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?