CMS-SMP-24-019

CMS-SMP-24-019 ; CERN-EP-2025-273
Measurement and effective field theory interpretation of the photon-fusion production cross section of a pair of W bosons in proton-proton collisions at $ \sqrt{s}= $ 13 TeV
CMS Collaboration
27 January 2026
Submitted to the Journal of High Energy Physics
Abstract: This analysis presents an observation of the photon-fusion production of W boson pairs using the CMS detector at the LHC. The total cross section of the $ \mathrm{W}^+\mathrm{W}^- $ production in photon fusion is measured using proton-proton collision data with an integrated luminosity of 138 fb$ ^{-1} $ collected with the CMS detector in 2016--2018 at a center-of-mass energy of $ \sqrt{s}= $ 13 TeV. Events are selected in the final state with one isolated electron and one isolated muon, and no additional tracks associated with the electron-muon production vertex. The total and fiducial production cross sections are 643 $ ^{+82}_{-78} $ fb and 3.96 $ ^{+0.53}_{-0.51} $ fb, respectively, in agreement with the standard model predictions of 631 $ \pm $ 126 fb and 3.87 $ \pm $ 0.77 fb. This agreement enables stringent constraints to be imposed on anomalous quartic gauge couplings within a dimension-8 effective field theory framework.
Links: e-print arXiv:2601.21574 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; CADI line (restricted) ;

Figures & Tables	Summary	References	CMS Publications

Figures
png pdf	Figure 1: Normalized simulated $ N_\text{tracks} $ (left) and acoplanarity (right) distributions for signal and background processes. The acoplanarity distribution is shown for events with $ N_\text{tracks}= $ 0.
png pdf	Figure 1-a: Normalized simulated $ N_\text{tracks} $ (left) and acoplanarity (right) distributions for signal and background processes. The acoplanarity distribution is shown for events with $ N_\text{tracks}= $ 0.
png pdf	Figure 1-b: Normalized simulated $ N_\text{tracks} $ (left) and acoplanarity (right) distributions for signal and background processes. The acoplanarity distribution is shown for events with $ N_\text{tracks}= $ 0.
png pdf	Figure 2: Observed and predicted $ p_{\mathrm{T}}^{\mathrm{e}\mu} $ distributions for events with $ N_\text{tracks}= $ 0 (SR, left) or 1 $ \leq N_\text{tracks} \leq $ 5 (CR, right), using 2016--2018 data. The distributions are shown after the maximum likelihood fit to the data ("postfit distributions"). The observed data and their associated Poissonian statistical uncertainty are shown with black markers with vertical error bars. The uncertainty band accouts for all sources of background and signal uncertainty, systematic as well as statistical, after the fit. The last bin includes the overflow. The lower panels show the ratio of data to sum of signal and background contributions, before (prefit, open red circles) and after (black full markers) the maximum likelihood fit.
png pdf	Figure 2-a: Observed and predicted $ p_{\mathrm{T}}^{\mathrm{e}\mu} $ distributions for events with $ N_\text{tracks}= $ 0 (SR, left) or 1 $ \leq N_\text{tracks} \leq $ 5 (CR, right), using 2016--2018 data. The distributions are shown after the maximum likelihood fit to the data ("postfit distributions"). The observed data and their associated Poissonian statistical uncertainty are shown with black markers with vertical error bars. The uncertainty band accouts for all sources of background and signal uncertainty, systematic as well as statistical, after the fit. The last bin includes the overflow. The lower panels show the ratio of data to sum of signal and background contributions, before (prefit, open red circles) and after (black full markers) the maximum likelihood fit.
png pdf	Figure 2-b: Observed and predicted $ p_{\mathrm{T}}^{\mathrm{e}\mu} $ distributions for events with $ N_\text{tracks}= $ 0 (SR, left) or 1 $ \leq N_\text{tracks} \leq $ 5 (CR, right), using 2016--2018 data. The distributions are shown after the maximum likelihood fit to the data ("postfit distributions"). The observed data and their associated Poissonian statistical uncertainty are shown with black markers with vertical error bars. The uncertainty band accouts for all sources of background and signal uncertainty, systematic as well as statistical, after the fit. The last bin includes the overflow. The lower panels show the ratio of data to sum of signal and background contributions, before (prefit, open red circles) and after (black full markers) the maximum likelihood fit.
png pdf	Figure 3: Distribution of $ p_{\mathrm{T}}^{\mathrm{e}\mu} $ for the difference between the observed number of events and the expected number of background events (black markers) compared with the SM prefit $ {\gamma\gamma\to\mathrm{W}^+\mathrm{W}^-} $ prediction (red line), and $ {\gamma\gamma\to\mathrm{W}^+\mathrm{W}^-} $ predictions for five benchmark points with nonzero EFT coefficients. The Poissonian statistical uncertainties associated with the observed data are represented by vertical error bars. The difference between the predictions for the SM and nonzero EFT coefficients is visible only in the overflow bin. The background uncertainty is shown with a gray band.
png pdf	Figure 4: Summary of observed limits on the $ f_\textrm{M} $ Wilson coefficients for this analysis and previous results by the CMS Collaboration [55,58,57,59,60]. The limits are arranged from most sensitive to least sensitive in descending order, with the current result highlighted in red. Horizontal error bars represent the 95% confidence level intervals. In some cases, limits on the Wilson coefficients are shown under the assumption of unitarity bounds, as indicated in the right-most column. The unitarity bound is defined as the scattering energy at which the aQGC coupling strength is set equal to the observed limit that would result in a scattering amplitude that violates unitarity [61].
png pdf	Figure 5: Summary of observed limits on the $ f_\textrm{T} $ Wilson coefficients for this analysis and previous results by the CMS Collaboration [58,57,56,55,60]. The limits are arranged from most sensitive to least sensitive in descending order, with the current result highlighted in red. Horizontal error bars represent the 95% confidence level intervals. In some cases, limits on the Wilson coefficients are shown under the assumption of unitarity bounds, as indicated in the right-most column. The unitarity bound is defined as the scattering energy at which the aQGC coupling strength is set equal to the observed limit that would result in a scattering amplitude that violates unitarity [61].

Tables
png pdf	Table 1: Selection criteria applied on the $ \mathrm{e}\mu $ SR [CR], and in the $ \mu\mu $ final state. The $ p_{\mathrm{T}} $ and pseudorapidity ranges correspond to different sets of triggers in different data-taking periods. The leading (subleading) lepton in the $ \mathrm{e}\mu $ SR [CR] must have $ p_{\mathrm{T}} > $ 24 (15) GeV.
png pdf	Table 2: Systematic uncertainties and their relative effects on the inclusive cross section measurement. An uncertainty of 2% in the signal cross section is considered in the EFT interpretation.
png pdf	Table 3: Observed and predicted event yields in the SR and CR. The signal and background yields are the result of the global fit including all sources of uncertainties.
png pdf	Table 4: The 95% CL intervals on EFT operators varied one at a time while fixing the other ones to zero. Odd operators are denoted with a tilde sign.

Summary

The observation of the photon-fusion production of W boson pairs using the CMS detector at the LHC is reported. The measurement utilizes proton-proton collision data collected in 2016--2018, corresponding to an integrated luminosity of 138 fb$ ^{-1} $ at $ \sqrt{s}= $ 13 TeV. The experimental strategy exploits the exclusive nature of the signal, requiring the absence of additional charged particles associated with the dilepton production vertex. Events are selected in the final state with one isolated electron and one isolated muon, and no additional tracks associated with the electron-muon production vertex. The analysis employs a maximum likelihood fit to the transverse momentum sum of the electron and muon to extract the cross section of the signal. The measured inclusive cross section for $ {\gamma\gamma\to\mathrm{W}^+\mathrm{W}^-} $ production is 643 $ ^{+82}_{-78} $ fb, whereas the fiducial cross section, defined in a phase space matching the experimental selection criteria, is 3.96 $ ^{+0.53}_{-0.51} $ fb. These results show excellent agreement with the standard model predictions of 631 $ \pm $ 126 fb and 3.87 $ \pm $ 0.77 fb for the inclusive and fiducial cross sections, respectively. Beyond the cross section measurement, this analysis provides the most stringent constraints to date on several anomalous quartic gauge couplings using dimension-8 operators in an effective field theory approach.

References
1	CMS Collaboration	Observation of $ \gamma\gamma\to\tau\tau $ in proton-proton collisions and limits on the anomalous electromagnetic moments of the $ \tau $ lepton	Rept. Prog. Phys. 87 (2024) 107801	CMS-SMP-23-005 2406.03975
2	CMS Collaboration	Exclusive $ \gamma\gamma \to \mu^+\mu^- $ production in proton-proton collisions at $ \sqrt{s}= $ 7 TeV	JHEP 01 (2012) 052	CMS-FWD-10-005 1111.5536
3	CMS Collaboration	Study of exclusive two-photon production of $ \mathrm{W}^+\mathrm{W}^- $ in pp collisions at $ \sqrt{s} = $ 7 TeV and constraints on anomalous quartic gauge couplings	JHEP 07 (2013) 116	CMS-FSQ-12-010 1305.5596
4	CMS Collaboration	Evidence for exclusive $ \gamma\gamma \to \mathrm{W}^+\mathrm{W}^- $ production and constraints on anomalous quartic gauge couplings in pp collisions at $ \sqrt{s}= $ 7 and 8 TeV	JHEP 08 (2016) 119	CMS-FSQ-13-008 1604.04464
5	CMS, TOTEM Collaboration	Observation of proton-tagged, central (semi)exclusive production of high-mass lepton pairs in pp collisions at 13 TeV with the CMS-TOTEM precision proton spectrometer	JHEP 07 (2018) 153	1803.04496
6	ATLAS Collaboration	Measurement of exclusive $ \gamma\gamma\rightarrow \mathrm{W}^+\mathrm{W}^- $ production and search for exclusive Higgs boson production in pp collisions at $ \sqrt{s} = $ 8 TeV using the ATLAS detector	PRD 94 (2016) 032011	1607.03745
7	ATLAS Collaboration	Observation of photon-induced $ \mathrm{W}^+\mathrm{W}^- $ production in pp collisions at $ \sqrt{s}= $ 13 TeV using the ATLAS detector	PLB 816 (2021) 136190	2010.04019
8	CMS Collaboration	HEPData record for this analysis, 2025	HEPData link
9	CMS Collaboration	The CMS experiment at the CERN LHC	JINST 3 (2008) S08004
10	CMS Collaboration	Development of the CMS detector for the CERN LHC Run 3	JINST 19 (2024) P05064	CMS-PRF-21-001 2309.05466
11	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
12	CMS Collaboration	The CMS trigger system	JINST 12 (2017) P01020	CMS-TRG-12-001 1609.02366
13	CMS Collaboration	Performance of the CMS high-level trigger during LHC Run 2	JINST 19 (2024) P11021	CMS-TRG-19-001 2410.17038
14	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
15	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
16	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
17	L. A. Harland-Lang, M. Tasevsky, V. A. Khoze, and M. G. Ryskin	A new approach to modelling elastic and inelastic photon-initiated production at the LHC: SuperChic 4	EPJC 80 (2020) 925	2007.12704
18	S. Bailey and L. A. Harland-Lang	Modeling $ \mathrm{W}^+\mathrm{W}^- $ production with rapidity gaps at the LHC	PRD 105 (2022) 093010	2201.08403
19	H.-S. Shao and D. d'Enterria	gamma-UPC: automated generation of exclusive photon-photon processes in ultraperipheral proton and nuclear collisions with varying form factors	JHEP 09 (2022) 248	2207.03012
20	J. Alwall et al.	The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations	JHEP 07 (2014) 079	1405.0301
21	R. Frederix and S. Frixione	Merging meets matching in MC@NLO	JHEP 12 (2012) 061	1209.6215
22	H.-S. Shao and D. d'Enterria	Dimuon and ditau production in photon-photon collisions at next-to-leading order in QED	JHEP 02 (2025) 023	2407.13610
23	T. Han, G. Valencia, and S. Willenbrock	Structure function approach to vector boson scattering in p p collisions	PRL 69 (1992) 3274	hep-ph/9206246
24	O. Mattelaer	On the maximal use of Monte Carlo samples: re-weighting events at NLO accuracy	EPJC 76 (2016) 674	1607.00763
25	P. Nason	A new method for combining NLO QCD with shower Monte Carlo algorithms	JHEP 11 (2004) 040	hep-ph/0409146
26	S. Frixione, P. Nason, and C. Oleari	Matching NLO QCD computations with parton shower simulations: the POWHEG method	JHEP 11 (2007) 070	0709.2092
27	S. Alioli, P. Nason, C. Oleari, and E. Re	A general framework for implementing NLO calculations in shower Monte Carlo programs: the POWHEG BOX	JHEP 06 (2010) 043	1002.2581
28	S. Alioli et al.	Jet pair production in POWHEG	JHEP 04 (2011) 081	1012.3380
29	S. Alioli, P. Nason, C. Oleari, and E. Re	NLO Higgs boson production via gluon fusion matched with shower in POWHEG	JHEP 04 (2009) 002	0812.0578
30	S. Frixione, G. Ridolfi, and P. Nason	A positive-weight next-to-leading-order Monte Carlo for heavy flavour hadroproduction	JHEP 09 (2007) 126	0707.3088
31	E. Re	Single-top Wt-channel production matched with parton showers using the POWHEG method	EPJC 71 (2011) 1547	1009.2450
32	R. Frederix, E. Re, and P. Torrielli	Single-top t-channel hadroproduction in the four-flavour scheme with POWHEG and aMC@NLO	JHEP 09 (2012) 130	1207.5391
33	T. Sj \"ostrand et al.	An introduction to PYTHIA 8.2	Comput. Phys. Commun. 191 (2015) 159	1410.3012
34	CMS Collaboration	Extraction and validation of a new set of CMS PYTHIA8 tunes from underlying-event measurements	EPJC 80 (2020) 4	CMS-GEN-17-001 1903.12179
35	NNPDF Collaboration	Parton distributions from high-precision collider data	EPJC 77 (2017) 663	1706.00428
36	GEANT4 Collaboration	GEANT 4---a simulation toolkit	NIM A 506 (2003) 250
37	CMS Collaboration	Particle-flow reconstruction and global event description with the CMS detector	JINST 12 (2017) P10003	CMS-PRF-14-001 1706.04965
38	CMS Collaboration	ECAL 2016 refined calibration and Run2 summary plots	CMS Detector Performance Summary CMS-DP-2020-021 CDS
39	CMS Tracker Group Collaboration	The CMS phase-1 pixel detector upgrade	JINST 16 (2021) P02027	2012.14304
40	CMS Collaboration	Track impact parameter resolution for the full pseudo rapidity coverage in the 2017 dataset with the CMS phase-1 pixel detector	CMS Detector Performance Summary CMS-DP-2020-049 CDS
41	G. Cowan, K. Cranmer, E. Gross, and O. Vitells	Asymptotic formulae for likelihood-based tests of new physics	EPJC 71 (2011) 1554	1007.1727
42	R. Barlow and C. Beeston	Fitting using finite Monte Carlo samples	Comput. Phys. Commun 77 (1993)
43	J. S. Conway	Incorporating nuisance parameters in likelihoods for multisource spectra	PHYSTAT 201 (2011) 115	1103.0354
44	CMS Collaboration	Measurement of the inelastic proton-proton cross section at $ \sqrt{s}= $ 13 TeV	JHEP 07 (2018) 161	CMS-FSQ-15-005 1802.02613
45	CMS Collaboration	Precision luminosity measurement in proton-proton collisions at $ \sqrt{s} = $ 13 TeV in 2015 and 2016 at CMS	EPJC 81 (2021) 800	CMS-LUM-17-003 2104.01927
46	CMS Collaboration	CMS luminosity measurement for the 2017 data-taking period at $ \sqrt{s} = $ 13 TeV	CMS Physics Analysis Summary link	CMS-PAS-LUM-17-004
47	CMS Collaboration	CMS luminosity measurement for the 2018 data-taking period at $ \sqrt{s} = $ 13 TeV	CMS Physics Analysis Summary link	CMS-PAS-LUM-18-002
48	CMS Collaboration	The CMS statistical analysis and combination tool: Combine	Comput. Softw. Big Sci. 8 (2024) 19	CMS-CAT-23-001 2404.06614
49	W. Verkerke and D. P. Kirkby	The RooFit toolkit for data modeling	link	physics/0306116
50	L. Moneta et al.	The RooStats project	PoS ACAT 057, 2010 link	1009.1003
51	CMS Collaboration	Measurement of $ \mathrm{W}^\pm\gamma $ differential cross sections in proton-proton collisions at $ \sqrt{s} = $ 13 TeV and effective field theory constraints	PRD 105 (2022) 052003	CMS-SMP-20-005 2111.13948
52	CMS Collaboration	$ \mathrm{W}^+\mathrm{W}^- $ boson pair production in proton-proton collisions at $ \sqrt{s} = $ 13 TeV	PRD 102 (2020) 092001	CMS-SMP-18-004 2009.00119
53	CMS Collaboration	Measurement of electroweak production of a W boson in association with two jets in proton-proton collisions at $ \sqrt{s}=13 \text {Te}\text {V} $	EPJC 80 (2020) 43	CMS-SMP-17-011 1903.04040
54	G. Durieux et al.	LHC EFT WG note: Basis for anomalous quartic gauge couplings	SciPost Phys. Comm. Rep. 6, 2025 link	2411.02483
55	CMS Collaboration	Measurements of production cross sections of WZ and same-sign WW boson pairs in association with two jets in proton-proton collisions at $ \sqrt{s} = $ 13 TeV	PLB 809 (2020) 135710	CMS-SMP-19-012 2005.01173
56	CMS Collaboration	Measurements of the pp $ \to \mathrm{W}^\pm\gamma\gamma $ and pp $ \to \mathrm{Z}\gamma\gamma $ cross sections at $ \sqrt{s} = $ 13 TeV and limits on anomalous quartic gauge couplings	JHEP 10 (2021) 174	CMS-SMP-19-013 2105.12780
57	CMS Collaboration	Measurement of the electroweak production of $ \mathrm{Z}\gamma $ and two jets in proton-proton collisions at $ \sqrt{s} = $ 13 TeV and constraints on anomalous quartic gauge couplings	PRD 104 (2021) 072001	CMS-SMP-20-016 2106.11082
58	CMS Collaboration	Measurement of the electroweak production of $ \mathrm{W}\gamma $ in association with two jets in proton-proton collisions at $ \sqrt{s} = $ 13 TeV	PRD 108 (2023) 032017	CMS-SMP-21-011 2212.12592
59	CMS, TOTEM Collaboration	Search for high-mass exclusive $ \gamma\gamma\to \mathrm{W}\mathrm{W} $ and $ \gamma\gamma\to \mathrm{Z}\mathrm{Z} $ production in proton-proton collisions at $ \sqrt{s} = $ 13 TeV	JHEP 07 (2023) 229	2211.16320
60	CMS Collaboration	Vector boson scattering and anomalous quartic couplings in final states with $ \ell\nu $qq or $ \ell\ell $qq plus jets using proton-proton collisions at $ \sqrt{s} = $ 13 TeV	Submitted to JHEP, 2025	CMS-SMP-22-011 2510.00118
61	E. d. S. Almeida, O. J. P. Eboli, and M. C. Gonzalez-–Garcia	Unitarity constraints on anomalous quartic couplings	PRD 101 (2020) 11	2004.05174