the framework of the factorization formalism. Our method applies to the case in which the helicity of the $\psi$ is not measured. In addition to the well-known color-singlet production mechanisms, there are equally important mechanisms in which the $c\overline{c}$ pair that forms the $\frac{J}{\psi }$ is initially produced in a color-octet state, in either a ${}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$, ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$, ${}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{}$, or ${}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}$ angular-momentum configuration. In our presentation, we faithfully follow the "matching" procedure, thereby shedding light on the NRQCD factorization formalism. We determine the short-distance coefficients appearing in the factorization formula, and we point out how one may systematically include relativistic corrections in these calculations.