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Production of Upsilon States in p+p collisions at \sqrt{s}=500 GeV with STAR: Cross Sections, Ratios, and Multiplicity Dependenc

Updated on Mon, 2025-04-28 03:22. Originally created by lkosarz on 2020-02-28 16:03.

This is the webpage for collecting documents for the paper review process of:

"Production of Upsilon States in p+p collisions at \sqrt{s} = 500 GeV with STAR: Cross Sections, Ratios, and Multiplicity Dependence"

PAs: Leszek Kosarzewski*, Jaroslav Bielcik, Daniel Kikoła, Manuel Calderon

*leszek.kosarzewski@gmail.com

Target journal: Physical Review D
Alternative journal: European Physical Journal C

Overleaf paper draft (GPC only): https://www.overleaf.com/project/65e67f4b53da778a1ad4a344

Paper draft: drupal.star.bnl.gov/STAR/system/files/Upsilon500_Paper_LK_v19.pdf
Technical notes: https://drupal.star.bnl.gov/STAR/system/files/Upsilon500_TechNotes_LK_v4.pdf
Proposal presentation: drupal.star.bnl.gov/STAR/system/files/Upsilon_PWGC_LK_2021_5_14.pdf

Responses to Peer Review:
https://drupal.star.bnl.gov/STAR/system/files/ResponseReview1.docx
https://drupal.star.bnl.gov/STAR/system/files/ResponseReview1.pdf

Responses to Collabration review:
drupal.star.bnl.gov/STAR/system/files/Responses_Creighton.docx
drupal.star.bnl.gov/STAR/system/files/Responses_IISER_Berhampur.docx
drupal.star.bnl.gov/STAR/system/files/Responses_Lehigh.docx
drupal.star.bnl.gov/STAR/system/files/Responses_SCNU.docx
drupal.star.bnl.gov/STAR/system/files/Responses_UIC.docx

Responses to GPC: drupal.star.bnl.gov/STAR/system/files/GPC_comments_2024.7.9.pdf
drupal.star.bnl.gov/STAR/system/files/GPC365_3rd_comment_Kong_response.docx
drupal.star.bnl.gov/STAR/system/files/Wangmei_Upsilon500_Paper_LK_v13.pdf
drupal.star.bnl.gov/STAR/system/files/Yi_comments_v14.docx
drupal.star.bnl.gov/STAR/system/files/Comments_Wangmei_v15.pdf

Responses to PWG comments to paper: https://drupal.star.bnl.gov/STAR/system/files/PWG_paper_responses_v6.pdf
Yi's comments to the paper: https://drupal.star.bnl.gov/STAR/system/files/PWG_paper_responses_v8_Yi.pdf
Isaac's comments to the paper: https://drupal.star.bnl.gov/STAR/system/files/PWG_paper_responses_v10_Isaac.pdf

Paper draft diff: https://drupal.star.bnl.gov/STAR/system/files/diff_Upsilon500_Paper_LK_v19-18.pdf
Paper draft (previous version): drupal.star.bnl.gov/STAR/system/files/Upsilon500_Paper_LK_v18.pdf

Responses to PWG comments to Technical notes: https://drupal.star.bnl.gov/STAR/system/files/PWG_notes_responses_v1.pdf
https://drupal.star.bnl.gov/STAR/system/files/PWG_notes_responses_v2.pdf

Technical notes diff: https://drupal.star.bnl.gov/STAR/system/files/diff_Upsilon500_TechNotes_LK_v2-4.pdf
Technical notes (previous version): drupal.star.bnl.gov/STAR/system/files/Upsilon500_TechNotes_LK.pdf

Analysis code: $CVSROOT/offline/paper/psn0826

Abstract:
We report measurements of $\varUpsilon(1S)$, $\varUpsilon(2S)$ and $\varUpsilon(3S)$ production in \textit{$p+p$} collisions at $\sqrt{s}=500\:\mathrm{GeV}$ by the STAR experiment in year 2011, corresponding to an integrated luminosity $\mathcal{L}_{int}=13\:\mathrm{pb^{-1}}$.
The results provide precise cross sections, transverse momentum ($p_{T}$) and rapidity ($y$) spectra, as well as cross section ratios for $p_{\mathrm{T}}<10\:\gevc$ and $|y|<1$.
The dependence of the $\varUpsilon$ yield on charged particle multiplicity has also been measured, offering new insights into the mechanisms of quarkonium production.
The data are compared to various theoretical models: the Color Evaporation Model (CEM) accurately describes the $\varUpsilon(1S)$ production, while the Color Glass Condensate + Non-relativistic Quantum Chromodynamics (CGC+NRQCD) model overestimates the data, particularly at low $p_{T}$.
Conversely, the Color Singlet Model (CSM) underestimates the rapidity dependence.
These discrepancies highlight the need for further development in understanding the production dynamics of heavy quarkonia in high-energy hadronic collisions.
The trend in the multiplicity dependence is consistent with CGC/Saturation and String Percolation models or $\varUpsilon$ production happening in multiple parton interactions modeled by PYTHIA8.

Table 1:
Summary of systematic uncertainties on the $\varUpsilon(1S+2S+3S)$ cross section vs. $p_{T}$ and $y$.

pT [GeV/c]
Uncertainty 0-10 0-2 2-4 4-6 6-8 8-10
Raw yield extraction ±1.2% ±4.1% ±2.0% ±1.0% ±0.1% ±5.9%
Fixed Υ(2S)/Υ(3S) ±0.3% ±0.3% ±0.9% ±0.3% ±2.8% ±0.9%
pT smearing ±1.2% ±1.2% ±0.8% ±0.5% ±0.7% ±0.5%
Tracking ±1.3% ±1.4% ±1.3% ±1.3% ±1.4% ±1.3%
Polarization ±0.3% ±1.5% ±0.2% ±0.4% ±0.5% ±0.5%
Trigger ±7.6% ±17.0% ±8.0% ±2.9% ±1.4% ±0.9%
Total ±7.9% ±17.6% ±8.4% ±3.4% ±3.5% ±6.2%
|y|<0.5 0.5<|y|<1.0
±0.3% ±2.8%
±0.7% ±1.3%
±0.7% ±0.9%
±1.3% ±1.3%
±0.1% ±1.2%
±9.4% ±5.5%
±9.6% ±6.0%


Table 2:
Summary of global (correlated) systematic uncertainties on the $\varUpsilon(1S+2S+3S)$ cross section.

Uncertainty Effect
Luminosity ±8%
Vertex ±1%
Tracking efficiency const. ±10%
Acceptance ±3%
nσe cut ±3.6%



Table 3:
Summary of systematic uncertainties on the $\normupsAll$.

Uncertainty 0 − ⟨Nch⟩ ⟨Nch⟩ − 2 ⟨Nch⟩ 2 ⟨Nch⟩ − 3 ⟨Nch⟩ 3 ⟨Nch⟩ − 8 ⟨Nch⟩
Number of iterations ±1.3% ±1.3% ±0.5% ±0.5%
Reconstruction
efficiency		 ±0.2% ±0.6% ±0.4% ±3.8%
Tracking const. ±9.2% ±4.9% ±2.8% ±0.4%
Tracking vs. pT ±1% ±1% ±1% ±14%
Nch from NBD ±0.3% ±1.8% ±10% ±6.6%
Raw yield extraction ±1.1% ±2.5% ±0.2% ±15.7%
pT smearing ±0.3% ±0.3% ±0.2% ±1.8%
Fixed Υ(2S)/Υ(3S) ±0.4% ±0.4% ±2.7% ±10.8%
4Cx tune ±4% ±0.2% ±3.5% ±13.1%
Total ±10.3% ±6.1% ±11.4% ±28.1%



Table 4:
Summary of systematic uncertainties on the normalized multiplicity.

Uncertainty 0 − ⟨Nch⟩ ⟨Nch⟩ − 2 ⟨Nch⟩ 2 ⟨Nch⟩ − 3 ⟨Nch⟩ 3 ⟨Nch⟩ − 8 ⟨Nch⟩
Iterations ±0.1% ±0.4% ±0.3% ±0.2%
Tracking ±3.5% ±3.7% ±4.0% ±3.6%
Nch from NBD ±0.1% ±2.7% ±2.1% ±2.6%
4Cx tune ±1.9% ±0.0% ±0.6% ±0.3%
Total ±4.0% ±4.6% ±4.6% ±4.5%



Figure 1:
Invariant mass $\mee$ distribution for unlike-sign (black full circles) and like-sign (blue hollow diamonds) electron pairs.
The curves correspond to combinatorial background (blue dashed-dotted line), correlated background (black dotted line),
$\varUpsilon(1S)$ (green), $\varUpsilon(2S)$ (orange), and $\varUpsilon(3S)$ (purple).
 The total (red) is a sum of the above components. Each curve has a corresponding uncertainty band obtained via. MC sampling technique and includes correlations between parameters.




Figure 2:
(a) Electron efficiencies vs. $p_{\mathrm{T}}^{e_{MC}}$. Illustrated is the combined effect of successive application of the acceptance and tracking efficiency (black diamonds), $E_{tow}/E_{clu}$ (blue rectangles), $E_{clu}/p$ (green circles), $R_{SMD}$ (brown stars) and $n\sigma_{e}$ along with L0 High Tower match (red crosses) requirements.
(b) Reconstruction efficiencies of $\varUpsilon(1S)$ (closed diamonds), $\varUpsilon(2S)$ (open diamonds), and $\varUpsilon(3S)$ (open circles) vs. $p_{\mathrm{T}}^{\varUpsilon_{MC}}$.


Figure 3:
Integrated cross section of $\varUpsilon(1S+2S+3S)$ measured by STAR at $\sqrt{s}=200\:\mathrm{GeV}$~\cite{bib:Ups:STAR:dAu} and $\sqrt{s}=500\:\mathrm{GeV}$ compared to other experimental results~\cite{bib:Ups:AtlasRatio, bib:Ups:CMS:Xsec, bib:UpsCDF, bib:Ups:CFSpFe, bib:Ups:CFSppt, bib:Ups:CFSpp, bib:Ups:CFSpPtCu, bib:Ups:E605_pCu, bib:Ups:E605_pBe, bib:Ups:CCOR2, bib:Ups:CCOR2, bib:Ups:E866}, CEM calculation (blue line)~\cite{bib:Frawley2008} and CSM calculation at LO (red dotted line and band) and NLO (red lines: solid, dashed, dotted)~\cite{bib:lansberg:energy} plotted vs. center of mass energy.


Figure 4:
(a) The $p_{\mathrm{T}}$ differential cross sections of $\varUpsilon(1S+2S+3S)$ (red circles), $\varUpsilon(2S+3S)$ (blue squares), $\varUpsilon(1S)$ (green diamonds), $\varUpsilon(2S)$ (black stars) and $\varUpsilon(3S)$ (brown crosses).
(b) Rapidity spectra for combined $\varUpsilon(1S+2S+3S)$ and each state separately (same as above). The hollow points at negative rapidity are mirror reflections of the forward rapidity data.

Figure 5:
(a) The $\varUpsilon(1S)$ data are compared to the CEM calculation for inclusive $\varUpsilon(1S)$ (gray band)~\cite{bib:CEM_shadow,bib:vogt:private}. The results are also compared to a CGC+NRQCD calculation for direct $\varUpsilon(1S)$ (purple shaded band) ~\cite{bib:upsCGC,bib:jpsi_cgc,bib:YQMa}.
(b) Comparison of a CGC+NRQCD calculation for $\varUpsilon(2S)$ (light blue shaded band) to STAR data.
(c) STAR data comparison with a CGC+NRQCD calculation for $\varUpsilon(3S)$ (brown shaded band).

Figure 6:
(a) The $\varUpsilon(1S)$ data are compared to CEM calculation for inclusive $\varUpsilon(1S)$ (gray band)~\cite{bib:CEM_shadow,bib:vogt:private} and CGC+NRQCD predictions for direct $\varUpsilon(1S)$ (purple shaded band) ~\cite{bib:upsCGC,bib:jpsi_cgc,bib:YQMa} and Color Singlet model calculations at LO (teal band) and NLO (gray checked band)~\cite{bib:ups_csm}.
(b) Comparison of CGC+NRQCD calculation for $\varUpsilon(2S)$ (light blue shaded band) to STAR data.
(c) STAR data comparison to CGC+NRQCD calculation for $\varUpsilon(3S)$ (brown shaded band).

Figure 7:
$\varUpsilon$ invariant cross sections scaled with $\sqrt{s}^{n}$, where $n=5.6$ vs. $x_{\mathrm{T}}$ for $\varUpsilon(1S)$ (green closed diamonds), $\varUpsilon(2S)$ (black open diamonds) and $\varUpsilon(3S)$ (brown open circles) measured by STAR.
The data are compared with $\varUpsilon(1S)$ results from Intersecting Storage Rings (ISR) (red open diamonds)~\cite{bib:UpsISR} and $\varUpsilon(1S)$, $\varUpsilon(2S)$, $\varUpsilon(3S)$ results measured by CDF (green open diamonds, blue open squares, black open crosses)~\cite{bib:UpsCDF} and ATLAS (green closed upward triangles, blue closed downward triangles, black open circles)~\cite{bib:Ups:AtlasRatio}.

Figure 8:
(a) Cross section ratios of $\frac{\varUpsilon(nS)}{\varUpsilon(1S)}$ as a function of energy, where
the STAR measured ratios are $\frac{\varUpsilon(2S)}{\varUpsilon(1S)}$ (red cross), $\frac{\varUpsilon(3S)}{\varUpsilon(1S)}$ (green cross) and $\frac{\varUpsilon(2S+3S)}{\varUpsilon(1S)}$ (blue cross) compared to fits to the world data from~\cite{bib:Ups:Ratios} (red, green and blue lines respectively) with STAR data included.
The uncertainties on the fits are shown as bands around each line.
Measurements by other experiments in $p+\bar{p}$~\cite{bib:Ups:CDFratio}, \textit{$p+p$}~\cite{bib:Ups:CFSpp, bib:Ups:E866, bib:UpsCMS_2010, bib:Ups:AtlasRatio, bib:Ups:LHCbRatio, bib:Ups:LHCb8Tev} are also shown along with $p+A$~\cite{bib:Ups:E605_pBe, bib:Ups:E605_pCu, bib:Ups:E866, bib:Ups:CFSppt}.
(b) Dependence of $\frac{\varUpsilon(nS)}{\varUpsilon(1S)}$ cross section ratios on charged particle multiplicity. The STAR data for $\frac{\varUpsilon(2S+3S)}{\varUpsilon(1S)}$ (blue crosses), $\frac{\varUpsilon(2S)}{\varUpsilon(1S)}$ (red crosses) and $\frac{\varUpsilon(3S)}{\varUpsilon(1S)}$ (green crosses) are fitted with a linear function (blue, red and green lines).
The $\frac{\varUpsilon(2S)}{\varUpsilon(1S)}$ and $\frac{\varUpsilon(3S)}{\varUpsilon(1S)}$ data are shifted horizontally along $N_{ch}$ by -1 and +1 for clarity.

Figure 9:
(a) Yield as a function of $N_{ch}$ measured in \textit{$p+p$} collisions. STAR $\varUpsilon$ results at $\sqrt{s}=500\:\mathrm{GeV}$ are compared to $J/\psi$ at $\sqrt{s}=200\:\mathrm{GeV}$~\cite{bib:Jpsi:pp:STAR:mult} as well as $J/\psi$ ALICE~\cite{bib:ALICE:JpsiEventAct} and $\varUpsilon$ at CMS~\cite{bib:Ups:CMSactivity}.
(b) STAR $\varUpsilon$ results are compared to model calculations: PYTHIA8 with STAR Heavy Flavor Tune~\cite{bib:STAR_HFtune}, CGC-based Saturation model~\cite{bib:EventAct:Jpsi:3pom,bib:EventAct:QQ:CGC} and Percolation model for $J/\psi$~\cite{bib:PercolationJpsi}.

Conclusions:

  • Spectra:
    • First $p_{T}$ spectrum measurement of $\varUpsilon$ states at RHIC energy
    • Both $p_{T}$ and rapidity spectra are reasonably well described by CEM calculation for inclusive $\varUpsilon(1S)$
    • CGC+NRQCD calculation for direct $\varUpsilon(nS)$ overestimates the data
    • CSM LO and NLO below the data
    • No $x_{T}$ scaling observed in the measured $x_{T}$ range
  • Ratios:
    • No significant dependence of $\varUpsilon(nS)/\varUpsilon(1S)$ cross section ratios on multiplicity observed
  • Normalized $\varUpsilon$ yield vs. normalized multiplicity:
    • Shows similar trend to $J/\psi$ and LHC data and models
    • Data for $p_{T}>0\:\mathrm{GeV/c}$ closer to linear dependence
    • $\varUpsilon(1S)$ data for $p_{T}>4\:\mathrm{GeV/c}$ indication of faster than linear rise       
    • Data qualitatively described by the models
Groups: