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### Magnetic Monopolesin the Cosmos and at the LHC

Arttu RajantieMoEDAL Physics WorkshopCERN, 20 June 2012

Dirac Monopole (1931)

A. Rajantie, Magnetic Monopoles in the Cosmos and at the LHC,

Vector potential

Dirac string: Singularity along

QM: Unobservable if

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”

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:

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

‘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

‘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)

‘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

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.

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

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)

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)

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

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→

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

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:

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

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:

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

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

Cosmic Rays

(Hogan et al 2008)

A. Rajantie, Magnetic Monopoles in the Cosmos and at the LHC,

- RICE (South Pole):
- Intermediate mass monopoles

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!

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

-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

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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