Monopoles The Mystery

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

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

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

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

Magnetic Monopole ₊g ∞ Singularity

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

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

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

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

MONOPOLE and EXOTICS DETECTOR At the LCH MoEDAL

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

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

Monopolium production and Decay Monopolium Decay Monopolium Vertex Monopolium production and Decay

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

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

Cross section monopole antimonopole annhilation Compararison Higgs and monopole antimonopole decay

Fixed binding energy 100GeV

Monopolium Cross Section Total Semi-elastic Elastic Inelastic

CROSS - SECTION

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,… ¨

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?