1. Monopoles
The Mystery

3. At the beginning there was Maxwell...
Vacuum
Symmetry under electromagnetic duality

4. MAXWELL Matter (Source) Duality Symmetry is explicitly Broken
In order to restore symmetry is necessary to introduce
Magnetic charge(MONOPOLE) and the magnetic current

6. With this transformation Duality Symmetry is restored in
Classical Electromagnetism
The Price to be pay is the introduction of MONOPOLE

7. The following step, Dirac... (1931-1934)
Monopole with Quatum Mechanics
Schrodinger equation for a particule moving in the
electromagnetic fields
Invariance under Gauge Transformation

8. Magnetic
Monopole ₊g ∞
Singularity

18. Big Bang predicts 1000 monopoles per nucleon
THE SEARCH
Monopoles of the usual Grand Unification
have masses of the order m >
Could only be produced in the first instants of the
Universe and only searchable in cosmic radiation
Big Bang predicts 1000 monopoles per nucleon
(disagreement with observation = no one observed)
The paradox is solved by Inflationary Cosmological Models,
that greatily reduced the monopole density

19. Monopole Searches in Accelarators
No Dirac prediction for monopole mass
“Lower Bound” using classical electron radius
by analogy:
Assuming:

23. e gβ Going from lepton production we replace Two photon s=1/2
Search of Monopole in Accelerators
Direct Searches ⇒ Monopole production as free particles
Going from lepton production we replace
Two photon s=1/2 e gβ
Drell-Yan

24. The experimental limits on monopole mass
The most recent limits on the monopole mass
HERA
e+ p – collisions
|n|=1,2,3,6
Tevatron
p p – collisions
Experiment E-882
(Al) |n|=1, M > 285 GeV
(Al) |n|=2, M > 355 GeV
(Be) |n|=3, M > 325 GeV
(Be) |n|=6, M > 420 GeV
LEP 2
e+ e- – collisions
(Al) M > 140 GeV
45 ≤ M < 102 GeV

25. MONOPOLE and EXOTICS DETECTOR At the LCH
MoEDAL

28. MONOPOLIUM DIRAC DIXIT: (1934) BOUND STATE MONOPOLE ANTIMONOPOLE
“…THE ATTRACTIVE FORCE BETWEEN TWO
MAGNETIC POLES IS 4692 TIME THAT BETWEEN
THE ELECTRON AND THE PROTON. THIS VERY
LARGE FORCE MAY PERHAPS ACCOUNT FOR
WHY THE MONOPOLES HAVE NEVER BEEN
SEPARATED …”
MONOPOLIUM

29. Monopolium Dynamics Monopolium production from photon fusion
Nonrelativistic bound state
Attributed to beam width aprox. 10 G eV

30. Monopolium production and Decay
Monopolium Decay
Monopolium Vertex
Monopolium production and Decay

31. Analysis of p-p scattering
Processes above the monopole Threshold M M M

32. Evaluation Energy Diferential Cross Section Elastic Scatering
Elastic photon spectrum
Elementary photon-photon cross section
= C.M energy pp system
= C.M energy of the photons
This procedure can be generalized easily to semi-elstic and inelastic case

33. Cross section monopole antimonopole annhilation
Compararison Higgs and monopole antimonopole decay

34. Fixed binding energy
100GeV

35. Monopolium Cross Section
Total
Semi-elastic
Elastic
Inelastic

36. CROSS - SECTION

37. Concluding Remarks
Dirac felt that he ¨would be surprised If Nature had made no use for it. It, being the Magnetic Monopole¨.
Ed Witten once asserted in his Loeb Lecture at Harvard, ¨almost all theoretical physicists believe in the existence of magnetic monopoles, or at least hope that is one¨.
Joshep Polchinsky, a string – theorist, described the existence of monopoles as ¨one of the safest bets that one can make about physics not yet seen¨ and that ¨their existence seems inevitable in any framework that explains the quantization of electric charge. Of course their mass scale and abundance are highly uncertain,… ¨

38. 11/23/10
CONCLUSIONS
Monopoles are hypothetical, but predicted by the most major theoretical models
No confirmed repeatable monopole events have been recorded
Strong lower limits on energy probably place Dirac monopoles on the reach of colliders
Strong upper limits on cosmic ray flux
Maybe finding reasons to their inexistence is more interesting than finding them?