CMS-BPH-22-009

CMS-BPH-22-009 ; CERN-EP-2024-155
Measurement of the polarizations of prompt and non-prompt $\mathrm{J}/\psi$ and $\psi \text{(2S)}$ mesons produced in pp collisions at $\sqrt{s} =$ 13 TeV
CMS Collaboration
20 June 2024
Phys. Lett. B 858 (2024) 139044
Abstract: The polarizations of prompt and non-prompt $\mathrm{J}/\psi$ and $\psi \text{(2S)}$ mesons are measured in proton-proton collisions at $\sqrt{s} =$ 13 TeV, using data samples collected by the CMS experiment in 2017 and 2018, corresponding to a total integrated luminosity of 103.3 fb $^{-1}$ . Based on the analysis of the dimuon decay angular distributions in the helicity frame, the polar anisotropy, $\lambda_\vartheta$ , is measured as a function of the transverse momentum, $p_{\mathrm{T}}$ , of the charmonium states, in the 25-120 and 20-100 GeV ranges for the $\mathrm{J}/\psi$ and $\psi \text{(2S)}$ , respectively. The non-prompt polarizations agree with predictions based on the hypothesis that, for $p_{\mathrm{T}} \gtrsim$ 25 GeV, the non-prompt $\mathrm{J}/\psi$ and $\psi \text{(2S)}$ are predominantly produced in two-body B meson decays. The prompt results clearly exclude strong transverse polarizations, even for $p_{\mathrm{T}}$ exceeding 30 times the $\mathrm{J}/\psi$ mass, where $\lambda_\vartheta$ tends to an asymptotic value around 0.3. Taken together with previous measurements, by CMS and LHCb at $\sqrt{s} =$ 7 TeV, the prompt polarizations show a significant variation with $p_{\mathrm{T}}$ , at low $p_{\mathrm{T}}$ .
Links: e-print arXiv:2406.14409 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ;

Figures & Tables	Summary	References	CMS Publications

Figures
png pdf	Figure 1: Measured dimuon decay length vs. mass distributions for the $\mathrm{J}/\psi$ (left) and $\psi \text{(2S)}$ (right) samples, showing the rectangular regions used in the analysis. The prompt and non-prompt signal regions are labeled PRS and NPS, respectively, while the remaining regions are non-signal (sideband) regions.
png pdf	Figure 1-a: Measured dimuon decay length vs. mass distributions for the $\mathrm{J}/\psi$ (left) and $\psi \text{(2S)}$ (right) samples, showing the rectangular regions used in the analysis. The prompt and non-prompt signal regions are labeled PRS and NPS, respectively, while the remaining regions are non-signal (sideband) regions.
png pdf	Figure 1-b: Measured dimuon decay length vs. mass distributions for the $\mathrm{J}/\psi$ (left) and $\psi \text{(2S)}$ (right) samples, showing the rectangular regions used in the analysis. The prompt and non-prompt signal regions are labeled PRS and NPS, respectively, while the remaining regions are non-signal (sideband) regions.
png pdf	Figure 2: Dimuon mass distributions measured for the non-prompt $\mathrm{J}/\psi$ (left) and $\psi \text{(2S)}$ (right) event samples, in the mentioned $p_{\mathrm{T}}$ bins. The total fit function (blue), the sum of the two CB functions and, only in the $\mathrm{J}/\psi$ case, the Gaussian function (red), and the background continuum (black) are also shown.
png pdf	Figure 2-a: Dimuon mass distributions measured for the non-prompt $\mathrm{J}/\psi$ (left) and $\psi \text{(2S)}$ (right) event samples, in the mentioned $p_{\mathrm{T}}$ bins. The total fit function (blue), the sum of the two CB functions and, only in the $\mathrm{J}/\psi$ case, the Gaussian function (red), and the background continuum (black) are also shown.
png pdf	Figure 2-b: Dimuon mass distributions measured for the non-prompt $\mathrm{J}/\psi$ (left) and $\psi \text{(2S)}$ (right) event samples, in the mentioned $p_{\mathrm{T}}$ bins. The total fit function (blue), the sum of the two CB functions and, only in the $\mathrm{J}/\psi$ case, the Gaussian function (red), and the background continuum (black) are also shown.
png pdf	Figure 3: Fraction of events in the NPS region due to continuum muon pairs, versus $p_{\mathrm{T}}$ , for the non-prompt $\mathrm{J}/\psi$ and $\psi \text{(2S)}$ events.
png pdf	Figure 4: Dimuon mass distributions measured for the prompt $\mathrm{J}/\psi$ (left) and $\psi \text{(2S)}$ (right) event samples, in the mentioned $p_{\mathrm{T}}$ bins. The total fit function (blue), the sum of the two CB functions and (only in the $\mathrm{J}/\psi$ case) the Gaussian function (red), and the background continuum (black) are also shown.
png pdf	Figure 4-a: Dimuon mass distributions measured for the prompt $\mathrm{J}/\psi$ (left) and $\psi \text{(2S)}$ (right) event samples, in the mentioned $p_{\mathrm{T}}$ bins. The total fit function (blue), the sum of the two CB functions and (only in the $\mathrm{J}/\psi$ case) the Gaussian function (red), and the background continuum (black) are also shown.
png pdf	Figure 4-b: Dimuon mass distributions measured for the prompt $\mathrm{J}/\psi$ (left) and $\psi \text{(2S)}$ (right) event samples, in the mentioned $p_{\mathrm{T}}$ bins. The total fit function (blue), the sum of the two CB functions and (only in the $\mathrm{J}/\psi$ case) the Gaussian function (red), and the background continuum (black) are also shown.
png pdf	Figure 5: Fraction of events in the PRS region due to continuum muon pairs, versus $p_{\mathrm{T}}$ , for the prompt $\mathrm{J}/\psi$ and $\psi \text{(2S)}$ events.
png pdf	Figure 6: Dimuon decay length distributions, integrated in $p_{\mathrm{T}}$ , measured for the sideband mass ranges mentioned in the legends, in the $\mathrm{J}/\psi$ (left) and $\psi \text{(2S)}$ (right) cases.
png pdf	Figure 6-a: Dimuon decay length distributions, integrated in $p_{\mathrm{T}}$ , measured for the sideband mass ranges mentioned in the legends, in the $\mathrm{J}/\psi$ (left) and $\psi \text{(2S)}$ (right) cases.
png pdf	Figure 6-b: Dimuon decay length distributions, integrated in $p_{\mathrm{T}}$ , measured for the sideband mass ranges mentioned in the legends, in the $\mathrm{J}/\psi$ (left) and $\psi \text{(2S)}$ (right) cases.
png pdf	Figure 7: Dimuon decay length distributions measured for the $\mathrm{J}/\psi$ (left) and $\psi \text{(2S)}$ (right) cases, in their mass signal windows, in the mentioned $p_{\mathrm{T}}$ bins. The vertical dashed lines mark the limits of the PR and NP ranges. The total fit function, as well as the individual contributions, are also shown.
png pdf	Figure 7-a: Dimuon decay length distributions measured for the $\mathrm{J}/\psi$ (left) and $\psi \text{(2S)}$ (right) cases, in their mass signal windows, in the mentioned $p_{\mathrm{T}}$ bins. The vertical dashed lines mark the limits of the PR and NP ranges. The total fit function, as well as the individual contributions, are also shown.
png pdf	Figure 7-b: Dimuon decay length distributions measured for the $\mathrm{J}/\psi$ (left) and $\psi \text{(2S)}$ (right) cases, in their mass signal windows, in the mentioned $p_{\mathrm{T}}$ bins. The vertical dashed lines mark the limits of the PR and NP ranges. The total fit function, as well as the individual contributions, are also shown.
png pdf	Figure 8: Variation with $p_{\mathrm{T}}$ of the fraction of events in the PRS region from non-prompt $\mathrm{J}/\psi$ and $\psi \text{(2S)}$ mesons.
png pdf	Figure 9: $\|\cos\vartheta_\mathrm{HX}\|$ distributions measured in the mass sidebands (shifted horizontally for better visibility), and their weighted average, for the prompt $\mathrm{J}/\psi$ (left) and non-prompt $\psi \text{(2S)}$ (right) samples, in the mentioned $p_{\mathrm{T}}$ bins.
png pdf	Figure 9-a: $\|\cos\vartheta_\mathrm{HX}\|$ distributions measured in the mass sidebands (shifted horizontally for better visibility), and their weighted average, for the prompt $\mathrm{J}/\psi$ (left) and non-prompt $\psi \text{(2S)}$ (right) samples, in the mentioned $p_{\mathrm{T}}$ bins.
png pdf	Figure 9-b: $\|\cos\vartheta_\mathrm{HX}\|$ distributions measured in the mass sidebands (shifted horizontally for better visibility), and their weighted average, for the prompt $\mathrm{J}/\psi$ (left) and non-prompt $\psi \text{(2S)}$ (right) samples, in the mentioned $p_{\mathrm{T}}$ bins.
png pdf	Figure 10: $\|\cos\vartheta_\mathrm{HX}\|$ distributions measured in the PRS $\mathrm{J}/\psi$ (left) and NPS $\psi \text{(2S)}$ (right) samples, of the terms of Eqs. (4) and (3), respectively, in the mentioned $p_{\mathrm{T}}$ bins.
png pdf	Figure 10-a: $\|\cos\vartheta_\mathrm{HX}\|$ distributions measured in the PRS $\mathrm{J}/\psi$ (left) and NPS $\psi \text{(2S)}$ (right) samples, of the terms of Eqs. (4) and (3), respectively, in the mentioned $p_{\mathrm{T}}$ bins.
png pdf	Figure 10-b: $\|\cos\vartheta_\mathrm{HX}\|$ distributions measured in the PRS $\mathrm{J}/\psi$ (left) and NPS $\psi \text{(2S)}$ (right) samples, of the terms of Eqs. (4) and (3), respectively, in the mentioned $p_{\mathrm{T}}$ bins.
png pdf	Figure 11: Ratios between the measured and simulated $\|\cos\vartheta_\mathrm{HX}\|$ distributions for the prompt and non-prompt $\mathrm{J}/\psi$ (left) and $\psi \text{(2S)}$ (right) events, in the $p_{\mathrm{T}}$ bins mentioned in the legends. The curves represent fits using Eq. (2) and excluding the largest $\|\cos\vartheta_\mathrm{HX}\|$ bins.
png pdf	Figure 11-a: Ratios between the measured and simulated $\|\cos\vartheta_\mathrm{HX}\|$ distributions for the prompt and non-prompt $\mathrm{J}/\psi$ (left) and $\psi \text{(2S)}$ (right) events, in the $p_{\mathrm{T}}$ bins mentioned in the legends. The curves represent fits using Eq. (2) and excluding the largest $\|\cos\vartheta_\mathrm{HX}\|$ bins.
png pdf	Figure 11-b: Ratios between the measured and simulated $\|\cos\vartheta_\mathrm{HX}\|$ distributions for the prompt and non-prompt $\mathrm{J}/\psi$ (left) and $\psi \text{(2S)}$ (right) events, in the $p_{\mathrm{T}}$ bins mentioned in the legends. The curves represent fits using Eq. (2) and excluding the largest $\|\cos\vartheta_\mathrm{HX}\|$ bins.
png pdf	Figure 12: The $\lambda_\vartheta$ parameter measured, as a function of $p_{\mathrm{T}}$ , for non-prompt $\mathrm{J}/\psi$ and $\psi \text{(2S)}$ mesons. The vertical bars represent the total uncertainties. Predicted polarizations of $\mathrm{J}/\psi$ mesons produced in ${\mathrm{B}} \to {\mathrm{J}/\psi} \, X$ decays are shown for three calculations [48,49], discussed in the text. The low- $p_{\mathrm{T}}$ CDF measurement [50] is also shown.
png pdf	Figure 13: The $\lambda_\vartheta$ parameter measured, as a function of $p_{\mathrm{T}}$ , for prompt $\mathrm{J}/\psi$ (left) and $\psi \text{(2S)}$ (right) mesons, in pp collisions at $\sqrt{s} =$ 13 TeV, compared to measurements made at 7 TeV by CMS [10] and LHCb [11,12]. The vertical bars represent the total uncertainties. The curves on the left panel are described in the text.
png pdf	Figure 13-a: The $\lambda_\vartheta$ parameter measured, as a function of $p_{\mathrm{T}}$ , for prompt $\mathrm{J}/\psi$ (left) and $\psi \text{(2S)}$ (right) mesons, in pp collisions at $\sqrt{s} =$ 13 TeV, compared to measurements made at 7 TeV by CMS [10] and LHCb [11,12]. The vertical bars represent the total uncertainties. The curves on the left panel are described in the text.
png pdf	Figure 13-b: The $\lambda_\vartheta$ parameter measured, as a function of $p_{\mathrm{T}}$ , for prompt $\mathrm{J}/\psi$ (left) and $\psi \text{(2S)}$ (right) mesons, in pp collisions at $\sqrt{s} =$ 13 TeV, compared to measurements made at 7 TeV by CMS [10] and LHCb [11,12]. The vertical bars represent the total uncertainties. The curves on the left panel are described in the text.

Tables
png pdf	Table 1: The $\lambda_\vartheta$ values measured in the HX frame, in bins of $p_{\mathrm{T}}$ , for the prompt and non-prompt $\mathrm{J}/\psi$ mesons, including the statistical (stat), systematic (syst), and total uncertainties.
png pdf	Table 2: The $\lambda_\vartheta$ values measured in the HX frame, as a function of $p_{\mathrm{T}}$ , for the prompt and non-prompt $\psi\mathrm{(2S)}$ mesons, indicating the statistical (stat), systematic (syst), and total uncertainties.

Summary

The prompt and non-prompt

$\mathrm{J}/\psi$ and

$\psi\mathrm{(2S)}$

$\lambda_\vartheta$ polarization parameters have been measured, in the helicity frame and for the

$|y| <$ 1.25 interval, using a sample of pp collisions at

$\sqrt{s} =$ 13 TeV collected in 2017 and 2018, corresponding to an integrated luminosity of 103.3 fb

$^{-1}$ . The results cover

$p_{\mathrm{T}}$ ranges significantly broader than previous measurements: 25-120 and 20-100 GeV, for the

$\mathrm{J}/\psi$ and

$\psi \text{(2S)}$ , respectively. The non-prompt

$\mathrm{J}/\psi$ and

$\psi \text{(2S)}$ polarization measurements are compatible with each other, regarding the

$p_{\mathrm{T}}$ dependence and the overall magnitude, plateauing at

$\lambda_\vartheta \approx -$ 0.2 for

$p_{\mathrm{T}} >$ 30 GeV. The measured trends agree with predictions based on the hypothesis that these charmonia are predominantly produced by two-body B meson decays, through colour-singlet processes. Regarding the prompt results, we see no evidence of strong transverse polarizations (

$\lambda_\vartheta$ approaching

$+$ 1), even at

$p_{\mathrm{T}}$ values exceeding 30 times the

$\mathrm{J}/\psi$ mass. Using NRQCD concepts, there is no evidence that, at very high

$p_{\mathrm{T}}$ , the transversely polarized

$^3 S_1^{[8]}$ and

$^3 P_J^{[8]}$ octet terms become dominant with respect to the unpolarized

$^1 S_0^{[8]}$ octet. Taken together with previous CMS and LHCb measurements, covering a lower

$p_{\mathrm{T}}$ domain, we see a significant variation of the prompt polarizations with

$p_{\mathrm{T}}$ , at low

$p_{\mathrm{T}}$ . These results will significantly constrain phenomenological analyses of charmonium production, so far mostly focused on

$p_{\mathrm{T}}$ -differential cross sections.

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