Abstract
We study heavy quarkonium production associated with gluons in e+e− annihilation as an illustration of the perturbative QCD (pQCD) factorization approach, which incorporates the first nonleading power in the energy of the produced heavy quark pair. We show how the renormalization of the four-quark operators that define the heavy quark pair fragmentation functions using dimensional regularization induces “evanescent” operators that are absent in four dimensions. We derive closed forms for short-distance coefficients for quark pair production to next-to-leading order ( {alpha}_s^2 ) in the relevant color singlet and octet channels. Using non-relativistic QCD (NRQCD) to calculate the heavy quark pair fragmentation functions up to v4 in the velocity expansion, we derive analytical results for the differential energy fraction distribution of the heavy quarkonium. Calculations for {}^3{S}_1^{left[1right]} and {}^1{S}_0^{left[8right]} channels agree with analogous NRQCD analytical results available in the literature, while several color-octet calculations of energy fraction distributions are new. We show that the remaining corrections due to the heavy quark mass fall off rapidly in the energy of the produced state. To explore the importance of evolution at energies much larger than the mass of the heavy quark, we solve the renormalization group equation perturbatively to two-loop order for the {}^1{S}_0^{left[8right]} case.
Highlights
Heavy quarkonium production is a subject of continuing interest [1,2,3]
We study heavy quarkonium production associated with gluons in e+e− annihilation as an illustration of the perturbative QCD factorization approach, which incorporates the first nonleading power in the energy of the produced heavy quark pair
We presented the first next-to-leading order (NLO) calculation of short-distance coefficients in the context of next-to-leading power (NLP) perturbative QCD factorization for heavy quarkonia, extending the quark pair fragmentation formalism developed in ref
Summary
Heavy quarkonium production is a subject of continuing interest [1,2,3]. The production of a heavy quarkonium state always involves an intrinsic hard scale, the heavy quark mass, mQ. Suppressing convolutions associated with the initial state, such factorized cross sections for the production of heavy quarkonium H can be represented as σpHQCD =. It should be noted that, rather than the full set of NLP non-perturbative functions, the formalism includes only the heavy quark pair fragmentation functions. We will apply this formalism to heavy quarkonium production in association with gluons for e+e− annihilation. For these processes, we provide the first closed expressions for the NLP short-distance coefficients at next-to-leading order (NLO). We show NLO pQCD predictions for different NRQCD channels at various center-of-mass (CM) energies, and include comparison to data from the Belle collaboration [23]
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