Magnetic monopoles and free fractionally charged states at accelerators and in cosmic rays
monopoles and free fractionally charged
Thomas W. Kephart 0 1 2 5
George K. Leontaris 0 1 2 3
Qaisar Shafi 0 1 2 4
0 Newark , DE 19716 , U.S.A
1 GR-45110 Ioannina , Greece
2 Nashville , TN 37235 , U.S.A
3 Physics Department, Theory Division, Ioannina University
4 Bartol Research Institute, University of Delaware , USA
5 Department of Physics and Astronomy, Vanderbilt University
Unified theories of strong, weak and electromagnetic interactions which have electric charge quantization predict the existence of topologically stable magnetic monopoles. Intermediate scale monopoles are comparable with detection energies of cosmic ray monopoles at IceCube and other cosmic ray experiments. Magnetic monopoles in some models can be significantly lighter and carry two, three or possibly even higher quanta of the Dirac magnetic charge. They could be light enough for their effects to be detected at the LHC either directly or indirectly. An example based on a D-brane inspired SU(3)C × SU(3)L × SU(3)R (trinification) model with the monopole carrying three quanta of Dirac magnetic charge is presented. These theories also predict the existence of color singlet states with fractional electric charge which may be accessible at the LHC.
Strings and branes phenomenology; Phenomenology of Field Theories in
2 Generalities for product group models
2.4 The 433 model
Monopoles, inflation and primordial gravity waves
Monopoles at the LHC
Monopoles in cosmic rays
mechanically, angular momentum must be quantized in units of ~ and this implies the
Dirac quantization condition (in units where ~ = c = 1)
where q is the electric charge, g is the magnetic charge and n is an integer. Dirac’s argument
is still compelling today but magnetic monopoles have eluded us after over eighty years
of searching. The discovery of magnetic monopoles would have wide reaching implication
for physics beyond the standard model. As a new energy regime has been opening up at
the Large Hadron Collider (LHC), it is important to be clear on what we expect could be
found as we extend the search for magnetic monopoles into this region. While some results
are expected to be model dependent, others will be universal. We discuss a class of models
that could have magnetic monopoles light enough to have implications for the LHC, as well
as heavier monopoles that may be observed in cosmic ray experiments.
gq = 2nπ ,
– 1 –
Generalities for product group models
Two familiar examples of product gauge groups with bifundamental fermions are the
PatiSalam (PS) model  and the trinification model . In the PS model the gauge group
is SU(4) × SU(
) × SU(
) and the fermions live in three [(
4, 2, 1
) + (4¯, 1, 2)] families which
reduces to three standard model (SM) families plus three right handed neutrinos. This
model can be embedded directly into SO(10) with no additional fermions. In trinification
models the gauge group is SU(3) × SU(3) × SU(3) and the fermions occupy three [(3, 3¯, 1) +
(1, 3, 3¯) + (3¯, 1, 3)] families which reduces to three standard model (SM) families plus the
additional content of three E6 families, including additional b-type quarks. Let us begin
by discussing the magnetic monopoles of these two models and their generalizations.
SU(3)c color singlet states that carry fractional (± 2e ) electric charge. Adding fundamental
fermions irreducible representations to the 422 model is an obvious extension. For instance,
since SU(2) is anomaly free, and as the 422 gauge group has no U(
) factors, we could
simply introduce (
1, 2, 1
) and (
1, 1, 2
) states in the fundamental representations of H which
provide the required SU(3)c singlet states that carry fractional charge. (Recall that the
known fermions belong in the bi-fundamental representations of H.) Moreover, we also
should include the conjugate pair (
4, 1, 1
) and (4¯, 1, 1) in the fundamental representations
of H, which transform as triplets and anti-triplets under SU(3)c and carry fractional charge
± 6 . These latter states could bind together to create, for instance, a new class of baryons
that carry electric charge ± 2 . They also could combine with the SM quarks to generate
fractionally charged hadrons. This leads to color singlet magnetic monopoles carrying
integer multiples of the Dirac charge , in this case g = ± 22αe . In principle, the scale of
the new fermions can be arranged to be light, perhaps even LHC accessible. The monopole
mass depends, of course, on the 422 breaking scale. Intermediate mass monopoles may
survive inflation as we will discuss.
As the gauge group for the trinification model (333 model) is H = SU(3)C × SU(3)L ×
SU(3)R and since all the SU(3)s are potentially anomalous, the simplest generalization
is to add fundamental fermion representations in conjugate pairs, e.g., (
3, 1, 1
) + (3¯, 1, 1).
There is also the possibility of adding combinations of fundamentals and bifundamentals
that cancel the anomaly. For instance, we could add [3(
3, 1, 1
) + 3(1, 3¯, 1)] + (3¯, 3, 1)] and
the theory would remain free of chiral anomalies. The additional fundamental fermions
lead to leptons with electric charges ± 23e and hence charge ±3e magnetic monopoles.
– 2 –
If all the gauge coupling constants of a product group start off equal at the GUT scale [7, 8],
then we expect the GUT scale to be rather high, MU ∼ 1016 GeV. However, there are cases
where equality at the GUT scale is not required. For instance, in orbifolded AdS5/S5
with abelian orbifolding group Zn and gauge group SU(3)n one finds that the gauge group
coupling constants can be related by rational fractions. For trinification models the ratios
are determined by how the three SU(3)s are diagonally embedded into the initial SU(3)n
group. (See  and the detailed discussion in .) This then allows the GUT scale to be
considerably lower since less RG running is required for unification.
Another way to lower or alter the GUT scale is by adding extra dimensions to allow
power law running of couplings [11–13]. Yet another is to add scalar thresholds [14–16] or
vector-like fermion thresholds. All these methods can be arranged to avoid proton decay at
a too rapid rate. For the remainder of this work we will assume one of these mechanisms is
operating to avoid proton decay and lower the GUT scale. This will allow the GUT
symmetry to break and U(
) factors to appear at a low scale, which in turn delivers light magnetic
monopoles with charges depending on the gauge group and fermionic content of the model.
The 433 model
Now let us consider extensions of the Pati-Salam and trinification models that naturally
contain both fundamental and bifundamental representations. The simplest case is based
on the gauge group SU(4)×SU(3)×SU(3) (433 model), where both the 422 and trinification
models can be embedded . However, these are not the only possibilities. In all there
are 18 inequivalent embeddings  of the standard model gauge group in SU(4) × SU(3) ×
SU(3). If we insist on bifundamental fermions at the 433 level, then the 433 model is
only anomaly free when families come in a multiple of three. At the 422 and trinification
level, the 433 model naturally delivers both fundamental and bifundamental fermions.
Hence fractional electric charge color singlets and multiply charged magnetic monopoles
are natural in the 433 model.
Our main objective here is to find allowed masses and charges of magnetic monopoles
and then suggest signatures for experimental searches. The 433 model is a good candidate
for a model that can have detectable multicharged magnetic monopoles. (Here we focus
only on models similar to the extended versions of the 422 and 333 models derivable from
the 433 model and will save the exploration of the full set of non equivalently embedded SMs
for further work.) The magnetic monopole spectrum for the extended versions of the 422
and 333 models under various model assumptions [19–22] then suggest where experimental
searches may have the best chance of success.
Trinification from intersecting D-brane scenario with observable monopoles
In this section we explore a string motivated trinification model with monopoles that can
be light enough to be observed, in future colliders as well as ongoing cosmic ray searches.
– 3 –
More specifically, we will present an interesting supersymmetric version which is realised
in the framework of intersecting D-branes. We will describe here the basic steps for such
a viable D-brane construction. The trinification group is generated by three stacks of
Dbranes, each stack containing three parallel almost coincident branes. Each stack gives rise
to a U(3) gauge group which results in the gauge symmetry [23–25]
U(3)C × U(3)L × U(3)R .
In this notation, the first U(3) contains the SU(3) color group of the SM gauge symmetry,
the second U(3) includes the weak SU(
)L, and the third U(3) contains the SU(
group. From the group relation U(3) ≃ SU(3) × U(
)/Z3, in addition to the standard
SU(3)3 trinification gauge symmetry, the D-brane analogue is augmented by three extra
U(1)’s. The final local symmetry can be written
SU(3)c × SU(3)L × SU(3)R × U(
)C × U(
)L × U(
The abelian U(
)C,L,R factors have mixed anomalies with the non-abelian SU(3)3 gauge
part, but there is an anomaly free combination,
)Z′ = U(
)C + U(
)L + U(
The anomalies associated with the two remaining combinations are cancelled by a
generalized Green-Schwarz mechanism and the corresponding bosons receive masses from
fourdimensional couplings involving the Ramond-Ramond scalars coming from the twisted
closed string spectrum [26, 27]. Furthermore, there is a remaining global symmetry
associated with U(
)C of the color gauge group factor U(3)C ≃ SU(3)C × U(
)C /Z3, which can
be identified with baryon number that is conserved at the perturbative level.
Next we briefly present the salient features of the spectrum. In intersecting D-branes
the fermion and Higgs fields are generated by open strings with ends attached either on
the same brane stack, or on two different brane stacks. In the most general picture (as
in the presence of orientifolds), there are also strings with one end attached on mirror
brane stacks giving rise to additional states. More precisely, open strings with ends on
two different brane stacks give rise to bifundamentals, while strings with both ends on the
same (or with one end on a mirror) stack introduce, among others, adjoint, antisymmetric
and singlet representations. For the trinification model in particular, the bifundamentals
are of the well-known form (3, 3¯, 1), (1, 3, 3¯) and (3¯, 1, 3).
Additional representations corresponding to open strings with ends on the same (or
mirror) stacks may appear in the massless spectrum. These transform only under one
gauge factor and they are formed according to 3 × 3 = 3¯ + 6 and 3 × 3¯ = 1 + 8. Note that
for the SU(3)3 symmetry, in particular, these can generate states in (
3, 1, 1
1, 3, 1
1, 1, 3
). All of these states are ‘charged’ under the U(1) factors.
– 4 –
different brane stacks and have the quantum numbers
The three lower indices refer to the three abelian factors U(
)C,L,R discussed above. The
Higgs content may be accommodated in the bifundamentals
There are also representations generated with both ends on the same brane stack, such as
= (3, 3¯, 1)(+1,−1, 0)
c = (3¯, 1, 3)(−1, 0,+1)
= (1, 3, 3¯)( 0,+1,−1) ,
Ha = (1, 3, 3¯)( 0,+1,−1), a = 1, 2 .
HL = (
1, 3, 1
HR = (
1, 1, 3
HC = (
3, 1, 1
and their complex conjugates (c.c.).
Under SU(3)C × SU(
)L × U(
)Y × U(
)Ω (where U(
)Ω is left over from the SU(3)R
breaking) the MSSM states have the following assignments
and similarly for the Higgs scalars Ha + c.c.
) generators XL′ and XR′ of SU(3)L and SU(3)R respectively
The ‘standard’ hypercharge assignment corresponds to a linear combination of the
HL = (
1, 3, 1
) = hˆ+
1, 2; − 2 , 0
+ νˆHL (1, 1; 0, 0)
HR = (
1, 1, 3
) = eˆcH (1, 1; 1, 0) + νˆHc+R (1, 1; 0, 1) + νˆHc−R (1, 1; 0, −1) ,
have non-zero components under U(1)Z′ defined in (3.3), and it turns out that, with respect
to (3.13), the states (3.14), (3.15) now carry the SM electric charges. Therefore, provided
)Z′ gauge boson remains massless down to the electroweak scale, the exotic
fractional states do not appear in this case. The mass of Z′ is affected by higher dimensional
anomalies and whether it becomes massive or not, depends on the details of the particular
Indeed, let Da, Db represent two stacks of the intersecting branes, where the topology
of the 6-dimensional compact space is factorised into three tori Ti, i = 1, 2, 3. Then,
the multiplicities of the chiral fermions decending from the Da-Db bifundamentals are
associated with the number of intersections
be fractional ± 3 , ± 3
Under the above hypercharge embedding, all MSSM particles obtained from the
decompositions in (3.11) acquire their SM charges. However, we have observed that additional
superfields are also available from strings with both ends attached on the same brane stack
and under the hypercharge assignment (3.12), they are fractionally charged. The electric
charges of the SU(
)L triplet components HL = (
1, 3, 1
) + c.c., in particular, are found to
We have seen already that in the present D-brane construction, the three additional
abelian factors define the anomaly free linear combination (3.3) which can be used to
redefine the hypercharge according to
Y ′ = Y +
16 Z′ = − 6
6 Z ,
where Z′ is the generator of U(
)Z′ in (3.3). Under this definition the hypercharge
assignments of the ordinary quarks and lepton fields are not altered. In contrast, the hypercharge
of the states
Y = − 6
Iab = Y(mainbi − mbinai) ,
– 6 –
where (nai, mai) are the winding numbers of the Da stack wrapping the two radii of the i-th
torus. Similar formulae can be written for fields arising from other sectors. The restrictions
on the nai, mai winding numbers originating from the RR-type tadpole conditions can be
readily satisfied. The mixed anomalies SU(3)2a × U(
)a are proportional to Iab and impose
additional restrictions on the nai, mai sets. For instance, after dimensional reduction the
ten-dimensional fields C2, C6 give the two-form fields C2 = B0 and B2i = RTj×Tk C6, and
similar formulae hold for their duals.
The coefficients involved in the anomaly cancellation conditions depend on the winding
numbers. The coefficient c0a = ma1ma2ma3, in particular, couples directly to the linear
combination (3.13) through B0
2 ∧ (Fc + Fl + Fr) where Fc,l,r are the corresponding field
fermion multiplicities require c0a 6= 0, and, as a result the corresponding gauge boson Z
becomes massive. In such a case, the new hypercharge definition cannot be implemented
and so the states (3.14), (3.15) remain with exotic fractional charges.
Gauge couplings, weak mixing angle and monopole mass in D brane trinification
The various stages of the symmetry breaking chain in the D-brane trinification model are
as follows. Initially, recall that for each brane stack U(3) ≃ SU(3) × U(
). The SU(3)L,R
symmetries are assumed to break at some intermediate scale between the Z boson mass
MZ ≈ 92 GeV and unification scale MU . The linear combination U(
)Z′ may also break
at any scale MZ′ < MU . However, if it is part of the hypercharge generator, this breaking
should occur at low energies.
In the present trinification version the three gauge couplings αL,R,C associated with the
three sets of D-brane stacks are not necessarily equal. Hence, in principle, there is enough
freedom to reconcile the low energy values of the gauge couplings with the
experimental measurements. Partial unification may lead to some constraints for the intermediate
breaking scales. In the most general scenario, we may assume that the gauge couplings of
)C,L,R differ from those of the corresponding SU(3) factors (perhaps due to threshold
effects, etc). Thus, we designate them with αL′ , αR′ , αC′ .
The generalized hypercharge embedding implies
where κ = 1 for the general case, while for κ = 0 we obtain the standard hypercharge
assignment. It is convenient to define the ‘harmonic’ average
– 7 –
sin2 θW =
, κ = 0, 1 .
4 1 + ααRL
+ κ 23 ααNL
αY − α2
− α3 MX
At MX = MR, it holds α2 = αL, α3 = αC while for the hypercharge we use formula (3.13)
for κ = 1 and αi′ = αi (a similar analysis can be easily performed for κ = 0). Also, for
mass scales MX in the energy scales between MR and MU , where MU is the GUT scale,
the SU(3)C gauge coupling is eliminated in this combination, so that
αL − αR
, for MR ≤ MX ≤ MU .
Then, the trinification breaking scale is independent of the aC coupling, thus the latter can
be fixed independently in order to give the known low energy value for α3. We can use now
the Renormalization Group Equations (RGEs) to determine the trinification breaking scale
as a function of the known low energy values of the gauge couplings and beta functions.
Matching the RGEs above and below the MR scale we find that is given by
For κ = 0 and αL = αR we obtain the standard definition and the value sin2 θW (MU ) = 38 at
the GUT scale. For αL′ = αL = αR′ = αR = αC′ = αC and κ = 1, sin2 θW (MU ) = 169 . For
αL′ 6= αL, αR′ 6= αR etc., the standard sin2 θW (MU ) = 83 is obtained if the condition α1R +
= α1L is fulfilled. Notice however, that although in a general D-brane configuration
such states are possible [23, 24], in a minimal intersecting D-brane scenario with just three
brane stacks, the requirement for three fermion families imply  a GUT mass for the
gauge boson of the anomaly free U(
)Z′ combination (3.3). In such a case this cannot be
used to modify the hypercharge generator and as a result, the representations (
1, 3, 1
remain with fractional electric charges. For our purposes, in search for lighter monopoles
κ = 0, we find that gR ≈
and assuming trinification breaking not too far from the EW scale, from eq. (3.17) setting
In the D-brane models a low unification scale is a plausible scenario since there is no
compelling reason that the couplings unify at a high scale. As an illustrative example, let
us see how this works in the present case. Let us designate the trinification scale with MR
and define the following combination at some scale MX ≤ MR:
MR = e β−2πβ′ A1Z − A1U
β = 6bY − 12b2 − b3 , β′ = 9(bR − bL) .
where AZ is given by AX when evaluated at MZ and AU = AX at MX = MR. Also, the
coefficients β, β′ are given by
For the particular case bL = bR, we get partial unification αL = αR and, since then
β′ = 0, the scale MR does not depend on MU and is fixed only in terms of the low energy
parameters. We obtain
MR = e β AZ MZ ≈ 7 × 1010GeV .
MR ∼ 106 GeV.
which is proportional to the difference of the inverse gauge couplings αL,R at the unification scale
MU (see text). On the ordinate are the values for the difference of the corresponding beta functions
β′/3. Curve (
) corresponds to MR ∼ 104 GeV, curve (
) to MR ∼ 105 GeV, and curve (3) to
trinification scale can be as low as 104 to 106 GeV.
In general, however, the string boundary conditions imply bL 6= bR and therefore various
posibilities emerge. In figure (
) we show contour plots for MR = 104, 105, 106 GeV in the
parameter space A1U , bR − bL. For reasonable values αL1,R ∼ O(10) and β′ ∝ bR − bL, the
The reader might wonder whether a low trinification breaking scale could have
catastrophic consequences for baryon number violating processes. Firstly, we recall that
trinification symmetry does not contain gauge boson mediated dimension six proton decay
operators. Secondly, as we have already pointed out, all baryon fields Q = (3, 3¯, 1) carry
the same charge under the abelian symmetry U(
)C and, therefore, the latter could play
the rˆole of baryon number. Finally, introducing a suitable ‘matter’ parity in order to
distinguish the Higgs and lepton multiplets, H = L = (1, 3, 3¯), the only allowed Yukawa coupling
involving the quark fields is QQcH. Thus, proton decay can be adequately suppressed in
this class of trinification models.
Before closing this section, we point out that a similar intersecting D-brane
configuration can be arranged for the 422 model where states with fractional charges ± 6 , ± 2e are
generated by open strings with appropriate boundary conditions. The states with electric
charges ± 6e also carry color and are therefore confined.
– 9 –
Magnetic monopoles can be problematic in the standard big bang cosmology. If they
are produced at a high, MU ∼ 1016GeV unification scale where a U(
) emerges from a
non-abelian gauge group, then they overclose the Universe in the standard hot big-bang
cosmology. This problem is solved by inflation which dilutes the monopoles, in some cases
to levels that agree with observation. Then, it is perfectly reasonable to ask the question:
how do primordial monopoles survive cosmic inflation?
This has been addressed in a number of ways by various authors and we very
briefly summarize a few of them. Firstly, suppose that the spontaneous breaking of
nonsupersymmetric SO(10) to the SM proceeds via the 422 symmetry, with inflation driven by
an SO(10) singlet field  using the Coleman-Weinberg potential. For this case a scalar
spectral index ns ∼ 0.96 − 0.97 is realized for a Hubble constant Hinf during inflation of
− 1014 GeV . This leads to the conclusion that monopoles associated with
the breaking of 422 at an energy scale close to Hinf can survive the inflationary epoch
and be present in our galaxy at an observable level. This SO(10) inflationary scenario also
predicts that the tensor to scalar ratio r, a canonical measure of gravity waves, is not much
smaller than 0.02 , which will be tested in the near future.
A somewhat different inflationary scenario based on a quartic potential with
nonminimal coupling of the inflaton field to gravity predicts an r value up to an order of
magnitude or so smaller  than the previous example. The monopole mass in this case
is around 1013–1014 GeV.
Monopoles arising in models such as supersymmetric trinification have been shown 
to survive primordial inflation by exploiting an epoch of thermal inflation – which
dilutes their number density to levels below the Parker bound. Depending on the model
details the monopole masses can vary from the intermediate to GUT scale.
If the theory has a product group that avoids proton decay without being broken at
a high scale and if the monopoles are not produced until near the electroweak scale, then
they could be eliminated by late time inflation, although this may not be easy to arrange.
Another possibility [40, 41] is to eliminate them or substantially reduce their numbers by
temporarily breaking the appropriate U(
). Then the monopoles find themselves on the end
of cosmic strings. The high tension in the strings causes efficient monopole-antimonopole
annihilation thereby solving the cosmic monopole problem. Either of these mechanisms
allows one to bring the monopole mass density down to a value that does not conflict with
present astrophysical observations.
Here we explore the possibility of detection of low and intermediate mass magnetic
monopoles, especially those that are multiply charged. For the detection of low mass
magnetic monopoles we focus on the LHC, and for the detection of intermediate mass
magnetic monopoles we focus on cosmic ray experiments.
There have been recent suggestions of light monopoles in the standard model [19–22] and
this possibility can also be explored in various branches of the 433 model. Singly charged
monopoles (i.e., charge n = 1) interact strongly with matter [42, 43] through their fine
2α ∼ 68 ,
and cross sections are enhanced by a factor of n2 for multiply charged monopoles. Hence
the reach of the LHC is long if it produces M M pairs. But as we discuss below,
production at the LHC requires that the M M pairs are fundamental, i.e., of Dirac type, since ’t
Hooft-Polyakov [44, 45] monopoles, being composite, are much harder to produce and their
production cross section has been estimated to be suppressed by greater than 30 orders of
magnitude relative to production of fundamental point-like monopoles . Hence,
composite monopoles are extremely unlikely to be accessible at the LHC. (For other possibilities
see also [47, 48])
Above threshold fundamental M M pairs will be copiously produced and easily detected
by their densely ionizing tracks in detectors. The MoEDAL experiments [49–54] searches
for monopoles both by tracking in layered material and by monopole capture in aluminum
bares that are run through superconducting detectors. Both these types of searches are
carried out offline.
Monopoles will be accelerated (or decelerated) in detector magnets, and will travel
on parabolic trajectories in constant magnetic fields. Hence their track will not look at
all like electrically charged particles traveling on helical orbits in magnetic fields. Track
reconstruction fitting routines can easily be made to distinguish the difference. Combining
ionization with tracking could make a monopole track even more unmistakable.
Below threshold virtual pairs of monopoles can contribute to loop diagrams for
scattering processes and alter cross sections from their predicted SM values. For example,
Drell-Yan like production cross sections qq¯ → XX could be enhanced.
Even though production cross sections of composite ’t Hooft-Polyakov monopoles are
too small for them to be produced at accelerators, this is not the case for point-like Dirac
While a full quantum theory of magnetic monopoles is lacking, limits on
Dirac monopole production have been obtained via a Drell-Yan model , and applied to
monopoles of 1, 2, 3 and 6 times the Dirac charge for 175 pb−1 exposure of pp¯ luminosity of
material in the collision regions of both D0 and CDF. The resulting monopole mass limits
are 256, 355, 410 and 375 GeV/c2 respectively, while the production cross section limits
are 0.6, 0.2, 0.07 and 0.2 pb respectively.
The fractional electric charges are also very interesting in these models and potentially
detectable. The electric charges are often in multiples of 21 e or 13 e, but other fractions of e
are possible in certain embeddings of the SM in the 433 model. In one case particle charges
come in fractions as small as 112 e .
In the past, many of the best magnetic monopole limits (a comprehensive list of
references can be found in the ‘Magnetic Monopole Bibliography,” of Giacomelli et al., [55, 56],)
have been based on cosmic ray experiments [57–61], but now there is also a dedicated
experiment at the LHC for this purpose. The MoEDAL experiment [49–54] mentioned above has
been specifically designed to search for magnetic monopoles and other highly ionizing
particles. The ATLAS experiment has also reported on their magnetic monopole search .
We hope the results presented here can provide additional motivation to these and other
The number density of monopoles emerging from an early universe phase transition is
determined by the Kibble mechanism [63, 64]. From the number density we determine the flux of
free monopoles with M < 1015 GeV accelerated to relativistic energies by the cosmic
magnetic fields. The general expression for the relativistic monopole flux may be written [42, 43]
The IceCube experiment has recently put a limit on the flux of light mildly relativistic
(β < 0.8) magnetic monopoles [65, 66]
Φ90%C.L. ∼ 10−18cm−2sr−1s−1 .
This in turn limits the cosmic density of magnetic monopoles, but it does not eliminate
the possibility that cosmic monopoles were all either inflated away or annihilated at the
electroweak scale but can now still be produced in accelerator or cosmic ray collisions if
they are point-like particles.
Magnetic monopoles in cosmic rays could have been produced in the early universe and
therefore could be of either composite ’t Hooft-Polyakov type or Dirac point-like type. The
Pierre Auger experiment has recently reported on a search for ultra relativistic magnetic
monopoles  and placed limits on their flux of 1×10−19 (cm2 sr s)−1 and 2.5×10−21 (cm2
sr s)−1 for Lorentz factors of γ = 109 and γ = 1012 respectively, and as mentioned above,
IceCube has also placed limits on the flux of relativistic and mildly relativistic magnetic
monopoles . For velocities above 0.51 c they see no flux above 1.55 × 10−18 (cm2 sr
s)−1. The best upper limit on the flux of nonrelativistic magnetic monopoles comes from
MACRO  who find 1.5 × 10−16 (cm2 sr s)−1 for 4 × 10−5 < β = v/c < 0.5, where all
fluxes above are quoted at the 90% C.L. Numerous other experiments have also placed
limits on the flux of magnetic monopoles in cosmic rays Baikal , SLIM , RICE 
and ANITA-II , with the best limit on ultra relativistic magnetic monopoles coming
from ANITA-II and the best limit on relativistic magnetic monopoles β = 0.9 coming from
IceCube , as discussed and summarized in .
Q.S. is supported in part by the DOE Grant DE-SC0013880. T.W.K and G.K.L. would
like to thank the Physics and Astronomy Department and Bartol Research Institute of the
University of Delaware for kind hospitality. Also, G.K.L. would like to thank LPTHE of
UPMC in Paris for kind hospitality during the final stages of this work.
This article is distributed under the terms of the Creative Commons
Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in
any medium, provided the original author(s) and source are credited.
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