The production of $\Upsilon(nS)$ mesons ($n=1,2,3$) in $p$Pb and Pb$p$ collisions at a centreofmass energy per nucleon pair $\sqrt{s_{NN}}=8.16$ TeV is measured by the LHCb experiment, using a data sample corresponding to an integrated luminosity of 31.8 nb$^{1}$. The $\Upsilon(nS)$ mesons are reconstructed through their decays into two oppositesign muons. The measurements comprise the differential production crosssections of the $\Upsilon(1S)$ and $\Upsilon(2S)$ states, their forwardtobackward ratios and nuclear modification factors, performed as a function of the transverse momentum \pt and rapidity in the nucleonnucleon centreofmass frame $y^*$ of the $\Upsilon(nS)$ states, in the kinematic range $p_{\rm{T}}<25$ GeV/$c$ and $1.5<y^*<4.0$ ($5.0<y^*<2.5$) for $p$Pb (Pb$p$) collisions. In addition, production crosssections for $\Upsilon(3S)$ are measured integrated over phase space and the production ratios between all three $\Upsilon(nS)$ states are determined. The measurements are compared to theoretical predictions and suppressions for quarkonium in $p$Pb collisions are observed.
Invariantmass distribution of $\mu^+\mu^$ pairs from the (left) $p$Pb and (right) Pb$p$ samples after the trigger and off\line selections. 
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Total efficiency $\varepsilon_{\mathrm{tot}} $ of the \Y1S meson as a function of its $p_{\mathrm{ T}}$ in different $y^*$ bins in (left) $p$Pb and (right) Pb$p$ collisions. The horizontal locations of the markers are roughly the centroids of the bins, with offsets from centre to aid in readability. 
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Doubledifferential crosssection for the \Y1S meson as a function of $p_{\mathrm{ T}}$ for different values of $y^*$ for the (left) forward $p$Pb and (right) backward Pb$p$ samples. The uncertainties are the sums in quadrature of the statistical and systematic components. The horizontal locations of the markers are roughly the centroids of the bins, with offsets from centre to aid in readability. 
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Crosssection of (left) \Y1S and (right) \Y2S production as a function of $y^*$ integrated over $p_{\mathrm{ T}}$ for the backward (negative $y^*$) and forward (positive $y^*$) samples, compared to the crosssection measured in $pp$, interpolated to $\sqrt{s_{\scriptscriptstyle\rm NN}} =8.16\mathrm{ Te V} $. In this and subsequent figures, the uncertainties shown are the sums in quadrature of the statistical and systematic components. 
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Crosssection of (top) \Y1S and (bottom) \Y2S production as a function of $p_{\mathrm{ T}}$ integrated over $y^*$ for the (left) forward and (right) backward samples compared to the crosssection measured in $pp$, interpolated to $\sqrt{s_{\scriptscriptstyle\rm NN}} =8.16\mathrm{ Te V} $. 
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Nuclear modification factors of the (left) \Y1S and (right) \Y2S mesons as a function of $y^*$ integrated over $p_{\mathrm{ T}}$ for the forward and backward samples. The bands correspond to the theoretical predictions for the nCTEQ15 and EPPS16 NNPDF sets, and the comovers model as reported in the text. 
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Nuclear modification factors of the (top) \Y1S and (bottom) \Y2S mesons as a function of $p_{\mathrm{ T}}$ integrated over $y^*$ for the (left) forward and (right) backward samples. The bands correspond to the theoretical predictions for the nCTEQ15 and EPPS16 NNPDF sets as reported in the text. 
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Forwardbackward ratio for the \Y1S as a function of (left) $p_{\mathrm{ T}}$ integrated over $y^*$ and (right) as a function of $y^*$ integrated over $p_{\mathrm{ T}}$ . The bands correspond to the theoretical calculations for the nCTEQ15 and EPPS16 NNPDF sets as reported in the text. 
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Forwardbackward ratio for the \Y2S compared with theoretical calculations for the nCTEQ15 and EPPS16 NNPDF sets as reported in the text. 
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Ratios between \Y2S and \Y1S crosssections as a function of (top) $p_{\mathrm{ T}}$ integrated over $y^*$, and as function of (bottom) $y^*$ integrated over $p_{\mathrm{ T}}$ , for $p$Pb and Pb$p$ collisions. The bands correspond to the theoretical predictions for the nCTEQ15 and EPPS16 NNPDF sets as reported in the text. 
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Double ratios for (left) \Y2S and (right) \Y3S. The bands correspond to the theoretical prediction for the comovers model as reported in the text. 
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Ratio of \Y1S to nonprompt $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu}$ crosssections as a function of $y^*$ integrated over $p_{\mathrm{ T}}$ , for $p$Pb and Pb$p$ collisions. 
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Animated gif made out of all figures. 
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Yields of $\Y1S$, $\Y2S$, $\Y3S$ mesons in $p$Pb and Pb$p$ samples as given by the fit. The uncertainties are statistical only. 
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Systematic uncertainties (in percent) on the crosssection measurements. The ranges indicate the minimum and maximum values in different bins, among all \Y nS states. 
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Ratio $R(\Y nS)$ in $pp$, $p$Pb, and Pb$p$ samples. The uncertainties are combinations of statistical and systematical components. 
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\Y1S production crosssection in $p$Pb, as a function of $ p_{\mathrm{ T}} $ and $y^*$. 
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\Y1S production crosssection in Pb$p$, as a function of $ p_{\mathrm{ T}} $ and $y^*$. 
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\Y1S production crosssection in $p$Pb and Pb$p$, as a function of $ p_{\mathrm{ T}} $. 
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\Y1S production crosssection in $p$Pb and Pb$p$, as a function of $y^*$. 
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\Y2S production crosssection in $p$Pb and Pb$p$, as a function of $ p_{\mathrm{ T}} $. 
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\Y2S production crosssection in $p$Pb, as a function of $y^*$. 
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Scaled $pp$ differential crosssection in $p_{\mathrm{ T}}$ at $\sqrt{s_{\scriptscriptstyle\rm NN}} =8.16$ TeV. The first uncertainty is statistical, the second is systematic, which includes the systematic uncertainty from the $pp$ measurement and that estimated by changing the interpolation function. 
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Scaled $pp$ differential crosssection in $y$ at $\sqrt{s_{\scriptscriptstyle\rm NN}} =8.16$ TeV. The first uncertainty is statistical, the second is systematic, which includes the systematic uncertainty from the $pp$ measurement and that estimated by changing the interpolation function. 
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$\Upsilon(1S)$ nuclear modification factor, $R_{p{\rm Pb}}^{\Upsilon(1S)}$, in $p$Pb and Pb$p$ as a function of $ p_{\mathrm{ T}} $ integrated over $y^*$ in the range $1.5 < y^* < 4.0$ for $p$Pb and $5.0 < y^* < 2.5$ for Pb$p$. 
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$\Upsilon(1S)$ nuclear modification factor, $R_{p{\rm Pb}}^{\Upsilon(1S)}$, in $p$Pb and Pb$p$ as a function of $y^*$ integrated over $ p_{\mathrm{ T}} $ in the range $0 < p_{\mathrm{ T}} < 25$ $ {\mathrm{ Ge V /}c} $ . 
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$\Upsilon(2S)$ nuclear modification factor, $R_{p{\rm Pb}}^{\Upsilon(2S)}$, in $p$Pb and Pb$p$ as a function of $ p_{\mathrm{ T}} $ integrated over $y^*$ in the range $1.5 < y^* < 4.0$ for $p$Pb and $5.0 < y^* < 2.5$ for Pb$p$. 
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$\Upsilon(2S)$ nuclear modification factor, $R_{p{\rm Pb}}^{\Upsilon(2S)}$, in $p$Pb and Pb$p$ as a function of $y^*$ integrated over $ p_{\mathrm{ T}} $ in the range $0 < p_{\mathrm{ T}} < 25$ $ {\mathrm{ Ge V /}c} $ . 
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$\Upsilon(1S)$ forwardtobackward ratio, $R_{{\rm FB}}^{\Upsilon(1S)}$, as a function of $ p_{\mathrm{ T}} $ integrated over $\vert y^* \vert$ in the range $2.5 < \vert y^* \vert < 4.0$. 
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$\Upsilon(1S)$ forwardtobackward ratio, $R_{{\rm FB}}^{\Upsilon(1S)}$, as a function of $\vert y^* \vert$ integrated over $ p_{\mathrm{ T}} $ in the range $0 < p_{\mathrm{ T}} < 25$ $ {\mathrm{ Ge V /}c} $ . 
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$\Upsilon(2S)$ forwardtobackward ratio, $R_{{\rm FB}}^{\Upsilon(2S)}$, as a function of $ p_{\mathrm{ T}} $ integrated over $\vert y^* \vert$ in the range $2.5 < \vert y^* \vert < 4.0$. 
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$\Upsilon(2S)$ forwardtobackward ratio, $R_{{\rm FB}}^{\Upsilon(2S)}$, as a function of $\vert y^* \vert$ integrated over $ p_{\mathrm{ T}} $ in the range $0 < p_{\mathrm{ T}} < 25$ $ {\mathrm{ Ge V /}c} $ . 
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$\Upsilon(2S)$ to $\Upsilon(1S)$ ratio, $R(\Y2S)$, in $p$Pb and Pb$p$ as a function of $ p_{\mathrm{ T}} $ integrated over $y^*$ in the range $1.5 < y^* < 4.0$ for $p$Pb and $5.0 < y^* < 2.5$ for Pb$p$. 
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$\Upsilon(2S)$ to $\Upsilon(1S)$ ratio, $R(\Y2S)$, in $p$Pb and Pb$p$ as a function of $y^*$ integrated over $ p_{\mathrm{ T}} $ in the range $0 < p_{\mathrm{ T}} < 25$ $ {\mathrm{ Ge V /}c} $ . 
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$\Upsilon(1S)$ to nonprompt $J/\psi$, in $p$Pb and Pb$p$ as a function of $y^*$ integrated over $ p_{\mathrm{ T}} $ in the range $0 < p_{\mathrm{ T}} < 25$ $ {\mathrm{ Ge V /}c} $ . The quoted uncertainties are the sum in quadrature of the statistical and systematic components. 
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Created on 27 February 2021.