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| CMS-SMP-25-005 ; CERN-EP-2026-183 | ||
| Measurement of the fragmentation properties of jets containing $ \Upsilon{\textrm{(nS)}} $ mesons in proton-proton collisions at $ \sqrt{s}= $ 13 TeV | ||
| CMS Collaboration | ||
| 28 July 2026 | ||
| Submitted to the Journal of High Energy Physics | ||
| Abstract: A measurement of the fragmentation properties of jets containing $ \Upsilon{\textrm{(nS)}} $ mesons using proton-proton collision data at $ \sqrt{s}= $ 13 TeV, corresponding to an integrated luminosity of 138 fb$ ^{-1} $, is presented. The $ \Upsilon{\textrm{(nS)}} $ mesons associated with jets are reconstructed via their decays producing pairs of oppositely charged muons. The longitudinal and transverse projections of the momenta of the $ \Upsilon{\textrm{(nS)}} $ mesons along the momenta of the corresponding jets are studied. The results are compared with Monte Carlo predictions, including recent developments in the modelling of quarkonia production in parton showers. The description of the data by these Monte Carlo predictions is found to be unsatisfactory, leaving room for improvements in the modelling of such processes. | ||
| Links: e-print arXiv:2607.25653 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Example diagrams for the hard production of $ \Upsilon{\textrm{(nS)}} $ mesons in the colour singlet (left) and colour octet mechanisms (right). |
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Figure 1-a:
Example diagrams for the hard production of $ \Upsilon{\textrm{(nS)}} $ mesons in the colour singlet (left) and colour octet mechanisms (right). |
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Figure 1-b:
Example diagrams for the hard production of $ \Upsilon{\textrm{(nS)}} $ mesons in the colour singlet (left) and colour octet mechanisms (right). |
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Figure 2:
Fits to the invariant mass distributions of $ \Upsilon{\textrm{(nS)}} $ candidates in two representative ranges of the jet $ p_{\mathrm{T}} $ and the fragmentation variables $ z $ (left) and $ p_{\mathrm{T}}^{\text{rel}} $ (right). The fit components, including signal and background functions, are also shown on the upper panels. The vertical error bars represent the statistical uncertainties on the data points. The lower panel shows the difference between the data and the fitted function, divided by the statistical uncertainty of the data. The model shows, in general, a good agreement with the data. |
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Figure 2-a:
Fits to the invariant mass distributions of $ \Upsilon{\textrm{(nS)}} $ candidates in two representative ranges of the jet $ p_{\mathrm{T}} $ and the fragmentation variables $ z $ (left) and $ p_{\mathrm{T}}^{\text{rel}} $ (right). The fit components, including signal and background functions, are also shown on the upper panels. The vertical error bars represent the statistical uncertainties on the data points. The lower panel shows the difference between the data and the fitted function, divided by the statistical uncertainty of the data. The model shows, in general, a good agreement with the data. |
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Figure 2-b:
Fits to the invariant mass distributions of $ \Upsilon{\textrm{(nS)}} $ candidates in two representative ranges of the jet $ p_{\mathrm{T}} $ and the fragmentation variables $ z $ (left) and $ p_{\mathrm{T}}^{\text{rel}} $ (right). The fit components, including signal and background functions, are also shown on the upper panels. The vertical error bars represent the statistical uncertainties on the data points. The lower panel shows the difference between the data and the fitted function, divided by the statistical uncertainty of the data. The model shows, in general, a good agreement with the data. |
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Figure 3:
Detector-level longitudinal profile for $ \Upsilon{\textrm{(1S)}} $ mesons (left) and transverse profile for $ \Upsilon{\textrm{(3S)}} $ mesons (right) for two different ranges of the jet transverse momentum. The error bars on the data distributions represent the statistical uncertainties. |
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Figure 3-a:
Detector-level longitudinal profile for $ \Upsilon{\textrm{(1S)}} $ mesons (left) and transverse profile for $ \Upsilon{\textrm{(3S)}} $ mesons (right) for two different ranges of the jet transverse momentum. The error bars on the data distributions represent the statistical uncertainties. |
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Figure 3-b:
Detector-level longitudinal profile for $ \Upsilon{\textrm{(1S)}} $ mesons (left) and transverse profile for $ \Upsilon{\textrm{(3S)}} $ mesons (right) for two different ranges of the jet transverse momentum. The error bars on the data distributions represent the statistical uncertainties. |
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Figure 4:
Transfer matrices for the longitudinal profile of jets containing $ \Upsilon{\textrm{(1S)}} $ mesons (left) and for the transverse profile of jets containing $ \Upsilon{\textrm{(3S)}} $ (right). Each transfer matrix parameterizes the migrations among the three bins on the jet $ p_{\mathrm{T}} $ used in the measurement, shown as boxes delimited by dashed lines, as well as among bins on $ z $ or $ p_{\mathrm{T}}^{\text{rel}} $. |
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Figure 4-a:
Transfer matrices for the longitudinal profile of jets containing $ \Upsilon{\textrm{(1S)}} $ mesons (left) and for the transverse profile of jets containing $ \Upsilon{\textrm{(3S)}} $ (right). Each transfer matrix parameterizes the migrations among the three bins on the jet $ p_{\mathrm{T}} $ used in the measurement, shown as boxes delimited by dashed lines, as well as among bins on $ z $ or $ p_{\mathrm{T}}^{\text{rel}} $. |
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Figure 4-b:
Transfer matrices for the longitudinal profile of jets containing $ \Upsilon{\textrm{(1S)}} $ mesons (left) and for the transverse profile of jets containing $ \Upsilon{\textrm{(3S)}} $ (right). Each transfer matrix parameterizes the migrations among the three bins on the jet $ p_{\mathrm{T}} $ used in the measurement, shown as boxes delimited by dashed lines, as well as among bins on $ z $ or $ p_{\mathrm{T}}^{\text{rel}} $. |
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Figure 5:
Relative values of the systematic uncertainties discussed in the text, together with the total uncertainty band, for the longitudinal and transverse profiles of $ \Upsilon{\textrm{(1S)}} $ (top), $ \Upsilon{\textrm{(2S)}} $ (middle) and $ \Upsilon{\textrm{(3S)}} $ mesons (bottom) in jets with 60 $ < p_{\mathrm{T}} < $ 75 GeV. |
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Figure 5-a:
Relative values of the systematic uncertainties discussed in the text, together with the total uncertainty band, for the longitudinal and transverse profiles of $ \Upsilon{\textrm{(1S)}} $ (top), $ \Upsilon{\textrm{(2S)}} $ (middle) and $ \Upsilon{\textrm{(3S)}} $ mesons (bottom) in jets with 60 $ < p_{\mathrm{T}} < $ 75 GeV. |
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Figure 5-b:
Relative values of the systematic uncertainties discussed in the text, together with the total uncertainty band, for the longitudinal and transverse profiles of $ \Upsilon{\textrm{(1S)}} $ (top), $ \Upsilon{\textrm{(2S)}} $ (middle) and $ \Upsilon{\textrm{(3S)}} $ mesons (bottom) in jets with 60 $ < p_{\mathrm{T}} < $ 75 GeV. |
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Figure 5-c:
Relative values of the systematic uncertainties discussed in the text, together with the total uncertainty band, for the longitudinal and transverse profiles of $ \Upsilon{\textrm{(1S)}} $ (top), $ \Upsilon{\textrm{(2S)}} $ (middle) and $ \Upsilon{\textrm{(3S)}} $ mesons (bottom) in jets with 60 $ < p_{\mathrm{T}} < $ 75 GeV. |
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Figure 5-d:
Relative values of the systematic uncertainties discussed in the text, together with the total uncertainty band, for the longitudinal and transverse profiles of $ \Upsilon{\textrm{(1S)}} $ (top), $ \Upsilon{\textrm{(2S)}} $ (middle) and $ \Upsilon{\textrm{(3S)}} $ mesons (bottom) in jets with 60 $ < p_{\mathrm{T}} < $ 75 GeV. |
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Figure 5-e:
Relative values of the systematic uncertainties discussed in the text, together with the total uncertainty band, for the longitudinal and transverse profiles of $ \Upsilon{\textrm{(1S)}} $ (top), $ \Upsilon{\textrm{(2S)}} $ (middle) and $ \Upsilon{\textrm{(3S)}} $ mesons (bottom) in jets with 60 $ < p_{\mathrm{T}} < $ 75 GeV. |
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Figure 5-f:
Relative values of the systematic uncertainties discussed in the text, together with the total uncertainty band, for the longitudinal and transverse profiles of $ \Upsilon{\textrm{(1S)}} $ (top), $ \Upsilon{\textrm{(2S)}} $ (middle) and $ \Upsilon{\textrm{(3S)}} $ mesons (bottom) in jets with 60 $ < p_{\mathrm{T}} < $ 75 GeV. |
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Figure 6:
Particle-level results for the longitudinal (left) and transverse profiles (right) of jets containing $ \Upsilon{\textrm{(1S)}} $ mesons in three different $ p_{\mathrm{T}} $ regions. The data (black points) are compared to the expectations of PYTHIA8.240 with the CP1 (blue) and CP5 tunes (red), as well as the PYTHIA8.310 predictions with the CP1 (orange) and CP5 tunes (violet). The vertical error bars represent the statistical uncertainties on the data points, while the grey bands represent the total experimental uncertainties. |
png pdf |
Figure 6-a:
Particle-level results for the longitudinal (left) and transverse profiles (right) of jets containing $ \Upsilon{\textrm{(1S)}} $ mesons in three different $ p_{\mathrm{T}} $ regions. The data (black points) are compared to the expectations of PYTHIA8.240 with the CP1 (blue) and CP5 tunes (red), as well as the PYTHIA8.310 predictions with the CP1 (orange) and CP5 tunes (violet). The vertical error bars represent the statistical uncertainties on the data points, while the grey bands represent the total experimental uncertainties. |
png pdf |
Figure 6-b:
Particle-level results for the longitudinal (left) and transverse profiles (right) of jets containing $ \Upsilon{\textrm{(1S)}} $ mesons in three different $ p_{\mathrm{T}} $ regions. The data (black points) are compared to the expectations of PYTHIA8.240 with the CP1 (blue) and CP5 tunes (red), as well as the PYTHIA8.310 predictions with the CP1 (orange) and CP5 tunes (violet). The vertical error bars represent the statistical uncertainties on the data points, while the grey bands represent the total experimental uncertainties. |
png pdf |
Figure 6-c:
Particle-level results for the longitudinal (left) and transverse profiles (right) of jets containing $ \Upsilon{\textrm{(1S)}} $ mesons in three different $ p_{\mathrm{T}} $ regions. The data (black points) are compared to the expectations of PYTHIA8.240 with the CP1 (blue) and CP5 tunes (red), as well as the PYTHIA8.310 predictions with the CP1 (orange) and CP5 tunes (violet). The vertical error bars represent the statistical uncertainties on the data points, while the grey bands represent the total experimental uncertainties. |
png pdf |
Figure 6-d:
Particle-level results for the longitudinal (left) and transverse profiles (right) of jets containing $ \Upsilon{\textrm{(1S)}} $ mesons in three different $ p_{\mathrm{T}} $ regions. The data (black points) are compared to the expectations of PYTHIA8.240 with the CP1 (blue) and CP5 tunes (red), as well as the PYTHIA8.310 predictions with the CP1 (orange) and CP5 tunes (violet). The vertical error bars represent the statistical uncertainties on the data points, while the grey bands represent the total experimental uncertainties. |
png pdf |
Figure 6-e:
Particle-level results for the longitudinal (left) and transverse profiles (right) of jets containing $ \Upsilon{\textrm{(1S)}} $ mesons in three different $ p_{\mathrm{T}} $ regions. The data (black points) are compared to the expectations of PYTHIA8.240 with the CP1 (blue) and CP5 tunes (red), as well as the PYTHIA8.310 predictions with the CP1 (orange) and CP5 tunes (violet). The vertical error bars represent the statistical uncertainties on the data points, while the grey bands represent the total experimental uncertainties. |
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Figure 6-f:
Particle-level results for the longitudinal (left) and transverse profiles (right) of jets containing $ \Upsilon{\textrm{(1S)}} $ mesons in three different $ p_{\mathrm{T}} $ regions. The data (black points) are compared to the expectations of PYTHIA8.240 with the CP1 (blue) and CP5 tunes (red), as well as the PYTHIA8.310 predictions with the CP1 (orange) and CP5 tunes (violet). The vertical error bars represent the statistical uncertainties on the data points, while the grey bands represent the total experimental uncertainties. |
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Figure 7:
Particle-level results for the longitudinal (left) and transverse profiles (right) of jets containing $ \Upsilon{\textrm{(2S)}} $ mesons in three different $ p_{\mathrm{T}} $ regions. The data (black points) are compared to the expectations of PYTHIA8.240 with the CP1 (blue) and CP5 tunes (red), as well as the PYTHIA8.310 predictions with the CP1 (orange) and CP5 tunes (violet). The vertical error bars represent the statistical uncertainties on the data points, while the grey bands represent the total experimental uncertainties. |
png pdf |
Figure 7-a:
Particle-level results for the longitudinal (left) and transverse profiles (right) of jets containing $ \Upsilon{\textrm{(2S)}} $ mesons in three different $ p_{\mathrm{T}} $ regions. The data (black points) are compared to the expectations of PYTHIA8.240 with the CP1 (blue) and CP5 tunes (red), as well as the PYTHIA8.310 predictions with the CP1 (orange) and CP5 tunes (violet). The vertical error bars represent the statistical uncertainties on the data points, while the grey bands represent the total experimental uncertainties. |
png pdf |
Figure 7-b:
Particle-level results for the longitudinal (left) and transverse profiles (right) of jets containing $ \Upsilon{\textrm{(2S)}} $ mesons in three different $ p_{\mathrm{T}} $ regions. The data (black points) are compared to the expectations of PYTHIA8.240 with the CP1 (blue) and CP5 tunes (red), as well as the PYTHIA8.310 predictions with the CP1 (orange) and CP5 tunes (violet). The vertical error bars represent the statistical uncertainties on the data points, while the grey bands represent the total experimental uncertainties. |
png pdf |
Figure 7-c:
Particle-level results for the longitudinal (left) and transverse profiles (right) of jets containing $ \Upsilon{\textrm{(2S)}} $ mesons in three different $ p_{\mathrm{T}} $ regions. The data (black points) are compared to the expectations of PYTHIA8.240 with the CP1 (blue) and CP5 tunes (red), as well as the PYTHIA8.310 predictions with the CP1 (orange) and CP5 tunes (violet). The vertical error bars represent the statistical uncertainties on the data points, while the grey bands represent the total experimental uncertainties. |
png pdf |
Figure 7-d:
Particle-level results for the longitudinal (left) and transverse profiles (right) of jets containing $ \Upsilon{\textrm{(2S)}} $ mesons in three different $ p_{\mathrm{T}} $ regions. The data (black points) are compared to the expectations of PYTHIA8.240 with the CP1 (blue) and CP5 tunes (red), as well as the PYTHIA8.310 predictions with the CP1 (orange) and CP5 tunes (violet). The vertical error bars represent the statistical uncertainties on the data points, while the grey bands represent the total experimental uncertainties. |
png pdf |
Figure 7-e:
Particle-level results for the longitudinal (left) and transverse profiles (right) of jets containing $ \Upsilon{\textrm{(2S)}} $ mesons in three different $ p_{\mathrm{T}} $ regions. The data (black points) are compared to the expectations of PYTHIA8.240 with the CP1 (blue) and CP5 tunes (red), as well as the PYTHIA8.310 predictions with the CP1 (orange) and CP5 tunes (violet). The vertical error bars represent the statistical uncertainties on the data points, while the grey bands represent the total experimental uncertainties. |
png pdf |
Figure 7-f:
Particle-level results for the longitudinal (left) and transverse profiles (right) of jets containing $ \Upsilon{\textrm{(2S)}} $ mesons in three different $ p_{\mathrm{T}} $ regions. The data (black points) are compared to the expectations of PYTHIA8.240 with the CP1 (blue) and CP5 tunes (red), as well as the PYTHIA8.310 predictions with the CP1 (orange) and CP5 tunes (violet). The vertical error bars represent the statistical uncertainties on the data points, while the grey bands represent the total experimental uncertainties. |
png pdf |
Figure 8:
Particle-level results for the longitudinal (left) and transverse profiles (right) of jets containing $ \Upsilon{\textrm{(3S)}} $ mesons in three different $ p_{\mathrm{T}} $ regions. The data (black points) are compared to the expectations of PYTHIA8.240 with the CP1 (blue) and CP5 tunes (red), as well as the PYTHIA8.310 predictions with the CP1 (orange) and CP5 tunes (violet). The vertical error bars represent the statistical uncertainties on the data points, while the grey bands represent the total experimental uncertainties. |
png pdf |
Figure 8-a:
Particle-level results for the longitudinal (left) and transverse profiles (right) of jets containing $ \Upsilon{\textrm{(3S)}} $ mesons in three different $ p_{\mathrm{T}} $ regions. The data (black points) are compared to the expectations of PYTHIA8.240 with the CP1 (blue) and CP5 tunes (red), as well as the PYTHIA8.310 predictions with the CP1 (orange) and CP5 tunes (violet). The vertical error bars represent the statistical uncertainties on the data points, while the grey bands represent the total experimental uncertainties. |
png pdf |
Figure 8-b:
Particle-level results for the longitudinal (left) and transverse profiles (right) of jets containing $ \Upsilon{\textrm{(3S)}} $ mesons in three different $ p_{\mathrm{T}} $ regions. The data (black points) are compared to the expectations of PYTHIA8.240 with the CP1 (blue) and CP5 tunes (red), as well as the PYTHIA8.310 predictions with the CP1 (orange) and CP5 tunes (violet). The vertical error bars represent the statistical uncertainties on the data points, while the grey bands represent the total experimental uncertainties. |
png pdf |
Figure 8-c:
Particle-level results for the longitudinal (left) and transverse profiles (right) of jets containing $ \Upsilon{\textrm{(3S)}} $ mesons in three different $ p_{\mathrm{T}} $ regions. The data (black points) are compared to the expectations of PYTHIA8.240 with the CP1 (blue) and CP5 tunes (red), as well as the PYTHIA8.310 predictions with the CP1 (orange) and CP5 tunes (violet). The vertical error bars represent the statistical uncertainties on the data points, while the grey bands represent the total experimental uncertainties. |
png pdf |
Figure 8-d:
Particle-level results for the longitudinal (left) and transverse profiles (right) of jets containing $ \Upsilon{\textrm{(3S)}} $ mesons in three different $ p_{\mathrm{T}} $ regions. The data (black points) are compared to the expectations of PYTHIA8.240 with the CP1 (blue) and CP5 tunes (red), as well as the PYTHIA8.310 predictions with the CP1 (orange) and CP5 tunes (violet). The vertical error bars represent the statistical uncertainties on the data points, while the grey bands represent the total experimental uncertainties. |
png pdf |
Figure 8-e:
Particle-level results for the longitudinal (left) and transverse profiles (right) of jets containing $ \Upsilon{\textrm{(3S)}} $ mesons in three different $ p_{\mathrm{T}} $ regions. The data (black points) are compared to the expectations of PYTHIA8.240 with the CP1 (blue) and CP5 tunes (red), as well as the PYTHIA8.310 predictions with the CP1 (orange) and CP5 tunes (violet). The vertical error bars represent the statistical uncertainties on the data points, while the grey bands represent the total experimental uncertainties. |
png pdf |
Figure 8-f:
Particle-level results for the longitudinal (left) and transverse profiles (right) of jets containing $ \Upsilon{\textrm{(3S)}} $ mesons in three different $ p_{\mathrm{T}} $ regions. The data (black points) are compared to the expectations of PYTHIA8.240 with the CP1 (blue) and CP5 tunes (red), as well as the PYTHIA8.310 predictions with the CP1 (orange) and CP5 tunes (violet). The vertical error bars represent the statistical uncertainties on the data points, while the grey bands represent the total experimental uncertainties. |
| Summary |
| A measurement of the fragmentation properties of jets containing $ \Upsilon{\textrm{(nS)}} $ quarkonia has been presented for the first time. The measurement is performed using the dimuon decays of the $ \Upsilon $ mesons and the jets containing the dimuon system. The measurements include the longitudinal profile $ z $, the distribution of the fraction of the jet momentum carried by the $ \Upsilon $ meson in the direction of the jet axis, and the transverse profile $ p_{\mathrm{T}}^{\text{rel}} $, the distribution of the momentum of the $ \Upsilon $ meson in the direction perpendicular to the jet axis. The results are compared with the predictions from PYTHIA8.240, in which $ \Upsilon $ mesons are generated directly from the matrix element, as well as with the PYTHIA8.310 predictions, using an alternative approach for the generation of quarkonia from the parton shower. Both PYTHIA versions make use of the CP1 and CP5 tunes. These measurements provide new and stringent tests of non-relativistic QCD (NRQCD). Compared with charmonium, bottomonium production is expected to be more reliably described within the NRQCD framework, because of the larger mass of the b quark, which improves the separation between perturbative and non-perturbative scales. Moreover, the inclusion of the transverse momentum profile of the $ \Upsilon $ meson relative to the jet axis further extends the sensitivity of these measurements to transverse-momentum-dependent aspects of quarkonium production, providing additional constraints on the dynamics of quarkonium formation beyond collinear fragmentation approaches. The results show important discrepancies between the data and the predictions, pointing to $ \Upsilon $ mesons carrying a smaller momentum fraction of the jet than what is predicted in the PYTHIA implementations of NRQCD. These results are consistent in magnitude with previous measurements of jets containing $ \mathrm{J}/\psi $ mesons by the LHCb and CMS Collaborations. While the PYTHIA8.310 improvements tend to go in the correct direction, showing less isolated quarkonia, these results suggest that further theoretical progress is needed to achieve a satisfactory description. Overall, the present measurement is expected to provide additional input to the so-called quarkonium polarization puzzle by constraining the long-distance matrix elements relevant to $ \Upsilon{\textrm{(nS)}} $ production in NRQCD. In particular, the simultaneous sensitivity to the longitudinal and transverse structure of $ \Upsilon{\textrm{(nS)}} $ production in jets may help to disentangle the interplay between colour-singlet and colour-octet production mechanisms in this context, as well as the contributions from higher angular momentum Fock states. |
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