Breakdown of NRQCD Factorization in Processes Involving Two Quarkonia and its Cure

Abstract

We study inclusive processes involving two heavy quarkonia in nonrelativisitic QCD (NRQCD) and demonstrate that, in the presence of two P-wave Fock states, NRQCD factorization breaks down, leaving uncanceled infrared singularities. As phenomenologically important examples, we consider the decay ${\rm Y}\to {\chi }_{cJ}+X$ via $b\bar{b}({}^3{P}_{J_b}^{[8]})\to c\bar{c}({}^3{P}_J^{[1]})+gg$ and the production process $e^{+}{e}^{-}\to J/\psi +{\chi }_{cJ}+X$ via $e^{+}{e}^{-}\to c\bar{c}({}^3{P}_{J_1}^{[8]})+c\bar{c}({}^3{P}_J^{[1]})+g$. We infer that such singularities will appear for double quarkonium hadroproduction at next-to-leading order. As a solution to this problem, we introduce to NRQCD effective field theory new types of operators whose quantum corrections absorb these singularities.

arXiv comment6 pages, 3 figures, matches journal version

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Cited by in corpus (7)

• New Observables in Inclusive Production of Quarkonia
• Complete NLO QCD study of single- and double-quarkonium hadroproduction in the colour-evaporation model at the Tevatron and the LHC
• Double prompt $J/\psi$ hadroproduction in the parton Reggeization approach with high-energy resummation
• Global analysis of $\psi (2S)$ inclusive hadroproduction at next-to-leading order in nonrelativistic-QCD factorization
• Associated production of prompt $J/\psi$ and ${\rm Y}$ mesons in $pp$ collisions at $\sqrt{s}=13\mathrm{TeV}$
• FKS subtraction for quarkonium production at NLO
• Prompt $J/\psi$-pair production at the LHC: impact of loop-induced contributions and of the colour-octet mechanism