Monopoles

The Mystery

At the beginning there was Maxwell...Vacuum

Symmetry under electromagnetic duality

Matter (Source)

MAXWELL

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

₊g

Singularity

Magnetic

Monopole

∞

THE SEARCHTHE SEARCH

Monopoles of the usual Grand UnificationMonopoles of the usual Grand Unification

have masses of the order m >have masses of the order m >

Could only be produced in the first instants of theUniverse 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 AccelaratorsMonopole Searches in Accelarators

No Dirac prediction for monopole mass

“Lower Bound” using classical electron radius

by analogy:by analogy:

Assuming:Assuming:

Going from lepton production we replace

e gβ Drell-YanTwo photon s=1/2

Search of Monopole in Accelerators Direct Searches Monopole production as free particles ⇒

The experimental limits on monopole mass

1 162 pbL

206.3 s GeV 300 s GeV18172 pbL

HERA e+ p – collisions

|n|=1,2,3,6

Tevatronp p – collisionsExperiment 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

(Al) M > 140 GeV

18172 pbL

45 ≤ M < 102 GeV

LEP 2 e+ e- – collisions

MoEDAL

MONOPOLE and EXOTICS DETECTOR At the LCH

DIRAC DIXIT: DIRAC DIXIT: (1934)(1934)

“…“…THE ATTRACTIVE FORCE BETWEEN TWO THE ATTRACTIVE FORCE BETWEEN TWO

MAGNETIC POLES IS 4692 TIME THAT BETWEEN MAGNETIC POLES IS 4692 TIME THAT BETWEEN

THE ELECTRON AND THE PROTON. THIS VERY THE ELECTRON AND THE PROTON. THIS VERY

LARGE FORCE MAY PERHAPS ACCOUNT FOR LARGE FORCE MAY PERHAPS ACCOUNT FOR

WHY THE MONOPOLES HAVE NEVER BEEN WHY THE MONOPOLES HAVE NEVER BEEN

SEPARATED …”SEPARATED …”

BOUND STATE MONOPOLE ANTIMONOPOLE

MONOPOLIUM

Monopolium Dynamics

Monopolium production from photon fusion

Nonrelativistic bound state

Attributed to beam width aprox. 10 G eV

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

= C.M energy pp system

= C.M energy of the photons

Elementary photon-photon cross section

Elastic photon spectrum

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

Total

Semi-elastic

Elastic

Inelastic

Monopolium Cross Section

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,… ¨

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?