Helicity Decomposition for Inclusive $J/ψ$ Production

TL;DR

The paper develops a general NRQCD-based method to compute inclusive productions of heavy quarkonia with defined polarization, introducing a matching framework that captures interference between different total angular momentum states and remains compatible with dimensional regularization. By applying the method to $q\bar q \to c\bar c$ and $gg \to c\bar c$, it provides explicit short-distance coefficients and polarized cross sections in terms of NRQCD matrix elements, including color-octet contributions and derivative operators. Rotational and heavy-quark spin symmetries, along with vacuum-saturation and velocity-scaling rules, are used to reduce the matrix elements, with explicit results specialized to $J/\psi$ production. The work reveals that polarized-production cross sections involve additional matrix elements and possible interference terms absent in unpolarized production, offering a more complete and regularization-friendly framework for quarkonium phenomenology.

Abstract

We present a general method for calculating inclusive cross sections for the production of heavy quarkonium states with definite polarization within the NRQCD factorization approach. Cross sections for polarized production can involve additional matrix elements that do not contribute to cross sections for unpolarized production. They can also include interference terms between parton processes that produce $Q \bar Q$ pairs with different total angular momentum. The interference terms cancel upon summing over polarizations. Our method can be generalized to $N$ dimensions and is therefore compatible with the use of dimensional regularization to calculate radiative corrections. We illustrate the method by applying it to the production of $J/ψ$ via the parton processes $q \bar q \to c \bar c$ and $g g \to c \bar c$.