Has Telescope Array Discovered Electroweak Monopole?

We propose the ultra high energy cosmic ray recently detected by Telescope Array to be the electroweak monopole, and present theoretical arguments which support this. This strongly motivates the necessity for the ``cosmic"MoEDAL experiment which could back up our proposal. To confirm this we propose Telescope Array to measure the magnetic charge of the ultra high energy cosmic ray particles with SQUID.

Recently the Telescope Array Group (TAG) has announced the detection of an ultra high energy cosmic ray (UHECR) of energy 244 EeV (244 × 10 18 eV) [1].This is the most recent confirmation of the existence of the UHECR particles, following the 320 EeV particle in 1991, 213 EeV particle in 1993, and 280 EeV particle in 2001 [2].This tells that the UHECR particles exist in nature.
The TAG (and similar previous) report is very interesting and remarkable in two aspects.First, the energy of the cosmic ray exeeds the Greisin-Zatsepin-Kuzmin (GZK) energy limit [3].Second, the arrival direction of the UHECR implies that it came from the Local Void.This is puzzling, because there are few known particles in nature which could produce such UHECR.
A natural candidate for the UHECR is the proton, but it is very difficult for proton to generate such high energy.A relativistic proton moving through the cosmic microwave background, after collision with the 3 K microwave photons becomes ∆ * and decays to nucleons and pions, And the mean free path for this process is known to be about 6 Mpc.This resonant scattering degrades the energy of the relativistic protons and prevent them to acquire the energy above 5×10 19 eV.This is the GZK limit [3].This implies that, if the UHECR of TAG is proton, it should have originated nearby, or should have energy far above the GZK limit.But these possibilities seems unlikely.
The other point is that the UHECR observed by TAG appears to come from the void, which suggests that the origin of this UHECR is not galactic center or other astronomical objects like the neutron stars.This is another puzzling feature of this UHECR [1].
From this we may conclude that the UHECR of TAG is not likely to be an ultra relativistic proton, or any known particle produced by the astronomical objects.This lack of a possible explanation for the UHECR is disappointing, and it has been suggested that this could be due to "an incomplete knowledge of particle physics" [1].The purpose of this Letter is to argue that the UHECR observed by TA could be the remnant electroweak monopole produced in the early universe during the electroweak phase transition.We present theoretical reasons to support this, and discuss how to confirm this proposal experimentally.
The proposition that the monopoles could be the source of the UHECR is not new [4].Obviously the monopole, if exists, becomes an ideal candidate for the UHECR particle.It has the strong magnetic interaction, stronger than the electric interaction of proton by the factor 1/α.It has the absolute stability guaranteed by the π 2 (S 2 ) monopole topology, which is required for the UHECR particles.Moreover, it may have the mass much heavier than the proton.For this reason it has been asserted that the grand unification monopole could generate the UHECR [5].But in this paper we argue that the electroweak ("Cho-Maison") monopole could be the UHECR particles.To do that we must understand why the electroweak monopole, not others, should be viewed as the UHECR of TAG.
With the advent of the Dirac monopole, the magnetic monopole has become an obsession in physics [6,7].After the Dirac monopole we have had the Wu-Yang monopole [8], the 'tHooft-Polyakov monopole [9], the grand unification monopole [10], and the electroweak monopole [11,12].But the electroweak monopole stands out as the most realistic monopole that exists in nature and could actually br detected by experiment [13][14][15][16][17][18].This is because the Dirac monopole in electrodynamics transforms to the electroweak monopole after the unification of the electromagnetic and weak interactions, and the Wu-Yang monopole in QCD becomes unobservable after the monopole condensation which confines the color.Moreover, the 'tHooft-Polyakov monopole exists only in a hypothetical theory, and the grand unification monopole which could have been amply produced at the grand unification scale in the early universe probably has become completely irrelevant at present universe after inflation.
Unlike other monopoles the electroweak monopole has the following unique features [11].First, the magnetic charge is not 2π/e but 4π/e, twice that of the Dirac monopole.This is because the period of the electromagnetic U(1) subgroup of the standard model is 4π, since the electromagnetic U(1) comes from the U(1) subgroup of SU (2).Second, the mass is of the order of several TeV, probably between 4 to 10 TeV.This is because the mass basically comes from the same Higgs mechanism which makes the W boson massive, except that here the coupling is magnetic (i.e., 4π/e).This makes the monopole mass 1/α times heavier than the W boson mass.In spite of this, the size of the monopole is set by the weak boson masses.This is because the monopole has the Higgs and W boson dressing which has the exponential damping fixed by the weak boson masses.Third, this is the monopole which exists within (not beyond) the standard model as the electroweak generalization of the Dirac monopole, as a hybrid between Dirac and 'tHooft-Polyakov monopoles.Finally, this monopole is absolutely stable.The topological stability must be obvious, but it also has the dynamical stability [18].
The importance of the electroweak monopole comes from the fact that it must exist if the standard model is correct.This means that the discovery of the monopole, not the Higgs particle, should be viewed as the final (and topological) test of the standard model.Moreover, if discovered, it will become the first topologically stable magnetically charged elementary particle in the history of physics [13].Furthermore, the monopoles produced in the early universe could play important roles in physics, in particular in cosmology [14].Indeed, when coupled to gravity, they automatically turn to the primordial magnetic black holes which could account for the dark matter, become the seed of stellar objects and galaxies, creating the large scale structures of the universe.As importantly, they could generate the intergalactic magnetic field, and could be the source of the ultra high energy cosmic rays [14].This makes the experimental detection of the electroweak monopole a most urgent issue after the discovery of the Higgs particle.For this reason MoEDAL and ATLAS at CERN are actively searching for the monopole [19][20][21].Since the electroweak monopole has unique characteristics, they could detect the monopole without much difficulty, if LHC could produce them.If the monopole mass exceeds 7 TeV, however, the present 14 Tev LHC may not be able to produce the monopoles.In this case we may have to wait for the next upgrading of LHC, or else look for the remnant monopoles produced in the early universe during the electroweak phase transition.
How can we detect the remnant electroweak monopoles?Obviously we could design a "cosmic" MoEDAL experiment located at high mountains to detect them, and this is in planning now.At this point one might wonder if the underground experiments like IceCube or Antares could be helpful.Unfortunately the underground experiments may have difficulty to detect them because the penetration length of the monopole in matters is expected to be very short (of the order of 10 meters in aluminum) because of the strong magnetic interaction [22,23].
Another way to detect the electroweak monopole is to detect UHECR particles which could be generated by the remnant monopoles, using the cosmic ray experiments.The primary purpose of this type of experiments, of course, is to detect the high energy cosmic rays (not the monopoles).Nevertheless this type of experiments could be used to detect the remnant monopoles, and in this connection the TA experiment could play an important role.The question here is why and how the remnant electroweak monopoles could be identified as the UHECR particles.Now, we are ready to discuss how they can become the UHECR particles.
To see this we first notice that the remnant electroweak monopoles could easily acquire the energy above the GZK limit from the intergalactic magnetic field.Since the average intergalactic magnetic field B is about 3 × 10 −6 G with the coherent length L of the order of 300 pc, we could estimate the monopole energy gain traveling through the intergalactic magnetic field to be [14] ∆E ≃ 4π e BL ≃ 1.2 × 10 20 eV. ( Moreover, we can easily show that the monopole energy loss due to the linear acceleration is completely negligible.This confirms that they could acquire the energy above the GZK limit without any problem. Moreover, unlike the proton, the monopole retains its energy traveling through the cosmic microwave background.This is because the photon-monopole scattering cross section is givden by the classical Thompson scattering cross section, which is many orders of magnitude down the photon-proton cross section described by (1).
Notice that (2) is independent of the monopole mass.So, depending on the mass the monopole (even with the above energy) could be relativistic or non-relativistic.For example, if it is the grand unification monopole of mass of 10 17 GeV, it becomes non-relativistic and thus can not generate relativistic secondaries in the cosmic ray shower.In contrast, (2) makes the electroweak monopole with mass of M W /α extremely relativistic, so that it could easily generates the relativistic showers.And in reality we do have the relativistic showers in the UHECR.This strongly indicates that the UHECR could be the electroweak monopole.In the following we will assume the monopole mass to be M = M W /α for simplicity.
How is the electromagnetic shower of the electroweak monopole?The magnetic field of the monopole B = (4π/e)r/r 2 , when boosted to the energy (2), generates the electric field ⃗ E = γβ⃗ v × ⃗ B. So, the electromagnetic energy loss of the relativistic electroweak monopole should be similar to that of a heavy charged particle of mass M W /α with similar γ factor (for our monopole with energy (2), we have γ ≥ 10 7 ) and charge 1/α.Moreover, the Cherenkov radiation of the monopole is enhanced by the factor (1/α) 2 , compared to that of the proton.This enhanced Cherenkov radiation is an important feature of the UHECR generated by the electroweak monopole, which could be useful in identifying the UHECR particle as the electroweak monopole.
As for the hadronic shower of the electroweak monopole, notice that the maximum fraction of the energy transferred from our monopole of mass M to the target particles with mass m is given by [5] Now, for our case we have This should be compared to the maximum energy transfer of the proton (with M ≃ m) which is not so different from (4).From this we may conclude that our monopoles transfer most of the energy in the first forward hadronic scattering, and thus produce an air shower resembling a typical hadron initiated shower.This implies that trying to identify the UHECR with hadronic shower pattern may not be a wise strategy.Now, we have to discuss the remnant electroweak monopole density at present universe.This is a complicated issue, but fortunately this has already been studied before [14].To summarize the results we start from the temperature dependent effective action of the standard model where V 0 is the zero-temperature potential, g * is the total number of distinct helicity states of the particles with mass smaller than T , C 1 and C 2 are the contributions from the weak bosons and fermions, m t is the top quark mass, and δV T is the slow-varying logarithmic corrections and the lighter quark contributions which we will neglect from now on.
The potential has three local extrema at The first extremum ρ s = 0 represents the Higgs vacuum of the symmetric (unbroken) phase, the second one ρ − (T ) represents the local maximum, and the third one ρ + (T ) represent the local minimum Higgs vacuum of the broken phase.It is charactrized by three temperatures, Above T 1 only ρ s = 0 becomes the true vacuum of the effective potential, and the electroweak symmetry remains unbroken.At the critical temperature T c , the two vacua ρ s and ρ + are degenerate and the electroweak phase transition starts.At T 2 we have only one vacuum ρ + with ρ 0 = ρ − , and the phase transition ends.So, in principle the electroweak phase transition is the first order.Since T 1 , T c , and T 2 are very close, however, the phase transition practically becomes the second order [14].The effective potential ( 6) is graphically shown in Fig. 1.
The monopole production in the second order phase transition is supposed to be described by the Kibble-Zurek mechanism, so that the monopole production start from T c .However, the thermal fluctuations of the Higgs vacuum which create the seed of the monopoles continue till the universe cools down to the Ginzburg temperature T G ≃ 57.6 GeV, where the monopole production stops [14,24].The Ginzburg temperature is shown in Fig. 1.So, the electroweak monopole formation takes place between T c and T G , or in average around T i , In time scale, we can say that the electroweak monopole production start from 1.8 × 10 −11 sec to 1.2 × 10 −10 sec after the big bang for the period of 10.3 × 10 −11 sec, or around 3.5 × 10 −11 sec after the big bang in average.
Two important parameters of the electroweak phase transition are the temperature dependent Higgs boson mass MH which determine the correlation length ξ = 1/ MH and the W-boson mass MW which determines the monopole mass M ≃ MW /α.The Higgs boson acquires its minimum mass 5.54 GeV at T = T c which approaches to the zero temperature value 125.2 GeV as the universe cools down.The W-boson which is massless before the symmetry breaking becomes massive toward the value 6.76 GeV at T c and 73.2 GeV at T G .This tells that the infant monopole masses at T c and T G are around 1.4 TeV and 10 TeV (with the adolescent mass 10.7 TeV).
According to the Kibble-Zurek mechanism the initial monopole density is determined by the mean value of two correlation lengths at T c and T G [25,26], From this we can estimate the initial density of the monopoles to be n i ≃ T 3 i /ξ 3 i ≃ 0.2 T 3 i .This estimate, however, has a defect that the energy within one correlation volume is not enough to provide the monopole mass.This is because the monopole mass is M W /α, but the size is fixed by M W .A natural way to cure this defect is to adopt a new correlation length ξi which satisfies the energy constraint, ξi = 1 α With this the initial monopole density is given by This is smaller than the Kibble-Zurek estimate by the factor α.
determine the remnant monopole density at present universe, however, we have to know how it evolves in cosmology.The evolution of the monopoles is determined by the Boltzmann's equation [27]  where H is the Hubble parameter and σ ≃ 1/3αT 2 is the monopole annihilation cross section.The solution of the evolution equation is shown in Fig. 2. Notice that the monopoles, as soon as produced, quickly annihilate each other.This is because at the initial stage of the monopole production, the capture radius of the monopole and anti-monopole is much bigger than the correlation length.This quickly reduces the initial monopole density by the factor 10 −6 .Moreover, the final value of the monopole density becomes independent of the initial value and approaches to n → 18.25 (T /M P ) × T 3 regardless of the initial condition, where M P is the Planck mass [27].And the monopole-antimonopole annihilation ceases at the temperature T f ≃ 60 MeV.This is below the muon decoupling temperature, which tells that the annihilation of the monopoles continues very long time.
Below T f the monopoles are free streaming, and we can estimate the remnant monopole density at the present universe.The monopole density at T f becomes which is much lower than the initial density given by (12).The number of monopole within the co-moving volume is conserved thereafter.But they still interact with the electron pairs in the hot plasma before decouple around T d ≃ 0.5 MeV, when the electron pairs disappear and the interaction rate becomes less than the Hubble expansion rate.Since the decoupling temperature of the electroweak monopole is much less than the monopole mass, the free streaming monopoles just after the decoupling start as completely non-relativistic.But eventually they become extremely relativistic by the acceleration of the intergalactic magnetic field.
Assuming that the expansion is adiabatic, the current number density and the energy density of the monopole is given by [14] where T 0 = 2.73 K = 2.35×10 −13 GeV is the temperature of the universe today and g is the effective number of degrees of freedom in entropy.So we have the current density of monopole where ρ c is the critical density of present universe and h ≃ 0.678 is the scaled Hubble constant in the unit H 0 /(100 km s −1 Mpc −1 ).This is about 1.3 × 10 −9 of the baryon density.This assures that the electroweak monopole does not alter the standard big bang cosmology in any significaly way.
In terms of the number density, this translates to about 6.1×10 −5 / Km 3 , or about 2.3×10 −13 n b , where n b is the number density of the baryons.This is roughly 10 5 times bigger than the monopole density set by the Parker bound [28], which implies that ( 15) is an over estimation.
Actually there are reasons that the real remnant monopole density could be much less [14].First, as the only heavy stable particle with mass about 10 4 times heavier than the proton, they can easily generate the density perturbation and might have been buried in galactic centers.Second, they have a very short penetration length in matters, so that most of them could have been trapped and filtered out by the stellar objects after collision with them.Third (and most importantly), when coupled to gravity, they automatically turn to Reissner-Nordstrom type black holes and become the premordial magnetic black holes.This strongly implies that indeed (15) could be made consistent with the Parker bound.
With this remark we can confidently say that the UHRCR particle observed by TA could be the remnant electroweak monopole produced in the early universe, as one of us has pointed out in an earlier work [14].In particular, our estimate of the monopole density appears to be consistent with the UHECR event rate at TA, and it comes from the void as TA indicated.
Unfortunately, this proposition could only be confirmed indirectly at TA at the moment, with the enhanced Cherenkov radiation of the monopole.To confirm this directly, TA should be able to measure the magnetic charge of the UHECR.In principle this could be done by installing SQUID to each of the surface detectors at TA.We hope that TAG could measure the magnetic charge of the UHECR with SQUID in the near future.The details of our discussions will be published in a separate paper [29].

FIG. 1 .
FIG.1.The temperature dependent effective potential(6) at various temperatures, where TG is the Ginzburg temperature.Notice that the potential at T1, Tc, T2 are almost indistinguishable.