Production via Fragmentation at the

The production of J/ψ at large transverse momenta (p⊥ > MJ/ψ) in pp̄ collisions is considered by including the mechanism of fragmentation. Both contributions of fragmentation to J/ψ and of fragmentation to χ states followed by radiative decay to J/ψ are taken into account. The latter is found to be dominant and larger than direct production. The overall theoretical estimate is shown to be nearly consistent with the experimental observation. E-mail addresses: cacciari@pv.infn. it greco@lnf.infn. it Figure 1: One of the diagrams for the gluon fragmentation function at the scale μ = 2mc. Figure 2: One of the diagrams for the charm fragmentation function, at the scale μ = 3mc. The study of the properties of the bound states of heavy quarks plays a central role in the understanding of Quantum Chromodynamics in that it stands on the very border between the perturbative and non-perturbative domain. In particular it is of key importance to have accurate estimates of the production cross sections at large tranverse momenta for precision tests of the theory and possible evidence of new phenomena. So far there has been an intensive experimental study of the cc̄ 1S vector bound state, namely J/ψ, in hadron collisions both at UA1 [1] and CDF [2]. The results have been compared with theoretical calculations [3] which take into account two different mechanisms for J/ψ production: direct charmonium production, including the contribution from the χ states, i.e. gg → J/ψ g gg, qq̄ → χg |→ J/ψ γ qg → χq |→ J/ψ γ (1) and the production resulting from B mesons decay pp̄ → bX |→ B → J/ψ X (2) A more recent version of this calculation, which makes use of the NLO prediction [4] for b production, is presented in ref. [5]. These calculations are in disagreement with the results form CDF, the J/ψ rate observed being actually higher, by a factor of two or more, than the predicted one [2, 5, 6]. It has however recently been pointed out by E. Braaten and T.C. Yuan [7] that at large p⊥ an additional production mechanism comes into play, namely the fragmentation of a gluon or a charm quark into a charmonium state. While being of higher order with respect to direct production by a power of the running coupling constant αs, this mechanism becomes dominant at large p⊥ because of a factor O(p 2 ⊥ /m2c) which overcomes the extra power of αs. The fragmentation functions describing these processes can be calculated perturbatively. Indeed it has been argued in [7] and subsequently shown at LO in [8] that J/ψ production via fragmentation will overcome the direct one (i.e. gg → J/ψ g) at p⊥ ∼ 6-8 GeV. A similar exercise for the χ production, when the total fragmentation probability ∫ D g (see below) times the gg → gg cross sections is compared to the direct production gg → χg, reveals that fragmentation should dominate for p⊥ already at ∼ 2 GeV. Since this result is at the limit of validity of the fragmentation function approach, we can however still expect that the fragmentation mechanism will dominate over the direct one at p⊥ values as low as 5-6 GeV. In this Letter we apply these ideas to a quantitative determination of the J/ψ production rate in hadron collisions, taking also into account the production via fragmentation processes of the χ states and subsequent radiative decays to J/ψ.