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We study the production of a forward meson and a backward jet with a large rapidity separation at the LHC using the BFKL formalism. We compare the predictions given by the Non Relativistic QCD (NRQCD) approach to charmonium prediction and by the Color Evaporation Model. In NRQCD, we find that the $^3 S_1^{, 8}$ part of the onium wavefunction is completely dominating the process. NRQCD and the color evaporation model give similar results, although a discrepancy seems to appear as the value of the transverse momenta of the charmonium and of the jet decrease.

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