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CMS-PAS-HIN-23-009
The Bjorken-$ x $ evolution of gluon fields probed via incoherent $ \mathrm{J}/\psi $ photoproduction in ultraperipheral PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV
Abstract: The cross section for incoherent $ \mathrm{J}/\psi $ photoproduction off lead nuclei is measured to probe the event-by-event fluctuations of the gluon field density within heavy nuclei across a broad range of Bjorken-$ x $. Results are obtained using PbPb ultraperipheral collisions at a nucleon-nucleon center-of-mass energy of 5.02 TeV collected by the CMS experiment at the CERN LHC, corresponding to an integrated luminosity of 1.52 nb$^{-1}$. The dependence of the cross section on the photon-nucleus center-of-mass energy per nucleon ($ W^{\mathrm{Pb}}_{\gamma\mathrm{N}} $) is studied from $ W^{\mathrm{Pb}}_{\gamma\mathrm{N}} \approx $ 40 GeV up to 400 GeV, corresponding to a Bjorken-$ x $ interval of 5.8 $ \times $ 10$^{-3}$ $ > x > $ 6.5 $\times$ 10$^{-5} $. The ratio of incoherent to coherent $ \mathrm{J}/\psi $ cross sections is found to be independent of $ W^{\mathrm{Pb}}_{\gamma\mathrm{N}} $ and $ x $ over the range studied. Significant nuclear suppression of incoherent $ \mathrm{J}/\psi $ photoproduction is observed. For $ x < $ 10$^{-4} $, the suppression is comparable to that observed in coherent $ \mathrm{J}/\psi $ photoproduction, becoming more pronounced as $ x $ increases.
Figures Summary References CMS Publications
Figures

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Figure 1:
The total differential incoherent $ \mathrm{J}/\psi $ photoproduction cross section versus $ |y| $ (left) and $ y $ (right) in PbPb UPCs at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV. The right panel shows the results after disentangling the directional correlation between the produced $ \mathrm{J}/\psi $ and emitted forward neutrons. The values at $ -y $ and $ +y $ correspond to the $ \mathrm{J}/\psi $-Xn(Same) and $ \mathrm{J}/\psi $-Xn(Opposite) requirements, respectively. Data from the ALICE experiment [ALICE:2023gcs] is also displayed. The vertical bars and shaded boxes represent the statistical and systematic uncertainties, respectively. The horizontal bars show the bin widths. Theoretical predictions from the LTA [63,64] are shown by curves.

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Figure 1-a:
The total differential incoherent $ \mathrm{J}/\psi $ photoproduction cross section versus $ |y| $ (left) and $ y $ (right) in PbPb UPCs at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV. The right panel shows the results after disentangling the directional correlation between the produced $ \mathrm{J}/\psi $ and emitted forward neutrons. The values at $ -y $ and $ +y $ correspond to the $ \mathrm{J}/\psi $-Xn(Same) and $ \mathrm{J}/\psi $-Xn(Opposite) requirements, respectively. Data from the ALICE experiment [ALICE:2023gcs] is also displayed. The vertical bars and shaded boxes represent the statistical and systematic uncertainties, respectively. The horizontal bars show the bin widths. Theoretical predictions from the LTA [63,64] are shown by curves.

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Figure 1-b:
The total differential incoherent $ \mathrm{J}/\psi $ photoproduction cross section versus $ |y| $ (left) and $ y $ (right) in PbPb UPCs at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV. The right panel shows the results after disentangling the directional correlation between the produced $ \mathrm{J}/\psi $ and emitted forward neutrons. The values at $ -y $ and $ +y $ correspond to the $ \mathrm{J}/\psi $-Xn(Same) and $ \mathrm{J}/\psi $-Xn(Opposite) requirements, respectively. Data from the ALICE experiment [ALICE:2023gcs] is also displayed. The vertical bars and shaded boxes represent the statistical and systematic uncertainties, respectively. The horizontal bars show the bin widths. Theoretical predictions from the LTA [63,64] are shown by curves.

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Figure 2:
The incoherent $ \mathrm{J}/\psi $ photoproduction cross section per $ \gamma \text{Pb} $ interaction as a function of $ W^{\mathrm{Pb}}_{\gamma\mathrm{N}} $ (lower axis) or Bjorken $ x $ (upper axis) from the CMS measurement. The ALICE mid-rapidity ($ |y| < $ 0.9) data [70] measured at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 2.76 TeV is also displayed. The vertical bars, the shaded and open boxes represent the statistical, experimental, and theoretical (photon flux) uncertainties, respectively. Theoretical predictions from IA and LTA [63,64], and CGC [71,72] are shown by the curves, where the shaded bands are the theoretical uncertainties.

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Figure 3:
The ratio between incoherent and coherent $ \mathrm{J}/\psi $ photoproduction cross section as a function of $ W^{\mathrm{Pb}}_{\gamma\mathrm{N}} $ from the CMS measurement. The midrapidity data in AuAu UPCs at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 200 GeV from STAR experiment [74] and in PbPb UPCs at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 2.76 TeV from ALICE experiment [70] are also displayed. The vertical bars and the shaded and open boxes of CMS data represent the statistical, experimental, and theoretical (photon flux) uncertainties, respectively. The vertical bars of STAR and ALICE data represent the total uncertainties. Theoretical predictions from the IA [73,64], LTA [63,64], and CGC [71,72] are shown by curves, where the shaded bands are the theoretical uncertainties.

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Figure 4:
The nuclear suppression factor $ \mathrm{S^{\mathrm{J}/\psi}} $ of incoherent $ \mathrm{J}/\psi $ photoproduction as a function of Bjorken $ x $ extracted from the CMS measurement. The ALICE mid-rapidity ($ |y| < $ 0.9) data [70] is also displayed. The $ \mathrm{S^{\mathrm{J}/\psi}} $ of coherent $ \mathrm{J}/\psi $ photoproduction from CMS [31] and ALICE [32] experiments are also displayed. The vertical bars and shaded and open boxes represent the statistical, experimental systematic, and theoretical systematic uncertainties, respectively. The prediction of $ \mathrm{S^{\mathrm{J}/\psi}} $ (incoherent) from the LTA [63,64] and CGC [71,72] models are shown by curves, where the shaded bands are the theoretical uncertainties.

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Figure 5:
The corrected transverse momentum spectra of $ \mu^{+}\mu^{-} $ pairs with a dimuon invariant mass in the $ \mathrm{J}/\psi $ mass window of (2.95 $ < m_{\mu^{+}\mu^{-}} < $ 3.25 GeV) in 0nXn(Same) and 0nXn(Opposite) events. The results of the fit are shown by the various curves. The vertical bars on the data points represent statistical uncertainty.

png pdf
Figure 5-a:
The corrected transverse momentum spectra of $ \mu^{+}\mu^{-} $ pairs with a dimuon invariant mass in the $ \mathrm{J}/\psi $ mass window of (2.95 $ < m_{\mu^{+}\mu^{-}} < $ 3.25 GeV) in 0nXn(Same) and 0nXn(Opposite) events. The results of the fit are shown by the various curves. The vertical bars on the data points represent statistical uncertainty.

png pdf
Figure 5-b:
The corrected transverse momentum spectra of $ \mu^{+}\mu^{-} $ pairs with a dimuon invariant mass in the $ \mathrm{J}/\psi $ mass window of (2.95 $ < m_{\mu^{+}\mu^{-}} < $ 3.25 GeV) in 0nXn(Same) and 0nXn(Opposite) events. The results of the fit are shown by the various curves. The vertical bars on the data points represent statistical uncertainty.
Summary
In summary, this note presents the first energy-dependent measurement of the incoherent $ \mathrm{J}/\psi $ photoproduction off lead nuclei, obtained from PbPb UPCs at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV using forward neutron tagging. The production cross section is reported as a function of $ W^{\mathrm{Pb}}_{\gamma\mathrm{N}} $ in the range of 40 $ < W^{\mathrm{Pb}}_{\gamma\mathrm{N}} < $ 400 GeV (corresponding to 5.8 $ \times $ 10$^{-3} $ $> x >$ 6.5 $\times$ 10$^{-5} $). The ratio of incoherent-to-coherent $ \mathrm{J}/\psi $ photoproduction cross sections, which directly probes the fluctuation of gluon field density, remains approximately constant at 0.3--0.5. This indicates similar $ x $ evolution for gluonic structure at nuclear and subnuclear levels, which challenges the notion of reaching the BDL. Incoherent $ \mathrm{J}/\psi $ photoproduction shows stronger suppression at lower $ x $ compared to the impulse approximation and a greater relative suppression at higher $ x $ compared to coherent photoproduction. Theoretical models, including nucleon substructure fluctuations, gluon saturation and nuclear shadowing, only partially account for the observed data, highlighting the need for further theoretical development.
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