Forward $J/\psi$ and very backward jet inclusive production at the LHC

In the spirit of Mueller-Navelet dijet production, we propose and study the inclusive production of a forward $J/\psi$ and a very backward jet at the LHC as an observable to reveal high-energy resummation effects à la Balitsky, Fadin, Kuraev, Lipatov. We obtain several predictions, which are based on the various mechanisms discussed in the literature to describe the production of the $J/\psi$, namely, nonrelativistic QCD singlet and octet contributions, and the color evaporation model.

Figure 1

The high-energy hadroproduction of a meson $M$ and a jet (here originating from a quark) with a large rapidity between them. Left: Born approximation. Right: inclusion of BFKL-like resummation effects due to multiple emissions of gluons and of higher order jet vertex corrections.

Figure 2

Left: square of the amplitude of the Born process. Right: symbolic factorized form of this squared amplitude involving, from top to bottom, the gluonic PDF, the impact factor describing the $gg\to M$ transition, the $t$-channel exchange of two off-shell gluons (in bold), the vertex describing the $gq\to \text{jet}$ transition, and the quark PDF. The crosses symbolically denote the appropriate Fierz structure in Lorentz space. Namely, from top to bottom, $g_{\perp }$ tensors for gluons, due to the collinear factorization of the gluon out of the upper PDF, ${\cancel{p}}_1$ and ${\cancel{p}}_2$ arising from the nonsense polarizations of the $t$-channel gluons in $k_t$-factorization, and finally ${\cancel{p}}_2$ and ${\cancel{p}}_1$ due to the collinear factorization of the quark out of the down PDF. The black fermions and curved gluon lines symbolize the trace over color and Lorentz indices after the use of the Fierz identity in these two spaces, while the blue (grey in printed black and white) gluons are traces over color after the use of the Fierz identity in color space.

Figure 3

The 6 diagrams contributing to the amplitude in color singlet NRQCD. The blobs with a cross symbolize the Fierz structure of Eq. (2.19).

Figure 4

The 3 diagrams contributing to the amplitude in color octet NRQCD. The blobs with a cross symbolize the Fierz structure of Eq. (2.43).

Figure 5

The 3 diagrams contributing to the amplitude in the color evaporation model.

Figure 6

Cross section at $\sqrt{s}=8\mathrm{TeV}$ as a function of the relative rapidity $Y$ between the $J/\psi$ and the jet, in four different kinematical configurations.

Figure 7

Cross section at $\sqrt{s}=13\mathrm{TeV}$ as a function of the relative rapidity $Y$ between the $J/\psi$ and the jet, in four different kinematical configurations.

Figure 8

Variation of $⟨\cos \phi ⟩$ at $\sqrt{s}=8\mathrm{TeV}$ as a function of the relative rapidity $Y$ between the $J/\psi$ and the jet, for the four kinematical cuts described in the text. The grey band corresponds to the results obtained when the $J/\psi$ production vertex is replaced by the leading order jet production vertex.

Figure 9

Variation of $⟨\cos \phi ⟩$ at $\sqrt{s}=13\mathrm{TeV}$ as a function of the relative rapidity $Y$ between the $J/\psi$ and the jet, for the four kinematical cuts described in the text. The grey band corresponds to the results obtained when the $J/\psi$ production vertex is replaced by the leading order jet production vertex.