The production of $J/psi$ mesons with rapidity $1.5<y<4.0$ or $-5.0<y<-2.5$
and transverse momentum $p_mathrm{T}<14 mathrm{GeV}/c$ is studied with the
LHCb detector in proton-lead collisions at a proton-nucleon centre-of-mass
energy $sqrt{s_{NN}}=5 mathrm{TeV}$. The analysis is based on a data sample
corresponding to an integrated luminosity of about $1.6 mathrm{nb}^{-1}$. For
the first time the nuclear modification factor and forward-backward production
ratio are determined separately for $J/psi$ mesons originating directly from
the proton-nucleon collision and from $b$-hadron decays.
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