pith. sign in

arxiv: 2604.16019 · v1 · submitted 2026-04-17 · ✦ hep-ph · nucl-ex

Systematic study of bottomonium production in proton-proton collisions at LHC energies

Biswarup Paul This is my paper

Pith reviewed 2026-05-10 08:50 UTC · model grok-4.3

classification ✦ hep-ph nucl-ex
keywords upsiloncross-sectioncross-sectionsfeed-downproductionratioscollisionscontributions
0
0 comments X

The pith

LO NRQCD calculations of Υ(nS) cross sections and ratios at LHC energies describe experimental data within uncertainties for pT > 4 GeV, showing saturation in ratios beyond pT ≈ 40 GeV.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Bottomonium particles are bound states of bottom quarks and their antiparticles, observed as Υ resonances with different excitation levels. The study applies non-relativistic quantum chromodynamics at leading order to predict how often these particles form in high-energy proton collisions at the LHC. Calculations include both direct production and feed-down decays from heavier states like Υ(3S) or chi_b states into lighter ones. Results are compared to measurements from four major LHC experiments across various energies and rapidities. Agreement holds when allowing for uncertainties from the choice of energy scales in the calculation, particularly at transverse momenta above 4 GeV. The ratios of cross sections between different Υ states become roughly constant at very high momenta.

Core claim

It is found that the experimental cross-sections and cross-section ratios are well described within the theoretical uncertainties arising due to the choices of the factorization and renormalization scales for pT > 4 GeV and pT > 0 GeV, respectively. Furthermore, the cross-section ratios exhibit a clear saturation behavior beyond pT ≈ 40 GeV.

Load-bearing premise

That leading-order NRQCD factorization with the included feed-down contributions and scale variations is sufficient to describe the data without significant higher-order corrections or unaccounted effects across the full pT range studied.

Figures

Figures reproduced from arXiv: 2604.16019 by Biswarup Paul.

Figure 1
Figure 1. Figure 1: Differential production cross-section of Υ(1S ) as a function of pT compared with the measurements by ATLAS [43], CMS [45], LHCb [50] and ALICE [41] in pp collisions at √ s = 7 TeV. The vertical error bars on the data points represent the statistical errors on the measurements, while the boxes correspond to the systematic uncertainties. The calculations corresponding to the sum of all contributions are sho… view at source ↗
Figure 2
Figure 2. Figure 2: Differential production cross-section of Υ(2S ) as a function of pT compared with the measurements by ATLAS [43], CMS [45], LHCb [50] in p-p collisions at √ s = 7 TeV. 7 [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Differential production cross-section of Υ(3S ) as a function of pT compared with the measurements by ATLAS [43], CMS [45], LHCb [50] in p-p collisions at √ s = 7 TeV. 8 [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: (Color online) Υ(2S )/Υ(1S ) production cross-section ratio (top panel) and Υ(3S )/Υ(1S ) production cross-section ratio (bottom panel) as a function of pT compared with the measurements by ATLAS [43] in pp collisions at √ s = 7 TeV. 9 [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: (Color online) Υ(2S )/Υ(1S ) production cross-section ratio (top panel), Υ(3S )/Υ(1S ) production cross-section ratio (middle panel) and Υ(3S )/Υ(2S ) production cross-section ratio (bottom panel) as a function of pT compared with the measurements by LHCb [50] and CMS [45] in pp collisions at √ s = 7 TeV. 10 [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Differential production cross-section of Υ(1S ) (top), Υ(2S ) (middle) and Υ(3S ) (bottom) as a function of pT compared with the measurements by LHCb [50] and CMS [47] in pp collisions at √ s = 13 TeV. 12 [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: (Color online) Υ(2S )/Υ(1S ) production cross-section ratio (top) and Υ(3S )/Υ(1S ) production cross-section ratio (middle) as a function of pT compared with the measurements by LHCb [52] and CMS [47] and prediction for Υ(3S )/Υ(2S ) production cross-section ratio (bottom) in pp collisions at √ s = 13 TeV. 13 [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗
read the original abstract

We present a comprehensive study of $\Upsilon(nS)$ ($n$ = 1, 2, 3) production in proton-proton ($pp$) collisions at various LHC energies and rapidity ranges within the framework of leading order non-relativistic quantum chromodynamics (NRQCD) factorization. The transverse momentum ($p_{\rm T}$)-dependent production cross-sections are calculated, incorporating both direct and feed-down contributions. Specifically, feed-down from $\Upsilon(2S)$, $\Upsilon(3S)$, $\chi_{bJ}(1P)$, and $\chi_{bJ}(2P)$ states to $\Upsilon(1S)$ is included, while $\Upsilon(2S)$ receives contributions from $\Upsilon(3S)$ and $\chi_{bJ}(2P)$. No significant feed-down is considered for $\Upsilon(3S)$. The computed cross-sections and cross-section ratios among different $\Upsilon$ states are compared with experimental measurements from ALICE, ATLAS, CMS and LHCb. It is found that the experimental cross-sections and cross-section ratios are well described within the theoretical uncertainties arising due to the choices of the factorization and renormalization scales for $p_{\rm T}$ $>$ 4 GeV and $p_{\rm T}$ $>$ 0 GeV, respectively. Furthermore, the cross-section ratios exhibit a clear saturation behavior beyond $p_{\rm T}$ $\approx$ 40 GeV.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on the applicability of LO NRQCD factorization, universality of long-distance matrix elements, and specific assumptions about which feed-down channels contribute; these are standard in the field but not independently derived here.

free parameters (2)
  • factorization and renormalization scales
    Varied to estimate theoretical uncertainty; specific central values chosen by hand.
  • long-distance matrix elements for Υ and χb states
    Standard NRQCD parameters, taken from or fitted to prior data.
axioms (2)
  • domain assumption Leading-order NRQCD factorization separates short-distance coefficients from long-distance matrix elements for these processes
    Invoked as the framework for all calculations in the abstract.
  • domain assumption Feed-down contributions are limited to the listed states with no significant others for Υ(3S)
    Explicitly stated in the abstract as the basis for the cross-section computations.

pith-pipeline@v0.9.0 · 5550 in / 1481 out tokens · 47978 ms · 2026-05-10T08:50:48.859552+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

70 extracted references · 70 canonical work pages · 5 internal anchors

  1. [1]

    G. T. Bodwin, E. Braaten, and G. P. Lepage, Phys. Rev. D51 1125 (1995)

    work page 1995

  2. [2]

    Baier, R

    R. Baier, R. Ruckl, Z. Phys. C 19, 251 (1983)

    work page 1983

  3. [3]

    Berger, D.L

    E.L. Berger, D.L. Jones, Phys. Rev. D 23, 1521–1530 (1981)

    work page 1981

  4. [4]

    Barbieri, R

    R. Barbieri, R. Gatto, E. Remiddi, Phys. Lett. B 61, 465 (1976)

    work page 1976

  5. [5]

    Bodwin, E

    G.T. Bodwin, E. Braaten, G.P. Lepage, Phys. Rev. D 46, 1914 (1992), arXiv:hep-lat/9205006

    work page internal anchor Pith review arXiv 1914

  6. [6]

    Fragmentation production of J/psi and psi' at the Tevatron

    E. Braaten, M.A. Doncheski, S. Fleming, M.L. Mangano, Phys. Lett. B 333, 548 (1994), arXiv:hep-ph/9405407

    work page Pith review arXiv 1994

  7. [7]

    D.P. Roy, K. Sridhar, Phys. Lett. B 339, 141 (1994), arXiv:hep- ph/9406386

    work page arXiv 1994

  8. [8]

    Cacciari, M

    M. Cacciari, M. Greco, Phys. Rev. Lett. 73, 1586 (1994), arXiv:hep- ph/9405241

    work page arXiv 1994

  9. [9]

    Abe et al

    F. Abe et al. (CDF Collaboration), Phys. Rev. Lett. 79, 572 (1997)

    work page 1997

  10. [10]

    Abe et al

    F. Abe et al. (CDF Collaboration), Phys. Rev. Lett. 79, 578 (1997)

    work page 1997

  11. [11]

    Braaten and S

    E. Braaten, S. Fleming, Phys. Rev. Lett. 74, 3327 (1995), arXiv:hep- ph/9411365

    work page arXiv 1995

  12. [12]

    Campbell, F

    J.M. Campbell, F. Maltoni, F. Tramontano, Phys. Rev. Lett. 98, 252002 (2007)

    work page 2007

  13. [13]

    Gong, J.X

    B. Gong, J.X. Wang, Phys. Rev. Lett. 100, 232001 (2008). 11 0 5 10 15 20 25 30 35 40 45 50 (GeV) Tp8 −107 −106 −105 −104 −103 −102 −101 −101 10 2 103

    work page 2008

  14. [14]

    (nb/GeV) y d T p /(d σ d = 13 TeV spp <4.5 y2<(1S) ΥLHCb, Prompt (1S) ΥNRQCD, Prompt (1S) direct ΥNRQCD, (2S) Υ(1S) from ΥNRQCD, (3S) Υ(1S) from ΥNRQCD, (1P) b0χ(1S) from ΥNRQCD, (1P) b1χ(1S) from ΥNRQCD, (1P) b2χ(1S) from ΥNRQCD, (2P) b0χ(1S) from ΥNRQCD, (2P) b1χ(1S) from ΥNRQCD, (2P) b2χ(1S) from ΥNRQCD, 0 20 40 60 80 100 120 (GeV) Tp8 −107 −106 −105 −...

    work page

  15. [15]

    (nb/GeV) y d T p /(d σ d = 13 TeV spp |<1.2 y|(1S) ΥCMS, Prompt (1S) ΥNRQCD, Prompt (1S) direct ΥNRQCD, (2S) Υ(1S) from ΥNRQCD, (3S) Υ(1S) from ΥNRQCD, (1P) b0 χ(1S) from ΥNRQCD, (1P) b1 χ(1S) from ΥNRQCD, (1P) b2 χ(1S) from ΥNRQCD, (2P) b0 χ(1S) from ΥNRQCD, (2P) b1 χ(1S) from ΥNRQCD, (2P) b2 χ(1S) from ΥNRQCD, 0 5 10 15 20 25 30 35 40 45 50 (GeV) Tp7 −1...

    work page

  16. [16]

    (nb/GeV) y d T p /(d σ d = 13 TeV spp <4.5 y2<(2S) ΥLHCb, inclusive (2S) ΥNRQCD, inclusive (2S) direct ΥNRQCD, (3S) Υ(2S) from ΥNRQCD, (2P) b0χ(2S) from ΥNRQCD, (2P) b1χ(2S) from ΥNRQCD, (2P) b2χ(2S) from ΥNRQCD, 0 20 40 60 80 100 120 (GeV) Tp8 −107 −106 −105 −104 −103 −102 −101 −101 10 2 103 104

    work page

  17. [17]

    (nb/GeV) y d T p /(d σ d = 13 TeV spp |<1.2 y|(2S) ΥCMS, Prompt (2S) ΥNRQCD, Prompt (2S) direct ΥNRQCD, (3S) Υ(2S) from ΥNRQCD, (2P) b0χ(2S) from ΥNRQCD, (2P) b1χ(2S) from ΥNRQCD, (2P) b2χ(2S) from ΥNRQCD, 0 5 10 15 20 25 30 35 40 45 50 (GeV) Tp6 −105 −104 −103 −102 −101 −101 10 2

    work page

  18. [18]

    (nb/GeV) y d T p /(d σ d = 13 TeV spp <4.5 y2<(3S) ΥLHCb, inclusive (3S) ΥNRQCD, inclusive 0 20 40 60 80 100 120 (GeV) Tp8 −107 −106 −105 −104 −103 −102 −101 −101 10 2 103 104

    work page

  19. [19]

    (nb/GeV) y d T p /(d σ d = 13 TeV spp |<1.2 y|(3S) ΥCMS, Prompt (3S) ΥNRQCD, Prompt Figure 6: Di fferential production cross-section of Υ(1S ) (top), Υ(2S ) (middle) and Υ(3S ) (bottom) as a function of pT compared with the measurements by LHCb [50] and CMS [47] in pp collisions at √s = 13 TeV . 12 0 2 4 6 8 10 12 (GeV) Tp0.1 0.15 0.2 0.25 0.3 0.35 0.4 0....

    work page

  20. [20]

    Polarizations of J/psi and psi(2S) Mesons Produced in ppbar Collisions at 1.96 TeV

    A. Abulencia et al. (CDF Collaboration), Phys. Rev. Lett. 99, 132001 (2007), arXiv:0704.0638 [hep-ex]

    work page Pith review arXiv 2007

  21. [21]

    Kang, J.W

    Z.B. Kang, J.W. Qiu, G. Sterman, Phys. Rev. Lett. 108, 102002 (2012)

    work page 2012

  22. [22]

    Gong, X.Q

    B. Gong, X.Q. Li, J.X. Wang, Phys. Lett. B 673, 197 (2009)

    work page 2009

  23. [23]

    Y .Q. Ma, K. Wang, K.T. Chao, Phys. Rev. D83, 111503 (2011)

    work page 2011

  24. [24]

    Butenschoen, B.A

    M. Butenschoen, B.A. Kniehl, Phys. Rev. Lett. 108, 172002 (2012)

    work page 2012

  25. [25]

    Chao, Y .Q

    K.T. Chao, Y .Q. Ma, H.S. Shao et al. , Phys. Rev. Lett. 108, 242004 (2012)

    work page 2012

  26. [26]

    Gong, L.P

    B. Gong, L.P. Wan, J.X. Wang et al., Phys. Rev. Lett.110, 042002 (2013)

    work page 2013

  27. [27]

    Measurement of J/Psi and Psi(2S) Polarization in ppbar Collisions at sqrt(s) = 1.8 TeV

    T. A ffolder et al. (CDF Collaboration), Phys. Rev. Lett. 85, 2886 (2000), arXiv:hep-ex/0004027

    work page Pith review arXiv 2000

  28. [28]

    Abelev et al

    B. Abelev et al. (ALICE Collaboration), Phys. Rev. Lett. 108, 082001 (2012)

    work page 2012

  29. [29]

    Aaijet al.(LHCb), Eur

    R. Aaij et al. (LHCb Collaboration), arXiv:1409.3612

    work page internal anchor Pith review arXiv

  30. [30]

    Butenschoen, Z.G

    M. Butenschoen, Z.G. He, B.A. Kniehl, Phys. Rev. Lett. 114, 092004 (2014)

    work page 2014

  31. [31]

    Han, Y .Q

    H. Han, Y .Q. Ma, C. Meng et al., Phys. Rev. Lett. 114, 092005 (2015)

    work page 2015

  32. [32]

    Zhang, Z

    H.F. Zhang, Z. Sun, W.L. Sang et al., Phys. Rev. Lett.114, 092006 (2014)

    work page 2014

  33. [33]

    Gong and J.-X

    B. Gong and J.-X. Wang, Phys. Rev. D 78, 074011 (2008)

    work page 2008

  34. [34]

    Artoisenet, J

    P. Artoisenet, J. M. Campbell, J. P. Lansberg, F. Maltoni and F. Tramon- tano, Phys. Rev. Lett. 101, 152001 (2008)

    work page 2008

  35. [35]

    Gong, J.-X

    B. Gong, J.-X. Wang, and H.-F. Zhang, Phys. Rev. D 83, 114021 (2011)

    work page 2011

  36. [36]

    Wang, Y .-Q

    K. Wang, Y .-Q. Ma, and K.-T. Chao, Phys. Rev. D85, 114003 (2012)

    work page 2012

  37. [37]

    Gong, L.P

    B. Gong, L.P. Wan, J.X. Wang et al., Phys. Rev. Lett.112, 032001 (2014)

    work page 2014

  38. [38]

    Acosta et al

    D. Acosta et al. (CDF Collaboration), Phys. Rev. Lett.88, 161802 (2002)

    work page 2002

  39. [39]

    Aaltonen et al

    T. Aaltonen et al. (CDF Collaboration), Phys. Rev. Lett. 108, 151802 (2012)

    work page 2012

  40. [40]

    Chatrchyan et al

    S. Chatrchyan et al. (CMS Collaboration), Phys. Rev. Lett. 110, 081802 (2013), arXiv:1209.2922 [hep-ex]

    work page internal anchor Pith review arXiv 2013

  41. [41]

    Aaij et al

    R. Aaij et al. (LHCb collaboration), JHEP 88, 1410 (2014)

    work page 2014

  42. [42]

    Aaij et al

    R. Aaij et al. (LHCb collaboration), Eur. Phys. J. C, 74, 3092 (2014)

    work page 2014

  43. [43]

    Feng, J.X

    Y . Feng, J.X. Wang, B. Gong, Chin. Phys. C 39, 123102 (2015)

    work page 2015

  44. [44]

    Han, Y .-Q

    H. Han, Y .-Q. Ma, C. Meng et al. , Phys. Rev. D 94, 014028 (2016), arXiv:1410.8537[hep-ph]

    work page internal anchor Pith review arXiv 2016

  45. [45]

    Y . Feng, B. Gong, C. H. Chang, J.X. Wang, Chin. Phys. C 45, 013117 (2021)

    work page 2021

  46. [46]

    Aaij et al., JHEP 12, 110 (2017), arXiv:1709.01301 [hep-ex]

    R. Aaij et al., JHEP 12, 110 (2017), arXiv:1709.01301 [hep-ex]

    work page internal anchor Pith review arXiv 2017

  47. [47]

    Abelev et al., (ALICE Collaboration) Eur

    B. Abelev et al., (ALICE Collaboration) Eur. Phys. J. C 74, 2974 (2014)

    work page 2014

  48. [48]

    Adam et al., (ALICE Collaboration) Eur

    J. Adam et al., (ALICE Collaboration) Eur. Phys. J. C 76, 184 (2016)

    work page 2016

  49. [49]

    Aad et al

    G. Aad et al. (ATLAS Collaboration), Phys. Lett. B 705, 9 (2011),

    work page 2011

  50. [50]

    Aad et al

    G. Aad et al. (ATLAS Collaboration), Phys. Rev. D87, 052004 (2013),

    work page 2013

  51. [51]

    Khachatryan et al

    V . Khachatryan et al. (CMS Collaboration), Phys. Lett. B 727, 101-125 (2013),

    work page 2013

  52. [52]

    A. M. Sirunyan et al. (CMS Collaboration), JHEP 05, 013 (2017)

    work page 2017

  53. [53]

    A. M. Sirunyan et al. (CMS Collaboration), Phys. Lett. B780, 251 (2018),

    work page 2018

  54. [54]

    Aaij et al

    R. Aaij et al. (LHCb Collaboration), Eur. Phys. J. C 74, 2835 (2014)

    work page 2014

  55. [55]

    Aaij et al

    R. Aaij et al. (LHCb Collaboration), JHEP 07, 069 (2023)

    work page 2023

  56. [56]

    Aaij et al

    R. Aaij et al. (LHCb Collaboration), Eur. Phys. J. C 72, 2025 (2012)

    work page 2025

  57. [57]

    Aaij et al

    R. Aaij et al. (LHCb Collaboration), JHEP 06, 064 (2013)

    work page 2013

  58. [58]

    Aaij et al

    R. Aaij et al. (LHCb Collaboration), JHEP 07, 134 (2018)

    work page 2018

  59. [59]

    Paul et al., J

    B. Paul et al., J. Phys. G: Nucl. Part. Phys. 42, 065101 (2015)

    work page 2015

  60. [60]

    J. F. Owens Review of Modern Physics, V ol. 59, 465 (1987)

    work page 1987

  61. [61]

    H. L. Lai. et al., Phys. Rev. D 82, 054021 (2010)

    work page 2010

  62. [62]

    Yu. L. Dokshitzer, G. Marchesini, B. R. Webber, Nucl. Phys. B 469, 93 (1996)

    work page 1996

  63. [63]

    Baier and R

    R. Baier and R. Ruckl, Z. Phys. C 19, 251 (1983)

    work page 1983

  64. [64]

    Gastmans, W

    R. Gastmans, W. Troost and T. T. Wu, Nucl. Phys. B 291, 731 (1987)

    work page 1987

  65. [65]

    Humpert, Phys

    B. Humpert, Phys. Lett. B 184, 105 (1987)

    work page 1987

  66. [66]

    P. L. Cho and A. K. Leibovich, Phys. Rev. D 53, 6203 (1996)

    work page 1996

  67. [67]

    P. L. Cho and A. K. Leibovich, Phys. Rev. D 53, 150 (1996)

    work page 1996

  68. [68]

    Navas et al

    S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024)

    work page 2024

  69. [69]

    Braaten, S

    E. Braaten, S. Fleming, and A. K. Leibovich, Phys. Rev. D 63, 094006 (2001)

    work page 2001

  70. [70]

    Sharma and I

    R. Sharma and I. Vitev, Phys. Rev C 87, 044905 (2013). 14

    work page 2013