The Amaterasu Cosmic Ray as a Magnetic Monopole and Implications for Extensions of the Standard Model

The Amaterasu cosmic ray particle appears to have come from the direction of the local cosmic void. We take this as evidence that it is a magnetic monopole rather than a proton or nucleus. This in turn strongly suggests physics at high energy is described by a quiver gauge theory.


Introduction:
The Greisen-Zatsepin-Kuzmin [1,2] limit ∼ 5 × 10 19 eV ( or GZK cutoff) is the upper bound on the energy of cosmic ray protons traveling from their production in distant galaxies through the intergalactic medium to us.The limit is due to cosmic ray proton energy being degraded by interacting with cosmic microwave background photons via the process p + γ → ∆ * → p + π 0 .The mean free path (mfp) for this process is ∼ 6 Mpc.The recent Amaterasu cosmic ray particle found by the Telescope Array Group [3] appears to have come from the direction of the local cosmic void, which subtends a solid angle of approximately 1.6 π and is at least 45 Mpc across [4,5], so it is unlikely that a cosmic ray proton could cross such a distance unscathed.(To make it all the way across the local void the particle would need an initial energy of about 10 23 eV which seems highly unlikely, given known acceleration mechanisms.)That leads us to conclude the following, either (i) there is a source of ultra high energy cosmic rays (UHECRs) within the void, (ii) the path of the Amaterasu particle was bent substantially by a foreground object, presumably within the Milky Way (see e.g., [6]), or (iii) the Amaterasu particle is not a proton or nucleus, but instead a magnetic monopole (MM) [7,8].We can think of free MMs as having no galactic source, but rather as particles that have wondered the Universe since their production in an early gauge theory phase transition.Option (i), a UHECR source is possible, but appears unlikely and has been analysed in detail by [9].While there are a few dwarf galaxies in the local void, the chances of producing UHECRs there is diminished by the ratio of the density of galaxies in the local group compared to the density off galaxies in the local void, roughly a factor of 10 3 , which renders option (i) unlikely.Option (ii), could be a UHECR proton or nucleus that appears to have originated in the local void, but in actuality was produced elsewhere, say in the local group, and who's path was bent by interacting with a local object containing a strong extended B-field to make it appear as if the particle came from the local void.Again we consider this possibility unlikely.Details of an analysis along these lines can be found in the extensive review by Anchordoqui [6].For other constraints on nearby sources of ultra high energy cosmic rays see [10].
The probability of bending such a high energy particle in the foreground, i.e., option (ii) would require an encounter with a strong magnetic field over a length scale L. Details can be extracted for such estimates from [6].Again this is highly unlikely and leads us to conclude that option (iii), that the Amaterasu particle was a magnetic monopole, is our best choice.
If we assume a magnetic monopole is the solution to the mystery of the Amaterasu particle, then we need to discuss the necessary properties of such a monopole and in what theories it might arise.First the monopole must be relativistic, which means it is relatively light.For example, if the monopole arose in an SU(5) grand unified theory, either SUSY or nonSUSY, then its mass would be M GU T /α or ∼ 10 17 GeV, or ∼ 10 26 eV, far too heavy to be relativistic.If we require a relativistic gamma factor of say, at least 10 3 , then the monopole mass should be roughly 10 17 eV (10 5 TeV) or less.That puts a strong constraint on models where magnetic monopoles appear.However, there is a large class of such models that we will discuss.
Requiring that monopoles not consume galactic magnetic fields faster than galactic dynamos can regenerate them results in the Parker bound is of 10 −15 /cm 2 /s/sr.The Parker bound is several orders of magnitude above the observed highest-energy cosmic ray flux of 1 per km 2 per century, hence does not constrain UHECRs.

Monopole Energy:
The kinetic energy gained by magnetic monopole on traveling along a magnetic field of coherence length ξ is [7] where is the magnetic charge according to the Dirac quantization condition, B is the magnetic field strength, ξ is the field's coherence.Allowing the monopole to random-walk through the n domains of coherent fields would increase the result by roughly √ n.Typical astrophysical magnetic fields in galaxies, galaxy cluster, AGN jets, etc. range from 0.1-100 µG while the coherence length of these fields range from 10 −4 − 30 Mpc.This leads to monopole energies in the range 1.7 × 10 20 to 5 × 10 23 eV.
See [8] for more details, and for a more recent comprehensive study of the acceleration of monopoles in intergalactic magnetic fields see [11].
It is important to note that the current bound on the flux of relativistic monopoles from while the observed flux of UHECRs is only about one per km 2 per century, or The Amaterasu event had energy E A = 2.44 × 10 20 eV and so falls within the expected monopole energy range, and it is also not disfavored by the Ice Cube bound.
The highest initial energy UHECR ever seen is the Fly's Eye event [13] at energy E F E = 3.2×10 20 eV.The Amaterasu event and two events from AGASA [14,15] at nominal energies E A1 = 2.46 × 10 20 eV and E A2 = 2.13 × 10 20 eV are all within 1 σ of each other, hence within errors of being second in energy to the Fly's Eye event.AGASA reported eleven events in all with energy above 10 20 eV.The Pierre Auger experiment has reported there 20 highest energy events range between 1.10 and 1.66 × 10 20 eV [16,17].

Monopole Direction:
The direction of the center of the local void is [4,5] (RA, Dec) = (279.5• , 18.0 • , ) while the arrival direction of the Amaterasu comic ray was (RA, Dec) = (255.9 which is well within the direction of the local void.Even if backtracked through the galactic field, a proton or nucleus still appears to originate within the local void [9].Given that there are no apparent sources of UHECR protons or nuclei within the local void and that it is highly unlikely that such a trajectory could have been bent by a foreground object within our galaxy, we are led to conclude that the Amaterasu particle was a magnetic monopole.
Since it was relativistic this constrains the monopole mass M ≤ 10 8 GeV.
We can also arrive at the following lower bound on the monopole mass by requiring the phase transition where monopoles are produced to be above the electroweak scale This makes it difficult for the symmetry breaking where monopoles were produced to be of standard grand unification type, i.e, in the SU(5), SO( 10), E 6 chain and more likely to be a quiver gauge theory of the type which we now discuss.

Models with Light Magnetic Monopoles:
The general class of quiver gauge theories are most easily arranged to have light magnetic monopoles since they can have separated gauge and flavor groups, and hence avoid proton decay with a low symmetry breaking scale where the U(1) appears that is associated with the monopole.The simplest examples of this are the Pati-Salam model (PS) [18] and the Trinification model (T) [19] with gauge groups SU( 4)×SU( 2)×SU( 2) and SU(3)×SU(3)× SU(3) respectively.
The appearance of monopoles in quiver gauge theories which generalise the original PS and T models has been analysed in [20][21][22][23].The last two of these papers used the LieART platform [24,25] to study, as the simplest extensions of PS and T, gauge groups with . By restricting the size of G, a manageably finite, but large, number of models are selected and studied more completely analysed than was previously accomplished by hand.Further papers on quiver gauge theories include [26][27][28][29][30][31].
Once we depart from the framework of GUTS, leptons with fractional electric charges e.g.(± e 2 , ± e 6 ), appear.Thus, if the Amaterasu cosmic ray is a monopole, it suggest the probable existence of fractionally-charged leptons in particle theory [20][21][22][23].Fractional electric charged particles in turn predicts multiplely charged monopoles in order that the Dirac relation ge = n /2 is maintained.
The mass of the magnetic monopoles can naturally be at an intermediate scale such as the expected mass of the Amaterasu particle and new particle physics, like fractional charged lepton, should be expected at a few T eV scale.Indirect evidence of monopoles may be accessible to the LHC where there are now dedicated monopole searches such as the MoEDAL experiment [32,33].Searches for the additional light particles, such as fractionallycharged leptons as predicted by such magnetic monopole theories, can be performed at the Large Hadron Collider (LHC).
Since we want a high energy monopole to look like the Amaterasu event, our interest is in baryonic monopoles, bound states of monopoles with both color magnetic and U(1) EM magnetic charge.These particles exist in various quiver gauge theories, but for the present discussion we focus on a model independent analysis.For a hard collision involving one of the constituent quarks in normal baryon, the quark winds up on the end of a QCD electric flux tube that typically breaks once it is long enough to fragment into mesons.If the initial collision is between a proton and a nucleus in our upper atmosphere, then a cascade follows and the remnants can be seen in a detector on the surface of the earth.For a collision involving an individual monopole within the baryonic monopoles, a string (color magnetic flux tube) forms, but it can not break unless there is enough energy to produce a monopoleantimonople pair.Consequently in most such collisions the color magnetic string oscillates and radiates light particles.But while this string is still stretched, the excited baryonic monopole's cross section is dramatically increased and further scattering takes place that can mimic the air shower of a ultra high energy proton or nucleus [8].

Conclusion:
Cosmic rays have historically played a major rôle in particle physics, such as the original discoveries of the positron and the muon.The Amaterasu cosmic ray is only one event but it is an extraordinary one.It is one of the most energetic cosmic rays ever recorded and the only one of those pointing back to the local void where there is no obvious source.This renders it unlikely that the primary is a proton or nucleus and leads to our favoured interpretation as the long-sought magnetic monopole predicted in beautiful theory invented by Dirac in 1931.(That the Amaterasu particle may be a magnetic monopole has also recently been suggested by [34].)If this is correct, it impacts on what is the most likely extension of the standard model of particle theory, for which we have suggested a quiver gauge theory with chiral fermions in bifundamental representations.This also predicts the probable existence of fractionally charged leptons which could be discovered at the LHC.
The remarkable and unexpected observation of the Amaterasu cosmic ray, reported first in November 2023, provides a potentially revolutionary step forward in the theory of particle physics.