The ALICE and LHCb collaborations have studied $J/\psi$\/ production at forward rapidities in protonlead collisions at $\sqrt{s}=5.02$ TeV using the dimuon channel. The evaluation of cold nuclear matter effects requires the knowledge of the corresponding $J/\psi$\/ crosssection in $ pp$ collisions at the same centreofmass energy and in the same kinematic range. In this note the interpolation procedure used to determine this quantity and the related consistency checks are described. Finally, the results from the two experiments on nuclear modification factors are shortly summarized and found to be in good agreement.
Comparison of powerlaw (top left), linear (top right) and exponential (bottom) interpolations for the energy dependence of the $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} $\/ production crosssections for the theoretical predictions given in Tab. 2. Ideally all curves should go through $\sigma(\sqrt{s}=5.02\mathrm{\,TeV} )=5.3 {\rm \,\upmu b} $. 
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Crosssection interpolation for the ALICE data. The point at $\sqrt{s}=5.02$ TeV is the result of the interpolation procedure, the error bar shows the result from error propagation of the experimental uncertainties of the measurements at $\sqrt{s}=2.76$\/ and $7$ TeV. 
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Crosssection interpolation by fitting theoretical predictions to the ALICE data points. 
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Crosssection interpolation for the LHCb data using three phenomenological models. The upper row shows the results for prompt $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} $ production (top left) and for $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} $ mesons from $b$hadron decays (top right). The bottom row plot shows the interpolation for inclusive $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} $ production. The points at $\sqrt{s}=5.02$ TeV are the nominal results of the interpolation procedure, the error bar is the result from error propagation of the experimental uncertainties of the measurements at $\sqrt{s}=2.76$, $7$\/ and $8$ TeV. 
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Differential crosssections $\mathrm{d}\sigma/\mathrm{d} y$\/ at $\sqrt{s}=2.76$\/ and $7\mathrm{\,TeV} $, as measured by ALICE. On the left hand plot the calculated values at $\sqrt{s}=5.02\mathrm{\,TeV} $\/ are separately shown for each interpolation function (linear, power law and exponential), together with their weighted average. The right hand figure shows fits to the interpolated $\mathrm{d}\sigma/\mathrm{d} y$\/ values at $\sqrt{s}=5.02\mathrm{\,TeV} $. See text for details. 
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Differential crosssection for inclusive $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} $ production in $ p\mathrm{Pb}$ collisions as a function of rapidity $y$\/ (left) and transverse momentum $ p_{\rm T} $\/ (right). 
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Nuclear modification factor as a function of rapidity. The left hand plot shows the measurements integrated over the accessible kinematic range of both experiments, the right hand plot displays the differential measurement by the ALICE collaboration. 
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Forwardbackward production ratio for inclusive $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} $\/ production in $ p\mathrm{Pb}$ collisions as a function of $ p_{\rm T} $\/ (left) and as a function of rapidity (right), for both experiments. 
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Animated gif made out of all figures. 
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Existing $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} $\/ crosssection measurements in $2.5<y<4.0$\/ from ALICE [10,9] and LHCb [11,12,13]. The LHCb crosssection at $\sqrt{s}=2.76$ TeV was obtained by rescaling the measured value to the rapidity interval $2.5<y<4.0$. At the other centreofmass energies the crosssections were calculated by integrating the published double differential measurements over the same rapidity range. The first quoted uncertainty is statistical and the second is systematic. 
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Crosssections in units of $\mu$b for prompt $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} $\/ production at $\sqrt{s}=2.76$, $5.02$ and $7\mathrm{\,TeV} $ as predicted by the LOCEM and FONLL models. The LOCEM/CTEQ6L predictions for factorization scales $\mu_{\rm F}=m_c/2$\/ and $\mu_{\rm F}=m_c$\/ are identical and listed only once. The minimum and maximum values for FONLL result from varying the renormalization scale $\mu_{\rm R}$\/ and the factorization scale $\mu_{\rm F}$\/ in the range $\mu_0/2 < \mu_{\rm R},\mu_{\rm F} <2\mu_0$\/ with the constraint $1/2<\mu_R/\mu_F<2$, having defined $\mu_0$\/ by $\mu^2_0 = p_{\rm T} ^2 +m_c^2$. 
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Crosssection interpolation of the ALICE data. See text for details on the assignment of the uncertainties. 
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Interpolated values of $\sigma(J/\psi)$ ($\mu$b) at $\sqrt{s}=5.02\mathrm{\,TeV} $\/ for LHCb. The quoted uncertainties are experimental. 
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Interpolation of $\mathrm{d}\sigma/\mathrm{d} y$, using ALICE data. The quoted uncertainties for the experimental data are statistical and systematic, respectively. For the interpolated values, the first uncertainty is related to the total uncertainties of the 2.76 and $7\mathrm{\,TeV} $ data, while the second is extracted from the dispersion of the results corresponding to the various fitting functions. 
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Interpolated $\mathrm{d}\sigma/\mathrm{d} y$\/ at $\sqrt{s}=5.02\mathrm{\,TeV} $, for the rapidity intervals corresponding to the binning adopted by ALICE in $ p\mathrm{Pb}$ studies. The first quoted uncertainty is related to the uncorrelated uncertainty obtained in the first step of the interpolation procedure. The second one is the $y$correlated uncertainty, while the third one comes from the maximum spread between the results obtained with the three interpolating functions. The last uncertainty represent the theoryrelated contribution. 
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Created on 09 December 2018.Citation count from INSPIRE on 09 December 2018.