The region $\eta>3$ is a kinematic range of interest for Higgs searches, QCD physics and beyond the Standard Model studies in $pp$ interactions at TeV energies. We explore the feasibility of measuring jets in the LHCb experiment, mainly devoted to precision measurements in the $b$physics domain, but covering the very forward region $2<\eta<4.5$. The jets reconstruction capabilities of LHCb are presented, together with some preliminary results on inclusive jets and dijets that show the potential interest of LHCb results for low$x$/high$Q^2$ perturbative QCD tests. The data have been taken at LHC during the 2010 runs at $\sqrt{s}=7$ TeV.
Region in the $\left(x,Q^{2}\right)$ plane accessible to LHCb (adapted from Ref. []). 
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Some illustrative events reconstructed in LHCb where the leading jet has $p_{T}^{jet}>$10 GeV/c from very early runs at 7 TeV. One of the runs on which we have tested the selection criteria. Jets reconstruction has been done with the $k_T$ algorithm in the Erecombination scheme with $R=1$ and $p_{T}^{cut}=1$ GeV/c. As {}"Underlying Event" (yellow) we classify any particle non clustered in the two jets with higher momentum, while "noise" is any track with $\chi^2/dof\ge10$. 
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Normalized differential raw transverse energy distribution compared with that obtained applying the $k_{T}$ algorithm to particles simulated with the LHCb Monte Carlo program (see text). 
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Distribution of the azimuthal angle difference $\Delta\phi=\phi_{jet_{1}}\phi_{jet_{2}}$ for the two leading jets in all events that have at least two jets with $p_{T}>20$ GeV$/c$. The peak at $\Delta\phi\approx\pi$ is evident. The full line is the result of the fit of the data with the sum of a polynomial background (dashed line) and a Gaussian function. 
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Differential distribution of the asymmetry parameter $A$, defined by Eq. 2, for the events in which the two jets have $\left\Delta\phi\pi\right<40^\circ$. 
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Invariant mass distribution for jet pairs with $p_{T1}$ and $p_{T2}$ $\geq20\:\textrm{GeV$/c$}$, $\left\Delta\phi\pi\right\leq40^\circ$ and $A\leq0.2$. The dashed histogram shows the LHCbMC (see text) simulated distribution. 
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Range in $(\tilde{x},\tilde{Q}^2)$, defined in the text, that could be experimentally accessible to LHCb through the measurement of dijets at $\sqrt{s}=7$ TeV. 
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Dijet $\tilde{x}$ distribution for various $\tilde{Q}^{2}$ ranges. 
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Animated gif made out of all figures. 
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Created on 11 July 2020.