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A<sc>bstract</sc> We compute the differential cross-section for direct quarkonium production accompanied by a gluon in high-energy deep inelastic scattering (DIS) at small-x. We employ the Non-Relativistic QCD factorization framework, focusing on theS-wave contribution to the formation of the quarkonium, and including both color singlet and octet contributions. Our short distance coefficients for the production of the heavy quark pair are obtained within the Color Glass Condensate effective field theory. Our results pave the way towards the next-to-leading order computation of direct quarkonium in DIS, as well as the study of azimuthal correlations of direct quarkonium and jet.
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Power expansion for heavy quarkonium production at next-to-leading order in e+e− annihilation
A bstract 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 ( $$ {\alpha}_s^2 $$ α 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 v 4 in the velocity expansion, we derive analytical results for the differential energy fraction distribution of the heavy quarkonium. Calculations for $$ {}^3{S}_1^{\left[1\right]} $$ 3 S 1 1 and $$ {}^1{S}_0^{\left[8\right]} $$ 1 S 0 8 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 $$ {}^1{S}_0^{\left[8\right]} $$ 1 S 0 8 case.
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- Award ID(s):
- 1915093
- PAR ID:
- 10230796
- Date Published:
- Journal Name:
- Journal of High Energy Physics
- Volume:
- 2020
- Issue:
- 9
- ISSN:
- 1029-8479
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/JHEP09(2020)046
