CMS-BPH-24-004

CMS-BPH-24-004 ; CERN-EP-2026-004
Measurement of the $ \Upsilon{\textrm{(1S)}} $, $ \Upsilon{\textrm{(2S)}} $, and $ \Upsilon{\textrm{(3S)}} $ differential cross sections in pp collisions at $ \sqrt{s} = $ 13.6 TeV
CMS Collaboration
27 January 2026
Submitted to the Journal of High Energy Physics
Abstract: The production cross sections of the $ \Upsilon{\textrm{(1S)}} $, $ \Upsilon{\textrm{(2S)}} $, and $ \Upsilon{\textrm{(3S)}} $ mesons are measured in proton-proton collisions at $ \sqrt{s}= $ 13.6 TeV, using a data sample collected in 2022 by the CMS experiment and corresponding to an integrated luminosity of 37.4 fb$ ^{-1} $. The measurement is performed in the $ \mu^{+}\mu^{-} $ decay channels, differentially as a function of transverse momentum in the 20--200 GeV range, in the $ \|y\| < $ 0.6 and 0.6 $ < \|y\| < $ 1.2 rapidity intervals.
Links: e-print arXiv:2601.20023 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; CADI line (restricted) ;

Figures & Tables	Summary	References	CMS Publications

Figures
png pdf	Figure 1: Invariant mass distributions of the dimuons measured in two illustrative $ p_{\mathrm{T}} $ and $ \|y\| $ ranges. The results of the fits are represented by the solid coloured lines (signal peaks), the dashed gray lines (background), and the solid black lines (total).
png pdf	Figure 1-a: Invariant mass distributions of the dimuons measured in two illustrative $ p_{\mathrm{T}} $ and $ \|y\| $ ranges. The results of the fits are represented by the solid coloured lines (signal peaks), the dashed gray lines (background), and the solid black lines (total).
png pdf	Figure 1-b: Invariant mass distributions of the dimuons measured in two illustrative $ p_{\mathrm{T}} $ and $ \|y\| $ ranges. The results of the fits are represented by the solid coloured lines (signal peaks), the dashed gray lines (background), and the solid black lines (total).
png pdf	Figure 2: Left: measured $ p_{\mathrm{T}} $-differential $ \Upsilon{\textrm{(1S)}} $ (red), $ \Upsilon{\textrm{(2S)}} $ (green), and $ \Upsilon{\textrm{(3S)}} $ (blue) cross sections times the $ \mu^{+}\mu^{-} $ decay branching fractions, per rapidity unit, in the 0--0.6 (filled circles) and 0.6--1.2 (open squares) $ \|y\| $ ranges. For visibility, the $ \Upsilon{\textrm{(1S)}} $ and $ \Upsilon{\textrm{(2S)}} $ values are scaled by factors of 100 and 10, respectively. Right: Corresponding $ \Upsilon{\textrm{(2S)}} $ over $ \Upsilon{\textrm{(1S)}} $ (green) and $ \Upsilon{\textrm{(3S)}} $ over $ \Upsilon{\textrm{(1S)}} $ (blue) ratios, in the 0--0.6 (filled circles) and 0.6--1.2 (open squares) $ \|y\| $ ranges. For visibility purposes, the data points are slightly displaced in the $ x $ axis. In both panels, the error bars represent the total uncertainties. The NRQCD curves are shown for illustration.
png pdf	Figure 2-a: Left: measured $ p_{\mathrm{T}} $-differential $ \Upsilon{\textrm{(1S)}} $ (red), $ \Upsilon{\textrm{(2S)}} $ (green), and $ \Upsilon{\textrm{(3S)}} $ (blue) cross sections times the $ \mu^{+}\mu^{-} $ decay branching fractions, per rapidity unit, in the 0--0.6 (filled circles) and 0.6--1.2 (open squares) $ \|y\| $ ranges. For visibility, the $ \Upsilon{\textrm{(1S)}} $ and $ \Upsilon{\textrm{(2S)}} $ values are scaled by factors of 100 and 10, respectively. Right: Corresponding $ \Upsilon{\textrm{(2S)}} $ over $ \Upsilon{\textrm{(1S)}} $ (green) and $ \Upsilon{\textrm{(3S)}} $ over $ \Upsilon{\textrm{(1S)}} $ (blue) ratios, in the 0--0.6 (filled circles) and 0.6--1.2 (open squares) $ \|y\| $ ranges. For visibility purposes, the data points are slightly displaced in the $ x $ axis. In both panels, the error bars represent the total uncertainties. The NRQCD curves are shown for illustration.
png pdf	Figure 2-b: Left: measured $ p_{\mathrm{T}} $-differential $ \Upsilon{\textrm{(1S)}} $ (red), $ \Upsilon{\textrm{(2S)}} $ (green), and $ \Upsilon{\textrm{(3S)}} $ (blue) cross sections times the $ \mu^{+}\mu^{-} $ decay branching fractions, per rapidity unit, in the 0--0.6 (filled circles) and 0.6--1.2 (open squares) $ \|y\| $ ranges. For visibility, the $ \Upsilon{\textrm{(1S)}} $ and $ \Upsilon{\textrm{(2S)}} $ values are scaled by factors of 100 and 10, respectively. Right: Corresponding $ \Upsilon{\textrm{(2S)}} $ over $ \Upsilon{\textrm{(1S)}} $ (green) and $ \Upsilon{\textrm{(3S)}} $ over $ \Upsilon{\textrm{(1S)}} $ (blue) ratios, in the 0--0.6 (filled circles) and 0.6--1.2 (open squares) $ \|y\| $ ranges. For visibility purposes, the data points are slightly displaced in the $ x $ axis. In both panels, the error bars represent the total uncertainties. The NRQCD curves are shown for illustration.
png pdf	Figure 3: Ratios of $ \Upsilon{\textrm{(1S)}} $ cross sections between this measurement, made at $ \sqrt{s} = $ 13.6 TeV, and previous measurements, made at 7 and 13 TeV [29,30], treating all uncertainties as uncorrelated. For visibility purposes, the data points are slightly displaced in the $ x $ axis.

Tables
png pdf	Table A1: The $ \Upsilon $(1S) differential cross section times dimuon branching fraction, $ \mathcal{B} \mathrm{d}^2\sigma/\mathrm{d}p_{\mathrm{T}}\mathrm{d}y $, in two rapidity ranges, for the unpolarized scenario. The relative uncertainties (statistical and systematic) are given in percent. The systematic uncertainties are considered to be fully correlated.
png pdf	Table A2: The $ \Upsilon $(2S) differential cross section times dimuon branching fraction, $ \mathcal{B} \mathrm{d}^2\sigma/\mathrm{d}p_{\mathrm{T}}\mathrm{d}y $, in two rapidity ranges, for the unpolarized scenario. The relative uncertainties (statistical and systematic) are given in percent. The systematic uncertainties are considered to be fully correlated.
png pdf	Table A3: The $ \Upsilon $(3S) differential cross section times dimuon branching fraction, $ \mathcal{B} \mathrm{d}^2\sigma/\mathrm{d}p_{\mathrm{T}}\mathrm{d}y $, in two rapidity ranges, for the unpolarized scenario. The relative uncertainties (statistical and systematic) are given in percent. The systematic uncertainties are considered to be fully correlated.
png pdf	Table A4: Scaling factors needed to obtain the $ \Upsilon $($ n $S) differential cross sections corresponding to two extreme polarization scenarios in the helicity frame, $ \lambda_{\theta}^{\mathrm{HX}} = + $ 1 or-1, from the values reported in Tables 1--3.

Summary

The cross sections of the $ \Upsilon{\textrm{(1S)}} $, $ \Upsilon{\textrm{(2S)}} $, and $ \Upsilon{\textrm{(3S)}} $ bottomonium states, times the branching fractions of their dimuon decays, were measured as a function of their transverse momentum in a broad $ p_{\mathrm{T}} $ range, from 20 to 200 GeV, in two rapidity regions, $ |y| < $ 0.6 and 0.6 $ < |y| < $ 1.2. The analysis was based on an event sample of pp collisions at $ \sqrt{s} = $ 13.6 TeV, collected by CMS in 2022 and corresponding to an integrated luminosity of 37.4 fb$ ^{-1} $. The reported cross sections include feed-down contributions from heavier bottomonia. These results are an important input to global fits of quarkonium cross sections and polarizations performed to extract the long-distance matrix elements that determine inclusive quarkonium production in the NRQCD framework.

References
1	Quarkonium Working Group Collaboration	Heavy quarkonium physics	CERN Yellow Reports: Monographs, CERN-2005-005, 2005 link	hep-ph/0412158
2	N. Brambilla et al.	Heavy quarkonium: progress, puzzles, and opportunities	EPJC 71 (2011) 1534	1010.5827
3	G. Bodwin, E. Braaten, and P. Lepage	Rigorous QCD analysis of inclusive annihilation and production of heavy quarkonium	PRD 51 (1995) 1125	hep-ph/9407339
4	M. Butenschön and B. A. Kniehl	$ \mathrm{J}/\psi $ production in NRQCD: A global analysis of yield and polarization	Nucl. Phys. B Proc. Suppl. 222 (2012) 151	1201.3862
5	K.-T. Chao et al.	$ \mathrm{J}/\psi $ polarization at hadron colliders in nonrelativistic QCD	PRL 108 (2012) 242004	1201.2675
6	M. Butenschön and B. A. Kniehl	Next-to-leading-order tests of NRQCD factorization with $ \mathrm{J}/\psi $ yield and polarization	Mod. Phys. Lett. A 28 (2013) 1350027	1212.2037
7	B. Gong, L.-P. Wan, J.-X. Wang, and H.-F. Zhang	Polarization for prompt $ \mathrm{J}/\psi $ and $ \psi\mathrm{(2S)} $ production at the Tevatron and LHC	PRL 110 (2013) 042002	1205.6682
8	P. Faccioli, C. Lourenço, J. Seixas, and H. Wöhri	Towards the experimental clarification of quarkonium polarization	EPJC 69 (2010) 657	1006.2738
9	M. Butenschön and B. A. Kniehl	$ \mathrm{J}/\psi $ polarization at Tevatron and LHC: nonrelativistic-QCD factorization at the crossroads	PRL 108 (2012) 172002	1201.1872
10	P. Faccioli et al.	Quarkonium production in the LHC era: A polarized perspective	PLB 736 (2014) 98	1403.3970
11	G. T. Bodwin et al.	Fragmentation contributions to hadroproduction of prompt $ \mathrm{J}/\psi $, $ \chi_{{\mathrm{c}}J} $, and $ \psi\mathrm{(2S)} $ states	PRD 93 (2016) 034041	1509.07904
12	P. Faccioli et al.	From identical S- and P-wave $ p_{\mathrm{T}} $ spectra to maximally distinct polarizations: probing NRQCD with $ \chi $ states	EPJC 78 (2018) 268	1802.01106
13	K. Wang, Y.-Q. Ma, and K.-T. Chao	$ \Upsilon $(1S) prompt production at the Tevatron and LHC in nonrelativistic QCD	PRD 85 (2012) 114003	1202.6012
14	B. Gong, L.-P. Wan, J.-X. Wang, and H.-F. Zhang	Complete next-to-leading-order study on the yield and polarization of $ \Upsilon $(1S,2S,3S) at the Tevatron and LHC	PRL 112 (2014) 032001	1305.0748
15	H. Han et al.	$ \Upsilon $($ n $S) and $ \chi_b $($ n $P) production at hadron colliders in nonrelativistic QCD	PRD 94 (2016) 014028	1410.8537
16	CMS Collaboration	Prompt and non-prompt $ \mathrm{J}/\psi $ production in pp collisions at $ \sqrt{s} = $ 7 TeV	EPJC 71 (2011) 1575	CMS-BPH-10-002 1011.4193
17	CMS Collaboration	$ \mathrm{J}/\psi $ and $ \psi\mathrm{(2S)} $ production in pp collisions at $ \sqrt{s} = $ 7 TeV	JHEP 02 (2012) 011	CMS-BPH-10-014 1111.1557
18	LHCb Collaboration	Measurement of $ \mathrm{J}/\psi $ production in pp collisions at $ \sqrt{s} = $ 7 TeV	EPJC 71 (2011) 1645	1103.0423
19	ALICE Collaboration	Rapidity and transverse momentum dependence of inclusive $ \mathrm{J}/\psi $ production in pp collisions at $ \sqrt{s} = $ 7 TeV	PLB 704 (2011) 442	1105.0380
20	ATLAS Collaboration	Measurement of the production cross-section of $ \psi\mathrm{(2S)} \to {\mathrm{J}/\psi} (\to \mu^{+} \mu^{-}) \pi^{+} \pi^{-} $ in pp collisions at $ \sqrt{s} = $ 7 TeV at ATLAS	JHEP 09 (2014) 079	1407.5532
21	CMS Collaboration	Measurement of $ \mathrm{J}/\psi $ and $ \psi\mathrm{(2S)} $ prompt double-differential cross sections in pp collisions at $ \sqrt{s} = $ 7 TeV	PRL 114 (2015) 191802	CMS-BPH-14-001 1502.04155
22	LHCb Collaboration	Measurement of forward $ \mathrm{J}/\psi $ production cross-sections in pp collisions at $ \sqrt{s} = $ 13 TeV	JHEP 10 (2015) 172	1509.00771
23	ATLAS Collaboration	Measurement of the differential cross-sections of prompt and non-prompt production of $ \mathrm{J}/\psi $ and $ \psi\mathrm{(2S)} $ in pp collisions at $ \sqrt{s} = $ 7 and 8 TeV with the ATLAS detector	EPJC 76 (2016) 283	1512.03657
24	ATLAS Collaboration	Measurement of the production cross-section of $ \mathrm{J}/\psi $ and $ \psi\mathrm{(2S)} $ mesons in pp collisions at $ \sqrt{s} = $ 13 TeV with the ATLAS detector	EPJC 84 (2024) 169	2309.17177
25	CMS Collaboration	Upsilon production cross section in pp collisions at $ \sqrt{s} = $ 7 TeV	PRD 83 (2011) 112004	CMS-BPH-10-003 1012.5545
26	LHCb Collaboration	Measurement of Upsilon production in pp collisions at $ \sqrt{s} = $ 7 TeV	EPJC 72 (2012) 2025	1202.6579
27	ATLAS Collaboration	Measurement of Upsilon production in 7 TeV pp collisions at ATLAS	PRD 87 (2013) 052004	1211.7255
28	CMS Collaboration	Measurement of the $ \Upsilon $(1S), $ \Upsilon $(2S), and $ \Upsilon $(3S) cross sections in pp collisions at $ \sqrt{s} = $ 7 TeV	PLB 727 (2013) 101	CMS-BPH-11-001 1303.5900
29	CMS Collaboration	Measurements of the $ \Upsilon $(1S), $ \Upsilon $(2S), and $ \Upsilon $(3S) differential cross sections in pp collisions at $ \sqrt{s} = $ 7 TeV	PLB 749 (2015) 14	CMS-BPH-12-006 1501.07750
30	CMS Collaboration	Measurement of quarkonium production cross sections in pp collisions at $ \sqrt{s}= $ 13 TeV	PLB 780 (2018) 251	CMS-BPH-15-005 1710.11002
31	ALICE Collaboration	$ \mathrm{J}/\psi $ polarization in pp collisions at $ \sqrt{s} = $ 7 TeV	PRL 108 (2012) 082001	1111.1630
32	CMS Collaboration	Measurement of the prompt $ \mathrm{J}/\psi $ and $ \psi\mathrm{(2S)} $ polarizations in pp collisions at $ \sqrt{s} = $ 7 TeV	PLB 727 (2013) 381	CMS-BPH-13-003 1307.6070
33	CMS Collaboration	Measurement of the $ \Upsilon $(1S), $ \Upsilon $(2S), and $ \Upsilon $(3S) polarizations in pp collisions at $ \sqrt{s} = $ 7 TeV	PRL 110 (2013) 081802	CMS-BPH-11-023 1209.2922
34	LHCb Collaboration	Measurement of $ \mathrm{J}/\psi $ polarization in pp collisions at $ \sqrt{s} = $ 7 TeV	EPJC 73 (2013) 2631	1307.6379
35	LHCb Collaboration	Measurement of $ \psi\mathrm{(2S)} $ polarisation in pp collisions at $ \sqrt{s} = $ 7 TeV	EPJC 74 (2014) 2872	1403.1339
36	CMS Collaboration	Constraints on the $ \chi_{c1} $ versus $ \chi_{c2} $ polarizations in proton-proton collisions at $ \sqrt{s} = $ 8 TeV	PRL 124 (2020) 162002	CMS-BPH-13-001 1912.07706
37	CMS Collaboration	Measurement of the polarizations of prompt and non-prompt $ \mathrm{J}/\psi $ and $ \psi\mathrm{(2S)} $ mesons produced in pp collisions at $ \sqrt{s} = $ 13 TeV	PLB 858 (2024) 139044	CMS-BPH-22-009 2406.14409
38	Y. Zhao et al.	Experimental review of the quarkonium physics at the LHC	Symmetry 17 (2025) 1521	2509.10330
39	CMS Collaboration	HEPData	HEPData record for this analysis link
40	CMS Collaboration	The CMS experiment at the CERN LHC	JINST 3 (2008) S08004
41	CMS Collaboration	Electron and photon reconstruction and identification with the CMS experiment at the CERN LHC	JINST 16 (2021) P05014	CMS-EGM-17-001 2012.06888
42	CMS Collaboration	Performance of the CMS muon detector and muon reconstruction with proton-proton collisions at $ \sqrt{s} = $ 13 TeV	JINST 13 (2018) P06015	CMS-MUO-16-001 1804.04528
43	CMS Collaboration	Description and performance of track and primary-vertex reconstruction with the CMS tracker	JINST 9 (2014) P10009	CMS-TRK-11-001 1405.6569
44	CMS Collaboration	Development of the CMS detector for the CERN LHC Run 3	JINST 19 (2024) P05064	CMS-PRF-21-001 2309.05466
45	CMS Collaboration	Performance of the CMS Level-1 trigger in proton-proton collisions at $ \sqrt{s} = $ 13 TeV	JINST 15 (2020) P10017	CMS-TRG-17-001 2006.10165
46	CMS Collaboration	The CMS trigger system	JINST 12 (2017) P01020	CMS-TRG-12-001 1609.02366
47	CMS Collaboration	Performance of the CMS high-level trigger during LHC Run 2	JINST 19 (2024) P11021	CMS-TRG-19-001 2410.17038
48	T. Sjöstrand et al.	An introduction to PYTHIA 8.2	Comput. Phys. Commun. 191 (2015) 159	1410.3012
49	C. Bierlich et al.	A comprehensive guide to the physics and usage of PYTHIA 8.3	SciPost Phys. Codebases 8, 2022 link	2203.11601
50	CMS Collaboration	Extraction and validation of a new set of CMS PYTHIA 8 tunes from underlying-event measurements	EPJC 80 (2020) 4	CMS-GEN-17-001 1903.12179
51	NNPDF Collaboration	Parton distributions from high-precision collider data	EPJC 77 (2017) 663	1706.00428
52	N. Davidson, T. Przedzinski, and Z. W \c a s	PHOTOS interface in C++: technical and physics documentation	Comput. Phys. Commun. 199 (2016) 86	1011.0937
53	GEANT4 Collaboration	GEANT 4---a simulation toolkit	NIM A 506 (2003) 250
54	W. Verkerke and D. P. Kirkby	The RooFit toolkit for data modeling	eConf C0303241 MOLT007, 2003	physics/0306116
55	M. J. Oreglia	A study of the reactions $ \psi^\prime \to \gamma \gamma \psi $	PhD thesis, Stanford University, 1980 link
56	Particle Data Group , S. Navas et al.	Review of particle physics	PRD 110 (2024) 030001
57	CMS Collaboration	Luminosity measurement for the 2022 pp data-taking period	CMS Physics Analysis Summary, 2022 link	CMS-PAS-LUM-22-001
58	M. Pivk and F. R. Le Diberder	sPlot: a statistical tool to unfold data distributions	NIM A 555 (2005) 356	physics/0402083
59	Y. Feng, B. Gong, C.-H. Chang, and J.-X. Wang	Complete study on polarization of $ \Upsilon $($ n $S) hadroproduction at QCD next-to-leading order	Chin. Phys. C 45 (2021) 013117	2009.03028