Abstract
We give predictions of J/ψ and ψ(2S) yields and polarizations in prompt production at hadron colliders based on non-relativistic QCD factorization formula. We calculate short-distance coefficients of all important color-octet intermediate channels as well as color-singlet channels up to $$ \mathcal{O}\left({\alpha}_S^4\right) $$ , i.e. next-to-leading order in α S . For prompt J/ψ production, we also take into account feeddown contributions from χ cJ (J=0,1,2) and ψ(2S) decays. Color-singlet long-distance matrix elements (LDMEs) are estimated by using potential model, and color-octet LDMEs are extracted by fitting the Tevatron yield data only. The predictions are satisfactory for both yields and polarizations of prompt J/ψ and prompt ψ(2S) production at the Tevatron and the LHC. In particular, we find our predictions for polarizations of prompt J/ψ production have only a little difference from our previous predictions for polarizations of direct J/ψ production.
Highlights
That, the crucial point to get these cancelations is the introduction of a relatively large pT cutoff for data in the lower pT region
Based on the NLO NRQCD calculation, a data-driven method is employed in ref. [11] to fit CO long-distance matrix elements (LDMEs)
In a recent study of J/ψ + γ production [30], the authors found that positivity of CO LDMEs are needed to guarantee a physical cross section, while the sets of CO LDMEs in refs. [5, 7] result in unphysical negative cross section for J/ψ + γ production at hadron colliders
Summary
We first list some details that are used in this article. The helicitysummed yields are calculated following the way mentioned in refs. [8, 13, 14], while the method of the polarisation is described in refs. [6, 15, 16]. Physical masses (in unit of GeV) of various charmonia [18]. We use CTEQ6M [17] as our default PDF. Masses of relevant charmonia in our article are shown in table 1. The full spin correlation of χcJ ’s spin density matrix element and J/ψ’s spin density matrix element including E1, M2 and E3 transitions has been explored in eq (C4) of ref. We use the normalized M2 amplitude aJ2 =1 = −6.26 × 10−2 for χc1 → J/ψ + γ, and the normalized M2 and E3 amplitudes aJ2 =2 = −9.3 × 10−2 and aJ3 =2 = 0 for χc2 → J/ψ + γ, which are measured by CLEO collaboration [21]. [12], we notice that the λθ is squared-amplitude dependent These extra spin-flip effects due to M2 and E3 transitions are negligible. We still keep it here since no extra effort is needed
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