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Magnetic Monopoles in the Cosmos and at the LHC

Magnetic Monopoles in the Cosmos and at the LHC. Arttu Rajantie MoEDAL Physics Workshop CERN, 20 June 2012. Maxwell Equations. Duality. Dirac Monopole (1931). Vector potential Dirac string: Singularity along QM: Unobservable if . Dirac Monopole (1931).

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Magnetic Monopoles in the Cosmos and at the LHC

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  1. Magnetic Monopolesin the Cosmos and at the LHC Arttu RajantieMoEDAL Physics WorkshopCERN, 20 June 2012

  2. Maxwell Equations Duality A. Rajantie, Magnetic Monopoles in the Cosmos and at the LHC,

  3. Dirac Monopole (1931) A. Rajantie, Magnetic Monopoles in the Cosmos and at the LHC, Vector potential Dirac string: Singularity along QM: Unobservable if

  4. Dirac Monopole (1931) A. Rajantie, Magnetic Monopoles in the Cosmos and at the LHC, Dirac quantisation condition:All electric and magnetic charges must satisfy Existence of monopoles would explain observed quantisation of electric charge “…one would be surprised if Nature had made no use of it”

  5. Dirac Monopole (1931) A. Rajantie, Magnetic Monopoles in the Cosmos and at the LHC, Magnetic Coulomb field: Magnetic charge localised at a point Divergent energy:

  6. QFT of Monopoles A. Rajantie, Magnetic Monopoles in the Cosmos and at the LHC, Full quantum calculation: Monopole loops Difficult to formulate: Two vector potentials (Schwinger 1975) Strong coupling

  7. ‘t Hooft-Polyakov Monopole (1974) A. Rajantie, Magnetic Monopoles in the Cosmos and at the LHC, Smooth “hedgehog” solution in SU(2)+adjoint Higgs Magnetic charge Finite mass

  8. ‘t Hooft-Polyakov Monopole (1974) Visualisation: www.vapor.ucar.edu A. Rajantie, Magnetic Monopoles in the Cosmos and at the LHC, Consistent quantum field theory setup Large : Still non-perturbative Lattice simulations: Mass, scattering (AR&Weir 2011)

  9. ‘t Hooft-Polyakov Monopole (1974) A. Rajantie, Magnetic Monopoles in the Cosmos and at the LHC, Exist whenever a simple Lie group is broken to something with a U(1) factor: Grand Unification

  10. Grand Unification energy Theory of Everything 1019GeV Grand Unified Theory 1016GeV Electro- weak Theory gravity strong weak electromagnetic 102GeV A. Rajantie, Magnetic Monopoles in the Cosmos and at the LHC, • Standard Model:EM & weak forces unified above 100 GeV • Grand Unified Theory (GUT): Electroweak & strong forces unified above 1016GeV • e.g.

  11. GUT Monopoles energy Theory of Everything 1019GeV Grand Unified Theory 1016GeV Electro- weak Theory gravity strong weak electromagnetic 102GeV A. Rajantie, Magnetic Monopoles in the Cosmos and at the LHC, Generic prediction of GUTs Mass typically at GUT scale Also dyons with both electric and magnetic charge

  12. GUT Monopoles energy Theory of Everything 1019GeV Grand Unified Theory 1016GeV Electro- weak Theory gravity strong weak electromagnetic 102GeV A. Rajantie, Magnetic Monopoles in the Cosmos and at the LHC, More complex GUTs,e.g. Monopoles with different charges Can be lightere.g. in an family unification model (Kephart et al)

  13. String Theory Monopoles A. Rajantie, Magnetic Monopoles in the Cosmos and at the LHC, S-duality:Any superstring theory has magnetic monopoles Typical mass Can be reduced by large extra dimensions or warped compactification, perhaps even to (Witten 2002)

  14. Other Light Monopoles energy Theory of Everything 1019GeV Grand Unified Theory 1016GeV Electro- weak Theory ? gravity strong weak electromagnetic 102GeV A. Rajantie, Magnetic Monopoles in the Cosmos and at the LHC, Massive range of energies between EW and GUT:Plenty of room for new physics Cho-Maison monopole (1996):Dirac solution generalised to electroweak theory Monopoles do not have to arise from unification

  15. Monopoles in Cosmology x A. Rajantie, Magnetic Monopoles in the Cosmos and at the LHC, Hot Big Bang:GUT symmetry breaksin a phase transition The Higgs field chooses a direction randomly Kibble (1976):Monopoles form, at least one per horizon→

  16. Monopole Problem A. Rajantie, Magnetic Monopoles in the Cosmos and at the LHC, Monopoles annihilate until they cannot find partners:Density decreases to (Zel’dovich & Khlopov 1979, Preskill 1979) Total energy density in the universe: Monopoles exceed this unless Guth (1981): Period of inflation (accelerating expansion) dilutes monopoles away

  17. Monopole Problem (Turner et al 1982) A. Rajantie, Magnetic Monopoles in the Cosmos and at the LHC, • Density constraint interms of flux :Monopoles hitting unit area per unit time • Uniform distribution:

  18. Parker Bound (1970) (Turner et al 1982) A. Rajantie, Magnetic Monopoles in the Cosmos and at the LHC, • Galactic magnetic fields • If , thiscreates a magnetic current, which dissipates the field • Sets an upper bound on flux • Bound gets weaker at higher

  19. Parker Bound (1970) (Turner et al 1982) A. Rajantie, Magnetic Monopoles in the Cosmos and at the LHC, • If , monopoles remain bound togalaxies • Constraint from the totalmass of the Milky Way:

  20. Cosmic Rays (Cabrera 1982) A. Rajantie, Magnetic Monopoles in the Cosmos and at the LHC, • Early detections: • Berkeley 1975, Stanford 1982, Imperial 1986 • All turned out to be false

  21. Cosmic Rays (Giacomelli et al 2011) A. Rajantie, Magnetic Monopoles in the Cosmos and at the LHC, • MACRO (Gran Sasso, Italy): • Upper bound over wide mass range

  22. Cosmic Rays (Hogan et al 2008) A. Rajantie, Magnetic Monopoles in the Cosmos and at the LHC, • RICE (South Pole): • Intermediate mass monopoles

  23. Monopole Problem? A. Rajantie, Magnetic Monopoles in the Cosmos and at the LHC, Preskill(1979): Monopole density today Light monopoles are relativistic, so Compatible with RICE bound only if Therefore we do need inflation to wipe out the monopoles!

  24. Accelerator Searches A. Rajantie, Magnetic Monopoles in the Cosmos and at the LHC, • Direct searches: • Tevatron, LEP, HERA → Lower bound • MoEDAL: Up to • Indirect searches: • Virtual monopoles • Large theoretical uncertainties

  25. -scale monopoles A. Rajantie, Magnetic Monopoles in the Cosmos and at the LHC, • Possible, but not really predicted by any theory • Perhaps large extra dimensions, or simply unrelated to unified theories • Mass relation means there would be lots of new exciting physics at accessible energies • Monopoles would be a fantastic probe: • Absolutely stable • Strong EM interaction • Easy to handle

  26. Summary A. Rajantie, Magnetic Monopoles in the Cosmos and at the LHC, • Monopoles are perhaps the best motivated new particles: • Explain charge quantisation • Exist in GUTs, string theory • Produced copiously in the early universe,wiped away by inflation: • Stringent bounds from astrophysics, cosmic rays • -scale monopoles possible • Detectable in MoEDAL • Would open up a window to exciting new physics • (For more: See AR, Contemporary Physics 2012)

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