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| CMS-HIN-24-011 ; CERN-EP-2026-160 | ||
| Measurement of the $ \gamma\gamma \to \tau^{+}\tau^{-} $ cross section and constraints on the anomalous magnetic moment of the $ \tau $ lepton in ultraperipheral PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV | ||
| CMS Collaboration | ||
| 21 July 2026 | ||
| Submitted to Physics Letters B | ||
| Abstract: The production of $ \tau $ lepton pairs via photon-photon fusion, $ \gamma\gamma \to \tau^{+}\tau^{-} $, is studied in ultraperipheral lead-lead collisions at a nucleon-nucleon center-of-mass energy of 5.02 TeV. The dataset, collected by the CMS experiment in 2018, corresponds to an integrated luminosity of 1.70$ \text{nb}^{-1}$. Four different $ \tau^{+}\tau^{-} $ decay final states are analyzed. A simultaneous likelihood fit to the measured lepton transverse momentum ($ p_{\mathrm{T}} $) distributions, which incorporates information from both spectral shape and normalization, is used to constrain the anomalous magnetic moment of the $ \tau $ lepton, $ a_{\tau} $, and to extract the cross section of the process. The measured 95% CL interval for $ a_{\tau} $ is $ -0.039 < a_{\tau} < $ 0.032. The fiducial cross section, $ \sigma_{\gamma\gamma\to\tau\tau}^\text{fid}= $ 555 $ ^{+60}_{-14} \mu\text{b} $ for tau leptons with $ p_{\mathrm{T}}^\tau > $ 1 GeV and pseudorapidity $ |\eta^\tau| < $ 3, is the most precise measurement for this process at the LHC to date and is in agreement with next-to-leading-order quantum electrodynamics predictions. | ||
| Links: e-print arXiv:2607.20148 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Diagram of the $ \text{PbPb}\xrightarrow{\gamma\gamma}\mathrm{b}^{(*)}\tau^{+}\tau^{-}\mathrm{b}^{(*)} $ process, with one tau lepton decaying leptonically and the other hadronically (3-prong final state). The charge-conjugate mode with a positive muon is implicitly included. The two $ \gamma\tau\tau $ vertices are sensitive to $ a_{\tau} $. The star superscript in $ \mathrm{b}^{(*)} $ indicates a possible electromagnetic excitation of the lead ion. |
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Figure 2:
Postfit distributions of the decay charged lepton $ p_{\mathrm{T}} $ for the $ \mu+1\text{-prong} $ (upper left), $ \mu+3\text{-prong} $ (upper right), $ \mu+\mathrm{e} $ (lower left), and $ \mathrm{e}+3\text{-prong} $ (lower right) channels. The data (black points with error bars indicating statistical uncertainties) are compared with the predicted $ \gamma\gamma\to\tau^{+}\tau^{-} $ signal for the fitted $ a_{\tau} = - $ 0.019 value (dark yellow histogram) plus the $ \gamma\gamma \to \mu^{+}\mu^{-}\gamma $ or $ \gamma\gamma \to \mathrm{e}^+\mathrm{e}^- $ (dark green histograms) and residual (pink histogram) backgrounds. The lower panels show the ratio of the data to the sum of signal plus backgrounds. The dashed blue bands show the total postfit uncertainty in the signal-plus-background. |
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Figure 2-a:
Postfit distributions of the decay charged lepton $ p_{\mathrm{T}} $ for the $ \mu+1\text{-prong} $ (upper left), $ \mu+3\text{-prong} $ (upper right), $ \mu+\mathrm{e} $ (lower left), and $ \mathrm{e}+3\text{-prong} $ (lower right) channels. The data (black points with error bars indicating statistical uncertainties) are compared with the predicted $ \gamma\gamma\to\tau^{+}\tau^{-} $ signal for the fitted $ a_{\tau} = - $ 0.019 value (dark yellow histogram) plus the $ \gamma\gamma \to \mu^{+}\mu^{-}\gamma $ or $ \gamma\gamma \to \mathrm{e}^+\mathrm{e}^- $ (dark green histograms) and residual (pink histogram) backgrounds. The lower panels show the ratio of the data to the sum of signal plus backgrounds. The dashed blue bands show the total postfit uncertainty in the signal-plus-background. |
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Figure 2-b:
Postfit distributions of the decay charged lepton $ p_{\mathrm{T}} $ for the $ \mu+1\text{-prong} $ (upper left), $ \mu+3\text{-prong} $ (upper right), $ \mu+\mathrm{e} $ (lower left), and $ \mathrm{e}+3\text{-prong} $ (lower right) channels. The data (black points with error bars indicating statistical uncertainties) are compared with the predicted $ \gamma\gamma\to\tau^{+}\tau^{-} $ signal for the fitted $ a_{\tau} = - $ 0.019 value (dark yellow histogram) plus the $ \gamma\gamma \to \mu^{+}\mu^{-}\gamma $ or $ \gamma\gamma \to \mathrm{e}^+\mathrm{e}^- $ (dark green histograms) and residual (pink histogram) backgrounds. The lower panels show the ratio of the data to the sum of signal plus backgrounds. The dashed blue bands show the total postfit uncertainty in the signal-plus-background. |
png pdf |
Figure 2-c:
Postfit distributions of the decay charged lepton $ p_{\mathrm{T}} $ for the $ \mu+1\text{-prong} $ (upper left), $ \mu+3\text{-prong} $ (upper right), $ \mu+\mathrm{e} $ (lower left), and $ \mathrm{e}+3\text{-prong} $ (lower right) channels. The data (black points with error bars indicating statistical uncertainties) are compared with the predicted $ \gamma\gamma\to\tau^{+}\tau^{-} $ signal for the fitted $ a_{\tau} = - $ 0.019 value (dark yellow histogram) plus the $ \gamma\gamma \to \mu^{+}\mu^{-}\gamma $ or $ \gamma\gamma \to \mathrm{e}^+\mathrm{e}^- $ (dark green histograms) and residual (pink histogram) backgrounds. The lower panels show the ratio of the data to the sum of signal plus backgrounds. The dashed blue bands show the total postfit uncertainty in the signal-plus-background. |
png pdf |
Figure 2-d:
Postfit distributions of the decay charged lepton $ p_{\mathrm{T}} $ for the $ \mu+1\text{-prong} $ (upper left), $ \mu+3\text{-prong} $ (upper right), $ \mu+\mathrm{e} $ (lower left), and $ \mathrm{e}+3\text{-prong} $ (lower right) channels. The data (black points with error bars indicating statistical uncertainties) are compared with the predicted $ \gamma\gamma\to\tau^{+}\tau^{-} $ signal for the fitted $ a_{\tau} = - $ 0.019 value (dark yellow histogram) plus the $ \gamma\gamma \to \mu^{+}\mu^{-}\gamma $ or $ \gamma\gamma \to \mathrm{e}^+\mathrm{e}^- $ (dark green histograms) and residual (pink histogram) backgrounds. The lower panels show the ratio of the data to the sum of signal plus backgrounds. The dashed blue bands show the total postfit uncertainty in the signal-plus-background. |
png pdf |
Figure 3:
Negative log-likelihood results from the combined fit to the decay-lepton $ p_{\mathrm{T}} $ distributions of the four $ \gamma\gamma \to \tau^{+}\tau^{-} $ channels (Fig. 2). Left: Likelihood surface in the $ (a_{\tau},\sigma^\text{fid}) $ plane with contours at $ -2\Delta\ln L = $ 1 and 4, UPCGEN prediction between $ a_{\tau} $ and $ \sigma^\text{fid} $ (black dotted curve, normalized to data), and best fit point along this curve (red star). Right: $ -2\Delta\ln L $ distributions for $ a_{\tau} $ (lower $ x $ axis) and $ \sigma^\text{fid} $ (upper $ x $ axis), evaluated along the dotted curve in the left panel, accounting for all uncertainties (black curve) and statistical uncertainties alone (blue dashed curve). The horizontal lines indicate the corresponding 68 and 95% CL intervals. |
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Figure 3-a:
Negative log-likelihood results from the combined fit to the decay-lepton $ p_{\mathrm{T}} $ distributions of the four $ \gamma\gamma \to \tau^{+}\tau^{-} $ channels (Fig. 2). Left: Likelihood surface in the $ (a_{\tau},\sigma^\text{fid}) $ plane with contours at $ -2\Delta\ln L = $ 1 and 4, UPCGEN prediction between $ a_{\tau} $ and $ \sigma^\text{fid} $ (black dotted curve, normalized to data), and best fit point along this curve (red star). Right: $ -2\Delta\ln L $ distributions for $ a_{\tau} $ (lower $ x $ axis) and $ \sigma^\text{fid} $ (upper $ x $ axis), evaluated along the dotted curve in the left panel, accounting for all uncertainties (black curve) and statistical uncertainties alone (blue dashed curve). The horizontal lines indicate the corresponding 68 and 95% CL intervals. |
png pdf |
Figure 3-b:
Negative log-likelihood results from the combined fit to the decay-lepton $ p_{\mathrm{T}} $ distributions of the four $ \gamma\gamma \to \tau^{+}\tau^{-} $ channels (Fig. 2). Left: Likelihood surface in the $ (a_{\tau},\sigma^\text{fid}) $ plane with contours at $ -2\Delta\ln L = $ 1 and 4, UPCGEN prediction between $ a_{\tau} $ and $ \sigma^\text{fid} $ (black dotted curve, normalized to data), and best fit point along this curve (red star). Right: $ -2\Delta\ln L $ distributions for $ a_{\tau} $ (lower $ x $ axis) and $ \sigma^\text{fid} $ (upper $ x $ axis), evaluated along the dotted curve in the left panel, accounting for all uncertainties (black curve) and statistical uncertainties alone (blue dashed curve). The horizontal lines indicate the corresponding 68 and 95% CL intervals. |
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Figure 4:
The $ a_{\tau} $ limits derived in this work for each individual decay channel and their combined result (five lower entries) compared with previous CMS [14,16], ATLAS [13], and DELPHI [12] measurements. The red and green bars indicate their corresponding 68 and 95% CL intervals. The SM value is indicated by the vertical dashed line. |
| Tables | |
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Table 1:
Summary of kinematic selection criteria applied in the four $ \gamma\gamma\to\tau^{+}\tau^{-} $ decay channels analyzed. The ``$ \pi $,lead'' and ``$ \pi $,sublead'' labels refer to the leading (highest $ p_{\mathrm{T}} $) and any subleading reconstructed charged hadrons or ``prongs'' (the second- and third-highest $ p_{\mathrm{T}} $ particles, assumed to be pions). |
| Summary |
| The production of tau lepton pairs via photon-photon fusion, $ \gamma\gamma \to \tau^{+}\tau^{-} $, has been studied in ultraperipheral lead-lead collisions at a center-of-mass energy of 5.02 TeV per nucleon pair. The data sample was collected by the CMS experiment in 2018 corresponding to an integrated luminosity of 1.70 $ \text{nb}^{-1}$. Four $ \tau^{+}\tau^{-} $ decay final states have been studied: $ \mu+1\text{-prong} $, $ \mu+3\text{-prong} $, $ \mathrm{e}+3\text{-prong} $, and $ \mu+\mathrm{e} $, in events where one muon, one electron, and 0, 1, or 3 charged hadrons (``prongs'') are produced exclusively. A simultaneous likelihood fit to the measured transverse momentum ($ p_{\mathrm{T}} $) distributions of the decay leptons in the four different $ \tau^{+}\tau^{-} $ final states, which incorporates information from both spectral shape and normalization, constrains the anomalous magnetic moment of the $ \tau $ lepton, $ a_{\tau} $, and provides the fiducial cross section of the process. A 95% CL interval $ -0.039 < a_{\tau} < $ 0.032 is set for $ a_{\tau} $ in a low-mass $ \tau^{+}\tau^{-} $ phase space complementary to that probed at higher invariant masses in similar photon-fusion processes in proton-proton collisions at the LHC. This new $ a_{\tau} $ limit reaches a sensitivity comparable to the existing constraints from electron-positron collisions at LEP. A cross section $ \sigma_{\gamma\gamma\to\tau\tau}^\text{fid}= $ 555 $ ^{+60}_{-14} \mu\text{b} $ is measured in a fiducial phase space, corresponding to tau lepton transverse momenta $ p_{\mathrm{T}}^{\tau} > $ 1 GeV and pseudorapidities $ |\eta^{\tau}| < $ 3. This cross section, the most precisely measured at the LHC for this process to date, is in agreement with next-to-leading-order quantum electrodynamics predictions. |
| References | ||||
| 1 | T. Aoyama, T. Kinoshita, and M. Nio | Theory of the anomalous magnetic moment of the electron | Atoms 7 (2019) 28 | |
| 2 | X. Fan, T. G. Myers, B. A. D. Sukra, and G. Gabrielse | Measurement of the electron magnetic moment | PRL 130 (2023) 071801 | 2209.13084 |
| 3 | Muon g-2 Collaboration | Measurement of the positive muon anomalous magnetic moment to 0.20 ppm | PRL 131 (2023) 161802 | 2308.06230 |
| 4 | T. Aoyama et al. | The anomalous magnetic moment of the muon in the standard model | Phys. Rept. 887 (2020) 1 | 2006.04822 |
| 5 | R. Aliberti et al. | The anomalous magnetic moment of the muon in the Standard Model: an update | Phys. Rept. 1143 (2025) 1 | 2505.21476 |
| 6 | A. Crivellin, M. Hoferichter, and J. M. Roney | Toward testing the magnetic moment of the tau at one part per million | PRD 106 (2022) 093007 | 2111.10378 |
| 7 | F. del Aguila, F. Cornet, and J. I. Illana | The possibility of using a large heavy-ion collider for measuring the electromagnetic properties of the tau lepton | PLB 271 (1991) 256 | |
| 8 | F. Cornet and J. I. Illana | Tau pair production via photon-photon collisions at LEP | PRD 53 (1996) 1181 | hep-ph/9503466 |
| 9 | S. Atag and A. A. Billur | Possibility of Determining $ \tau $ Lepton Electromagnetic Moments in $ {\gamma\gamma \to \tau^{+}\tau^{-}} $ Process at the CERN-LHC | JHEP 11 (2010) 060 | 1005.2841 |
| 10 | L. Beresford and J. Liu | New physics and tau $ g- $ 2 using LHC heavy ion collisions | PRD 102 (2020) 113008 | 1908.05180 |
| 11 | M. Dyndal, M. Klusek-Gawenda, M. Schott, and A. Szczurek | Anomalous electromagnetic moments of $ \tau $ lepton in $ {\gamma\gamma\to\tau^{+}\tau^{-}} $ reaction in PbPb collisions at the LHC | PLB 809 (2020) 135682 | 2002.05503 |
| 12 | DELPHI Collaboration | Study of tau-pair production in photon-photon collisions at LEP and limits on the anomalous electromagnetic moments of the tau lepton | EPJC 35 (2004) 159 | hep-ex/0406010 |
| 13 | ATLAS Collaboration | Observation of the $ \gamma\gamma \to \tau^{+}\tau^{-} $ process in PbPb Collisions and constraints on the $ \tau $-Lepton Anomalous Magnetic Moment with the ATLAS Detector | PRL 131 (2023) 151802 | 2204.13478 |
| 14 | CMS Collaboration | Observation of $ \tau $ lepton pair production in ultraperipheral lead-lead collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV | PRL 131 (2023) 151803 | CMS-HIN-21-009 2206.05192 |
| 15 | ATLAS Collaboration | Differential measurements of $ \gamma\gamma\to\tau^{+}\tau^{-} $ and constraints on $ \tau $-lepton electromagnetic moments in PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV with ATLAS | Submitted for publication, 2026 | 2605.04584 |
| 16 | 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 |
| 17 | S. Eidelman and M. Passera | Theory of the tau lepton anomalous magnetic moment | Mod. Phys. Lett. A 22 (2007) 159 | hep-ph/0701260 |
| 18 | A. J. Baltz et al. | The physics of ultraperipheral collisions at the LHC | Phys. Rept. 458 (2008) 1 | 0706.3356 |
| 19 | CMS Collaboration | Overview of high-density QCD studies with the CMS experiment at the LHC | Phys. Rept. 1115 (2025) 219 | CMS-HIN-23-011 2405.10785 |
| 20 | G. Baur, K. Hencken, and D. Trautmann | Electromagnetic dissociation as a tool for nuclear structure and astrophysics | Prog. Part. Nucl. Phys. 51 (2003) 487 | nucl-th/0304041 |
| 21 | 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 |
| 22 | H.-S. Shao and L. Simon | Automated next-to-leading order QCD and electroweak predictions of photon-photon processes in ultraperipheral collisions | JHEP 07 (2025) 020 | 2504.10104 |
| 23 | CMS Collaboration | HEPData record for this analysis | link | |
| 24 | CMS Collaboration | The CMS experiment at the CERN LHC | JINST 3 (2008) S08004 | |
| 25 | CMS Collaboration | Development of the CMS detector for the CERN LHC Run 3 | JINST 19 (2024) P05064 | CMS-PRF-21-001 2309.05466 |
| 26 | CMS Collaboration | Performance of the CMS level-1 trigger in proton-proton collisions at $ \sqrt{\smash[b]{s}}= $ 13 TeV | JINST 15 (2020) P10017 | CMS-TRG-17-001 2006.10165 |
| 27 | CMS Collaboration | The CMS trigger system | JINST 12 (2017) P01020 | CMS-TRG-12-001 1609.02366 |
| 28 | CMS Collaboration | Performance of the CMS high-level trigger during LHC Run 2 | JINST 19 (2024) P11021 | CMS-TRG-19-001 2410.17038 |
| 29 | 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 |
| 30 | 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 |
| 31 | 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 |
| 32 | CMS Tracker Group Collaboration | The CMS Phase-1 pixel detector upgrade | JINST 16 (2021) P02027 | 2012.14304 |
| 33 | CMS Collaboration | Calibration of the CMS hadron calorimeters using proton-proton collision data at $ \sqrt{\smash[b]{s}}= $ 13 TeV | JINST 15 (2020) P05002 | CMS-PRF-18-001 1910.00079 |
| 34 | CMS Collaboration | Status of zero degree calorimeter for CMS experiment | AIP Conf. Proc. 867 (2006) 258 | nucl-ex/0608052 |
| 35 | CMS Collaboration | Particle-flow reconstruction and global event description with the CMS detector | JINST 12 (2017) P10003 | CMS-PRF-14-001 1706.04965 |
| 36 | CMS Collaboration | Performance of reconstruction and identification of $ \tau $ leptons decaying to hadrons and $ \nu_{\!\tau} $ in pp collisions at $ \sqrt{\smash[b]{s}}= $ 13 TeV | JINST 13 (2018) P10005 | CMS-TAU-16-003 1809.02816 |
| 37 | CMS Collaboration | Jet energy scale and resolution in the CMS experiment in pp collisions at 8 TeV | JINST 12 (2017) P02014 | CMS-JME-13-004 1607.03663 |
| 38 | CMS Collaboration | Performance of missing transverse momentum reconstruction in proton-proton collisions at $ \sqrt{\smash[b]{s}}= $ 13 TeV using the CMS detector | JINST 14 (2019) P07004 | CMS-JME-17-001 1903.06078 |
| 39 | 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 |
| 40 | 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 |
| 41 | N. Burmasov, E. Kryshen, P. Buehler, and R. Lavicka | UPCGEN: A Monte Carlo simulation program for dilepton pair production in ultra-peripheral collisions of heavy ions | Comput. Phys. Commun. 277 (2022) 108388 | 2111.11383 |
| 42 | T. Sjöstrand et al. | An introduction to PYTHIA 8.2 | Comput. Phys. Commun. 191 (2015) 159 | 1410.3012 |
| 43 | M. Chrzaszcz, T. Przedzinski, Z. Was, and J. Zaremba | TAUOLA of $ \tau $ lepton decays\textemdashframework for hadronic currents, matrix elements and anomalous decays | Comput. Phys. Commun. 232 (2018) 220 | 1609.04617 |
| 44 | L. A. Harland-Lang, V. A. Khoze, and M. G. Ryskin | Exclusive LHC physics with heavy ions: SuperChic 3 | EPJC 79 (2019) 39 | 1810.06567 |
| 45 | GEANT4 Collaboration | GEANT 4---a simulation toolkit | NIM A 506 (2003) 250 | |
| 46 | CMS Collaboration | Measurement of light-by-light scattering and the Breit--Wheeler process, and search for axion-like particles in ultraperipheral PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV | JHEP 08 (2025) 006 | CMS-HIN-21-015 2412.15413 |
| 47 | L. A. Harland-Lang | Exciting ions: A systematic treatment of ultraperipheral heavy ion collisions with nuclear breakup | PRD 107 (2023) 093004 | 2303.04826 |
| 48 | N. Cr é pet, D. d'Enterria, and H.-S. Shao | Improved modeling of photon-photon processes in ultraperipheral collisions at hadron colliders | PoS DIS 124, 2025 link |
2409.18485 |
| 49 | O. Behnke, K. Kr | Data analysis in high energy physics: A practical guide to statistical methods | öninger, T. Schörner-Sadenius, and G. Schott, eds., Wiley-VCH, Weinheim, Germany, ISBN 978-3-527-4-3, 978-3-527-65344-7, 978-3-527-65343-0, 2013 | |
| 50 | CMS Collaboration | Luminosity measurement for lead-lead collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV in 2015 and 2018 at CMS | Submitted to EPJC, 2025 | CMS-LUM-20-002 2503.03946 |
| 51 | CMS Collaboration | The CMS Statistical Analysis and Combination Tool: Combine | Comput. Softw. Big Sci. 8 (2024) 19 | CMS-CAT-23-001 2404.06614 |
| 52 | D. d'Enterria and C. Loizides | Progress in the Glauber model at collider energies | Ann. Rev. Nucl. Part. Sci. 71 (2021) 315 | 2011.14909 |
| 53 | ATLAS Collaboration | Exclusive dimuon production in ultraperipheral PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV with ATLAS | Phys. Rev. C 104 (2021) 024906 | 2011.12211 |
| 54 | S. Dittmaier, T. Engel, J. L. H. Ariza, and M. Pellen | Electroweak corrections to $ \tau^{+}\tau^{-} $ production in ultraperipheral heavy-ion collisions at the LHC | JHEP 08 (2025) 051 | 2504.11391 |
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Compact Muon Solenoid LHC, CERN |
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