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

Biswarup Paul

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

classification ✦ hep-ph nucl-ex

keywords upsiloncross-sectioncross-sectionsfeed-downproductionratioscollisionscontributions

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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: 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: 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: 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: (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: (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: 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: (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.

Desk Editor's Note private letter to a colleague

This is a careful LO NRQCD phenomenology paper that reproduces LHC Υ data within scale-variation bands after including feed-down, but the uncertainty prescription is the usual one and does not benchmark against NLO.

read the letter

The paper runs a systematic leading-order NRQCD calculation for Υ(1S,2S,3S) production at LHC energies, folding in feed-down from higher bottomonium states and comparing both absolute cross sections and ratios to ALICE, ATLAS, CMS, and LHCb measurements. It reports that the data sit inside the bands obtained by varying factorization and renormalization scales by a factor of two, for pT above 4 GeV, and notes that the ratios flatten above roughly 40 GeV. That is the main result on offer: a consistent numerical exercise across several datasets and states using the established framework. The feed-down treatment is explicit and the ratio plots are a useful addition for anyone who needs quick reference numbers. The work is straightforward and the implementation appears reproducible from the description. The soft spot is exactly the one the stress-test flags. At LO the scale variation is large, but literature on quarkonium shows that NLO corrections can shift both normalization and shape by tens of percent even after scale variation. Without an explicit NLO comparison or an alternative uncertainty estimate, the statement that the data are “well described within uncertainties” rests on the assumption that the LO bands are conservative rather than optimistic. The long-distance matrix elements are taken from prior fits, so the exercise is closer to a consistency check than an independent test. For a reader who already works in this subfield and wants a single reference that collects the LHC bottomonium data with standard LO inputs, the paper is serviceable. It does not open new theoretical ground or resolve the known tension between LO and data at moderate pT. I would send it to a referee who knows the NRQCD literature; the calculation itself is solid enough to merit that step, even if the final claims need the usual caveats about higher orders.

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)

Reference graph

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