Abstract
Electrically charged particles can be created by the decay of strong enough electric fields, a phenomenon known as the Schwinger mechanism1. By electromagnetic duality, a sufficiently strong magnetic field would similarly produce magnetic monopoles, if they exist2. Magnetic monopoles are hypothetical fundamental particles that are predicted by several theories beyond the standard model3,4,5,6,7 but have never been experimentally detected. Searching for the existence of magnetic monopoles via the Schwinger mechanism has not yet been attempted, but it is advantageous, owing to the possibility of calculating its rate through semi-classical techniques without perturbation theory, as well as that the production of the magnetic monopoles should be enhanced by their finite size8,9 and strong coupling to photons2,10. Here we present a search for magnetic monopole production by the Schwinger mechanism in Pb–Pb heavy ion collisions at the Large Hadron Collider, producing the strongest known magnetic fields in the current Universe11. It was conducted by the MoEDAL experiment, whose trapping detectors were exposed to 0.235 per nanobarn, or approximately 1.8 × 109, of Pb–Pb collisions with 5.02-teraelectronvolt center-of-mass energy per collision in November 2018. A superconducting quantum interference device (SQUID) magnetometer scanned the trapping detectors of MoEDAL for the presence of magnetic charge, which would induce a persistent current in the SQUID. Magnetic monopoles with integer Dirac charges of 1, 2 and 3 and masses up to 75 gigaelectronvolts per speed of light squared were excluded by the analysis at the 95% confidence level. This provides a lower mass limit for finite-size magnetic monopoles from a collider search and greatly extends previous mass bounds.
This is a preview of subscription content, access via your institution
Access options
Access Nature and 54 other Nature Portfolio journals
Get Nature+, our best-value online-access subscription
$29.99 / 30 days
cancel any time
Subscribe to this journal
Receive 51 print issues and online access
$199.00 per year
only $3.90 per issue
Buy this article
- Purchase on Springer Link
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
Data availability
All data used to produce the results of this work, along with the data points shown in the main figures of the paper are stored either on CERN lxplus server or on CERN’s GitLab. They are available upon request to the corresponding author without specific conditions. Source data are provided with this paper.
Code availability
All code used to produce the results of this work, including code to perform statistical analysis and produce the figures, is stored on CERN’s GitLab server and is available upon request to the corresponding author without specific conditions.
References
Schwinger, J. On gauge invariance and vacuum polarization. Phys. Rev. 82, 664–679 (1951).
Affleck, I. K. & Manton, N. S. Monopole pair production in a magnetic field. Nucl. Phys. B 194, 38–64 (1982).
Dirac, P. A. M. Quantised singularities in the electromagnetic field. Proc. R. Soc. London A 133, 60–72 (1931).
’t Hooft, G. Magnetic monopoles in unified gauge theories. Nucl. Phys. B 79, 276–284 (1974).
Polyakov, A. M. Particle spectrum in quantum field theory. JETP Lett. 20, 194–195 (1974).
Wen, X.-G. & Witten, E. Electric and magnetic charges in superstring models. Nucl. Phys. B 261, 651–677 (1985).
Mavromatos, N. E. & Mitsou, V. A. Magnetic monopoles revisited: models and searches at colliders and in the cosmos. Int. J. Mod. Phys. A 35, 2030012 (2020).
Ho, D. L.-J. & Rajantie, A. Classical production of ’t Hooft–Polyakov monopoles from magnetic fields. Phys. Rev. D 101, 055003 (2020).
Ho, D. L.-J. & Rajantie, A. Instanton solution for Schwinger production of ’t Hooft–Polyakov monopoles. Phys. Rev. D 103, 115033 (2021).
Gould, O., Ho, D. L.-J. & Rajantie, A. Towards Schwinger production of magnetic monopoles in heavy-ion collisions. Phys. Rev. D 100, 015041 (2019).
Huang, X.-G. Electromagnetic fields and anomalous transports in heavy-ion collisions—a pedagogical review. Rep. Prog. Phys. 79, 076302 (2016).
MoEDAL Collaboration. Magnetic monopole search with the full MoEDAL trapping detector in 13 TeV pp collisions interpreted in photon-fusion and Drell–Yan production. Phys. Rev. Lett. 123, 021802 (2019).
Guth, A. H. Inflationary universe: a possible solution to the horizon and flatness problems. Phys. Rev. D 23, 347–356 (1981).
Witten, E. Baryons in the 1/N expansion. Nucl. Phys. B 160, 57–115 (1979).
Drukier, A. K. & Nussinov, S. Monopole pair creation in energetic collisions: is it possible? Phys. Rev. Lett. 49, 102–105 (1982).
Blagojević, M. & Senjanović, P. The quantum field theory of electric and magnetic charge. Phys. Rep. 157, 233–346 (1988).
Cho, Y. & Maison, D. Monopole configuration in Weinberg–Salam model. Phys. Lett. B 391, 360–365 (1997).
Kimm, K., Yoon, J. H. & Cho, Y. M. Finite energy electroweak dyon. Eur. Phys. J. C 75, 67 (2015).
Ellis, J., Mavromatos, N. E. & You, T. The price of an electroweak monopole. Phys. Lett. B 756, 29–35 (2016).
Mavromatos, N. E. & Sarkar, S. Magnetic monopoles from global monopoles in the presence of a Kalb–Ramond field. Phys. Rev. D 95, 104025 (2017).
Arunasalam, S. & Kobakhidze, A. Electroweak monopoles and the electroweak phase transition. Eur. Phys. J. C 77, 444 (2017).
Mavromatos, N. E. & Sarkar, S. Regularized Kalb–Ramond magnetic monopole with finite energy. Phys. Rev. D 97, 125010 (2018).
Hung, P. Q. Topologically stable, finite-energy electroweak-scale monopoles. Nucl. Phys. B 962, 115278 (2021).
Sauter, F. Über das Verhalten eines Elektrons im homogenen elektrischen Feld nach der relativistischen Theorie Diracs. Z. Phys. 69, 742–764 (1931).
Heisenberg, W. & Euler, H. Consequences of Dirac’s theory of positrons. Z. Phys. 98, 714–732 (1936).
Kaspi, V. M. & Beloborodov, A. M. Magnetars. Ann. Rev. Astron. Astrophys. 55, 261–301 (2017).
Gould, O., Ho, D. L.-J. & Rajantie, A. Schwinger pair production of magnetic monopoles: momentum distribution for heavy-ion collisions. Phys. Rev. D 104, 015033 (2021).
MoEDAL Collaboration. First search for dyons with the full MoEDAL trapping detector in 13 TeV pp collisions. Phys. Rev. Lett. 126, 071801 (2021).
Milton, K. A. Theoretical and experimental status of magnetic monopoles. Rep. Prog. Phys. 69, 1637–1711 (2006).
The MoEDAL Collaboration. The physics programme of the MoEDAL experiment at the LHC. Int. J. Mod. Phys. A 29, 1430050 (2014).
Gamberg, L., Kalbfleisch, G. R. & Milton, K. A. Direct and indirect searches for low-mass magnetic monopoles. Found. Phys. 30, 543–565 (2000).
Agostinelli, S. et al. Geant4—a simulation toolkit. Nucl. Instrum. Meth. A 506, 250–303 (2003).
The MoEDAL Collaboration. Search for magnetic monopoles with the MoEDAL prototype trapping detector in 8 TeV proton–proton collisions at the LHC. J. High Energy Phys. 2016, 67 (2016).
He, Y. D. Search for a Dirac magnetic monopole in high energy nucleus–nucleus collisions. Phys. Rev. Lett. 79, 3134–3137 (1997).
Gould, O. & Rajantie, A. Magnetic monopole mass bounds from heavy-ion collisions and neutron stars. Phys. Rev. Lett. 119, 241601 (2017).
ATLAS Collaboration. Search for magnetic monopoles in √s = 7 TeV pp collisions with the ATLAS detector. Phys. Rev. Lett. 109, 261803 (2012).
ATLAS Collaboration. Search for magnetic monopoles and stable particles with high electric charges in 8 TeV pp collisions with the ATLAS detector. Phys. Rev. D 93, 052009 (2016).
ATLAS Collaboration. Search for magnetic monopoles and stable high-electric-charge objects in 13 TeV proton–proton collisions with the ATLAS Detector. Phys. Rev. Lett. 124, 031802 (2020).
Kobayashi, T. Monopole–antimonopole pair production in primordial magnetic fields. Phys. Rev. D 104, 043501 (2021).
Clemencic, M. et al. The LHCb simulation application, Gauss: design, evolution and experience. J. Phys. Conf. Ser. 331, 032023 (2011).
King, M. Simulation of the MoEDAL experiment. Nucl. Part. Phys. Proc. 273–275, 2560–2562 (2016).
Kharzeev, D. E., McLerran, L. D. & Warringa, H. J. The effects of topological charge change in heavy ion collisions: “event by event P and CP violation”. Nucl. Phys. A 803, 227–253 (2008).
Gursoy, U., Kharzeev, D. & Rajagopal, K. Magnetohydrodynamics, charged currents and directed flow in heavy ion collisions. Phys. Rev. C 89, 054905 (2014).
ALICE Collaboration. Centrality determination of Pb–Pb collisions at \(\sqrt{{s}_{{\rm{NN}}}}\) = 2.76 TeV with ALICE. Phys. Rev. C 88, 044909 (2013).
ALICE Collaboration. Centrality dependence of particle production in p–Pb collisions at \(\sqrt{{s}_{{\rm{NN}}}}\) = 5.02 TeV. Phys. Rev. C 91, 064905 (2015).
Deng, W.-T. & Huang, X.-G. Event-by-event generation of electromagnetic fields in heavy-ion collisions. Phys. Rev. C 85, 044907 (2012).
Baltz, A. J. The physics of ultraperipheral collisions at the LHC. Phys. Rep. 458, 1–171 (2008).
Kruglov, S. I. Pair production and vacuum polarization of vector particles with electric dipole moments and anomalous magnetic moments. Eur. Phys. J. C 22, 89–98 (2001).
Gould, O. & Rajantie, A. Thermal Schwinger pair production at arbitrary coupling. Phys. Rev. D 96, 076002 (2017).
Wolschin, G. Aspects of relativistic heavy-ion collisions. Universe 6, 61 (2020).
Tuchin, K. Time and space dependence of the electromagnetic field in relativistic heavy-ion collisions. Phys. Rev. C 88, 024911 (2013).
Inghirami, G. et al. Magnetic fields in heavy ion collisions: flow and charge transport. Eur. Phys. J. C 80, 293 (2020).
Cecchini, S., Patrizii, L., Sahnoun, Z., Sirri, G. & Togo, V. Energy losses of magnetic monopoles in aluminum, iron and copper. Preprint at https://arxiv.org/abs/1606.01220 (2016).
Alvarez, L. W. et al. A magnetic monopole detector utilizing superconducting elements. Rev. Sci. Instrum. 42, 326–330 (1971).
De Roeck, A. et al. Development of a magnetometer-based search strategy for stopped monopoles at the large hadron collider. Eur. Phys. J. C 72, 2212 (2012).
Malkus, W. V. R. The interaction of the Dirac magnetic monopole with matter. Phys. Rev. 83, 899–905 (1951).
Bracci, L. & Fiorentini, G. Binding of magnetic monopoles and atomic nuclei. Phys Lett. B 124, 493–496 (1983).
Bracci, L. & Fiorentini, G. Interactions of magnetic monopoles with nuclei and atoms: formation of bound states and phenomenological consequences. Nucl. Phys. B 232, 236–262 (1984).
Bracci, L. & Fiorentini, G. On the capture of protons by magnetic monopoles. Nucl. Phys. B 249, 519–532 (1985).
Olaussen, K. & Sollie, R. Form factor effects on nucleus–magnetic monopole binding. Nucl. Phys. B 255, 465–479 (1985).
Olaussen, K., Olsen, H. A., Osland, P. & Øverbø, I. Proton capture by magnetic monopoles. Phys. Rev. Lett. 52, 325–328 (1984).
Goebel, C. Binding of monopole to nuclei. In Monopole ’83 (ed. Stone, J. L.) 333–337 (Plenum, 1984).
Ruijgrok, Th. W., Tjon, J. A. & Wu, T. T. Monopole chemistry. Phys. Lett. B 129, 209–212 (1983).
Ruijgrok, T. Binding of matter to a magnetic monopole. Acta Phys. Pol. B 15, 305–314 (1983).
Lipkin, H. J. Effects of magnetic monopoles on nuclear wave functions and possible catalysis of nuclear beta decay and spontaneous fission. Phys. Lett. B 133, 347–350 (1983).
Lipkin, H. J. Monoponucleosis — the wonderful things that monopoles can do to nuclei if they are there. In Monopole ’83 (ed. Stone, J. L.) 347–358 (Plenum, 1984).
Acknowledgements
We thank CERN for the LHC’s successful Run-2 operation, as well as the support staff from our institutions without whom MoEDAL could not be operated. We acknowledge the invaluable assistance of particular members of the LHCb Collaboration: G. Wilkinson, R. Lindner, E. Thomas and G. Corti. Computing support was provided by the GridPP Collaboration, in particular by the Queen Mary University of London and Liverpool grid sites. This work was supported by grant PP00P2 150583 of the Swiss NSF; by the UK Science and Technology Facilities Council via the grants ST/L000326/1, ST/L00044X/1, ST/N00101X/1, ST/P000258/1, ST/P000762/1, ST/T000732/1, ST/T000759/1 and ST/T000791/1; by the Generalitat Valenciana via a special grant for MoEDAL and via the projects PROMETEO-II/2017/033 and PROMETEO/2019/087; by MCIU/AEI/FEDER, UE via the grants FPA2016-77177-C2-1-P, FPA2017-85985-P, FPA2017-84543-P and PGC2018-094856-B-I00; by the Physics Department of King’s College London; by NSERC via a project grant; by the V-P Research of the University of Alberta (UofA); by the Provost of the UofA; by UEFISCDI (Romania); by the INFN (Italy); by the Estonian Research Council via a Mobilitas Pluss grant MOBTT5; by the Research Funds of the University of Helsinki; and by the NSF grant 2011214 to the University of Alabama MoEDAL group. A.R. was also supported by Institute for Particle Physics Phenomenology Associateship.
Author information
Authors and Affiliations
Contributions
The Monopole and Exotics Detector at the LHC was constructed and is maintained by the MoEDAL collaboration. A large number of authors contributed to the data processing, detector calibration and Monte Carlo simulations used in this work. The MoEDAL collaboration acknowledges the substantial contributions to this manuscript from A.U. and I.O. (simulation, statistical analysis, result plots, paper writing); O.G., D.L.-J.H. and A.R. (theoretical calculations, paper writing); and N.E.M. and J.P. (paper writing). The manuscript was reviewed and edited by the collaboration and all authors approved the final version of the manuscript.
Corresponding author
Ethics declarations
Competing interests
The authors declare no competing interests.
Peer review information
Nature thanks Muneto Nitta, Steve Ahlen and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
Additional information
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Extended data figures and tables
Extended Data Fig. 1 Mean expected rate of Schwinger MMs (Rexp).
The mean expected rate of MMs with 1gD (left) and 2gD (right) magnetic charge in the MMT as a function of the MM mass in the FPA model. The black line corresponds to the default geometry. The grey region corresponds to the systematic error, which is dominated by the material budget. The 95% confidence level mass exclusion region is shown in blue.
Extended Data Fig. 2 Transverse momentum distribution of Schwinger MMs.
The transverse momentum distribution for Schwinger MMs derived from the FPA, as a function of MM mass (M) plotted versus MM β.
Rights and permissions
About this article
Cite this article
Acharya, B., Alexandre, J., Benes, P. et al. Search for magnetic monopoles produced via the Schwinger mechanism. Nature 602, 63–67 (2022). https://doi.org/10.1038/s41586-021-04298-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1038/s41586-021-04298-1
This article is cited by
-
Searches for magnetic monopoles
Nature Reviews Physics (2022)
Comments
By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.
