Monopoles
The Mystery
At the beginning there was
Maxwell...
Vacuum
Symmetry under electromagnetic duality
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
Magnetic
Monopole
₊g
∞
Singularity
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:
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
HERA
Tevatron
LEP 2
e+ p – collisions
p p – collisions
e+ e- – collisions
s  300 GeV
L  62 1 pb
1
|n|=1,2,3,6
(Al) M > 140 GeV
Experiment E-882
L  172  8 pb1
(Al) |n|=1, M > 285 GeV
(Al) |n|=2, M > 355 GeV
(Be) |n|=3, M > 325 GeV
(Be) |n|=6, M > 420 GeV
s  206.3 GeV
L  172  8 pb1
45 ≤ M < 102 GeV
MONOPOLE and EXOTICS DETECTOR At the LCH
MoEDAL
BOUND STATE MONOPOLE ANTIMONOPOLE
DIRAC DIXIT:
(1934)
“…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 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,…
¨
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?