Very low $x$ gluon density determined by LHCb exclusive $J/\psi$ data

The low $x$ behaviour of the gluon density $xg(x,\mu^2)$ at scale $\mu^2=2.4$ GeV$^2$ is determined using exclusive $J/\psi$ production data from HERA and LHCb within the framework of collinear factorisation at next-to-leading order (NLO). It is shown that in the interval $3\times 10^{-6} < x <10^{-3}$ the gluon distribution function grows as $xg(x,\mu^2)\propto x^{-\lambda}$ with $\lambda=0.135\pm 0.006$. The impact this experimental data will have for the global parton distribution function (PDF) analyses in this low $x$ domain is quantified. No indication in favour of parton density saturation is observed.