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Magnetic Monopoles and Dark Matter V

Magnetic Monopoles and Dark Matter V

ISSN 1063-7761, Journal of Experimental and , 2018, Vol. 127, No. 4, pp. 638–646. © Pleiades Publishing, Inc., 2018. Original Russian Text © V.V. Burdyuzha, 2018, published in Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2018, Vol. 154, No. 4, pp. 751–760.

NUCLEI, , FIELDS, GRAVITATION, AND ASTROPHYSICS

Magnetic Monopoles and Dark V. V. Burdyuzha Astrospace Center, Lebedev Physical Institute, Russian Academy of Sciences, Profsoyuznaya ul. 84/32, Moscow, 117997 Russia e-mail: [email protected] Received October 8, 2017; in final form, May 29, 2018

Abstract—Schwinger’s idea about the magnetic world of the early , in which magnetic charges (monopoles) and magnetic (g+g–) could be formed, is developed. In the present-day Universe mag- netic charges with energies in the GeV range can be formed in the magnetospheres of young pulsars in super- strong magnetic fields. Spectroscopic features of magnetic atoms and possibilities for their observations are discussed. Relic magnetic atoms can contribute up to 18% to the dark matter density. The gamma-ray excess at our Galactic center could arise under two- annihilation of magnetic charges as a cooperative effect from stars. A sharp physical difference of Schwinger’s magnetic world from Dirac’s present-day elec- tric world is pointed out. Artificial magnetic monopoles are also mentioned briefly.

DOI: 10.1134/S1063776118100011

1. INTRODUCTION However, not all of the “neglected” In electrodynamics the problem of magnetic magnetic charges, especially in the context of the early charges has not been completely clarified, although Universe. Furthermore, Sakharov [9] pointed out that the assertion that there are no free magnetic charges in black miniholes could evaporate heavy monopoles. has become fixed owing to Maxwell’s classical The inflationary cosmological model was developed equations. The problem has not become clearer even to avoid a great over-excess (up to 16 orders of magni- after the detection of structures similar to Dirac mag- tude) of high-energy GUT monopoles (GUT stands netic charges in laboratory conditions [1–3]. They for ). Zel’dovich and Khlopov were called artificial magnetic monopoles. Therefore, [10] showed that the present-day concentration of the authors of [1–3] predict a revolution in physics. In relic monopoles with energies in the TeV range is contrast, in this paper we transfer some of the “revolu- extremely low (10–19 cm–3). Schwinger published the tionary ideas” to the cosmos. Magnetic atoms and review “A Magnetic Model of Matter” in UFN [11], even isolated magnetic charges that are “blown out”, thereby predicting the magnetic world of the early as and , from young neutron stars Universe. In addition, an interesting remark was made can exist in cosmic conditions and, what is more, in [12]: “monopoles cannot play any role in the Stan- probably not all of the high-energy relic magnetic dard Model, and in its usual extensions, up to the atoms have decayed. Planck scale, on which they can lead to space discrete- Magnetic charges were first mentioned by Curie ness.” [4] more than 120 years ago. They were detected by the Here we want to draw attention to the possibility of Austrian Ehrenhaft [5] and the Soviet physi- detecting monopoles with energies in the GeV range in cist Sizov [6]. However, nobody believed these scien- cosmic conditions and to enhance the role of high- tists, because in Maxwell’s equations divB = 0 and energy magnetic monopoles in the early Universe. Maxwell’s equations are “sacred”. Sizov in his time The main reason for our desire to revisit the leptogen- was not even certified as a scientist, because he was esis is a huge magnitude of magnetic forces. In the concerned with “rubbish”. Magnetic charges of high symmetric (Schwinger) case, the magnetic forces are energies 1015–1016 GeV were probably observed in stronger than the electric ones approximately by a fac- cosmic rays by Cabrera [7]. However, there were only tor of ~20000 (Section 3). The question about the two events in his experiment and, what is more, these influence of these forces on the generation of were observed on Saint Valentine’s Day, which asymmetry of the Universe immediately arises here, caused distrust of the physical community. And, of because all of the known effects leading to CP-sym- course, the main argument for the impossibility to metry breaking are weak. observe isolated magnetic poles (monopoles) comes The detection of artificial magnetic charges in from the course of theoretical physics by Landau and ice as a result of geometrical (magnetic) frustration is Lifshitz [8]. actually a very interesting event emitting Dirac mono-

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1 poles. The deconfinement of effective magnetic International Space Station, but this question requires charges in a crystal lattice (to be more precise, the an additional study. Magnetic charges (monopoles) 1 deconfinement of zero-dimension point topological and atoms consisting of them should be included in defects) arises at temperatures close to absolute zero. the composition of dark matter. Our explanation of the Note that the spectrum of topological defects in spin gamma-ray excess at the Galactic center in the energy 2 systems includes vortices, solitonic vortices, skyrmi- range 1–3 GeV is the combined effect from the anni- 3 ons, monopoles, and knots [13]. The new term “mag- hilation of produced magnetic charges in the magne- netricity” (by analogy with electricity) and even such a tospheres of a large number of young neutron stars— term as “magnetolyte” (by analogy with electrolyte) pulsars (this hypothesis will be discussed in Section 5). were introduced for the emerged current of magnetic Here we will focus our attention on magnetic charges. These experiments and magnetic frustration monopoles with energies in the GeV range. Mono- physics are described in detail in [13–17]. poles of very high energies (1015–1016 GeV), of course, In other words, for the appearance of a current of will be investigated also, but more briefly. Their detec- such magnetic charges the topological order in crystals tion is envisaged in the Dubna experiment on Lake is violated due to magnetic frustration [17]. As Bram- Baikal [23, 24] and in many other experiments world- well [16], one of the ideologists of , mono- wide. Sullivan and Fryberger [25] consider the execu- 3 3 poles, and magnetricity, said, “magnetricity is a cur- tion of an experiment in Japan by the BELLE II Col- rent of thermally excited defects in spin ice”. Possibly, laboration at the KEK facility aimed at searching for it should be added to this definition that it is necessary magnetic monopoles with a mass of 4–5 GeV/c2 for to take into account the spin correlations. The study of the natural, in their opinion, case where the electric magnetic systems in low-temperature physics includes and magnetic charges are equal to each other, i.e., several physical concepts: spin ice, magnetic mono- e = g. poles, anomalous Kondo and Hall effects [18]. In the opinion of Zvyagin [18], we already observe a new physics in frustrated and it is probably hard 3. PHYSICAL SUBSTANTIATION not to agree with this. OF THE PRESENCE OF MAGNETIC CHARGES 2. MAGNETIC CHARGES, Formally, Maxwell’s classical equations do not THEIR ENERGIES, AND THEIR SEARCH suggest a complete symmetry of electric and magnetic processes and these equations yield correct results, Magnetic monopoles have been and are being although the presence of magnetic charges (g) can searched for in various energy ranges from 1016 GeV to explain the electric quantization. An important a few GeV or even lower and, of course, their search is dependence was derived in his time by Dirac [26]: conducted by various methods. At the Large eg Collider this is the MoEDAL experiment. A brief the- ==±±±k ,k 0,1,2,3,... (1) ory of leptonic magnetic monopoles is presented in c 2 [19, 20] and it was shown that a light magnetic mono- (k is the quantum number). This classical pole could be included in a consistent way in the Stan- definition of k differs from its quantum definition dard Model through the extension of the leptonic sec- given in the review [11]. In his time Dirac accepted the tor, i.e., a magnetic analog of the has challenge of Curie [4] and suggested the existence of been created. Leptonic magnetic monopoles can be an elementary magnetic charge. The relation between focused. A special accelerator is being built in France the charges g = 68.5e follows from the condition (1) at for this purpose [19]. Note that the observation of a k = 1, i.e., the magnetic charge is very large and this is moving with charge g = 137e and its main peculiarity. Furthermore, we know well that a mass larger than 100 masses was announced 2 the fine-structure constant αe = e /c = 1/137 charac- in [21]. It should also be noted that many papers, terizes the force of attraction (or repulsion) between which make no sense to cite here, were devoted to α 2  closing the subject of the existence of magnetic two electric charges. Accordingly, g = g /c = 34.25 charges (monopoles). will characterize the force of attraction (or repulsion) between two magnetic charges. The ratio of these two Our interest in magnetic charges is associated with constants is the realization of a GeV monopolium (g+g–) atomic system in cosmic conditions, by analogy with positro- gc2 / + – = 4692.25. nium (e e ) [22], in which some transitions can be ec2 / observed in the gamma-ray range before annihilation, α ≫ as, incidentally, in , but in the case of pos- Since g 1, accurate quantum-mechanical calcula- itronium this is the millimeter and radio bands. Fur- tions of the level structure of magnetic atoms (g+g–) thermore, in principle, it is possible to detect isolated cannot be made. Schwinger [11] hypothesized that the magnetic charges in cosmic experiments onboard the coefficient k in Eq. (1) could take only even values.

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For k = 2 we will then have g = 137e and the ratio of monopolium, at huge redshifts z ~ 1010–1011, to form the fine-structure constants Schwinger’s magnetic world. A monopole pair with an energy in the GeV range (along with an electron–pos- gc2 / = 18769 itron one) could be formed in the magnetospheres of ec2 / young pulsars in the superstrong magnetic fields of is larger than that in Dirac’s case by a factor of 4. The neutron stars and be blown out from them. Leptonic- spectroscopy of the more symmetric magnetic world mass magnetic monopoles [19, 20] are an interesting will differ radically from the spectroscopy of our phenomenon, especially since, as has already been (Dirac) world. The huge ratio of these constants could noted, a special accelerator is being built in France for not but affect the physical processes in the early Uni- their search. Dual particles, dions, “stay aloof” in cur- verse, when magnetic monopoles were formed. Of rent physics, but they have not yet been detected, course, magnetic charges immediately after their pro- although they, along with magnetic monopoles, could duction were bound due to a very strong magnetic be “implicated” in CP violation in the early Universe. interaction into the simplest atomic system, monop- We will also mention the possible existence of such olium (g+g–), whose spectral features should be dis- particles as magnetic , i.e., the next level of mat- cussed and we should consider how they can be ter already in the magnetic world. observed.

In [26] Dirac wrote out his famous relativistic 2 equation in the form 4. MONOPOLES WITH GeV/c MASSES IN THE VIEW OF DIRAC AND SCHWINGER Hpm222ψ=(), + ψ (2) Dirac’s theory does not predict the magnetic whose structure suggests the presence of a second par- monopole mass, but it is often assumed that the ticle. As it turned out later, this led to the detection of monopole mass can be the . However, these could also be magnetic charges of different signs. Here it is pertinent to note 2 mgem= (/) two more points. First, quite long ago Schwinger [11] ge (6) =≈≈2 drew attention to the possible existence of a new dual 4692.25mmep 2.56 2.4 GeV/ c . (dion) that has both electric, (–1/3)e, and magnetic, (2/3)g, charges. The quantization condition In this case, the classical monopole radius is equal to for these two charges will then be the classical electron radius, which is probably natural:

eg12− eg 21 = k. (3) ==22/, 22 /. (7) c rgmcremcggee Here k is an integer, while the electric (e = 1/3) and If, however, the monopole radius is set equal to the magnetic (g = 2/3) charges are fractional. Dions are classical proton radius (~0.8 × 10–13 cm), then a con- particles with spin s = 1/2. The second remark is asso- siderably larger value of m ≈ 8.7m is obtained for the ciated with Parker’s limit [27]. The essence of this g p remark is that the galactic magnetic should not monopole mass. A detailed discussion about the change and magnetic monopoles should not reduce it masses of magnetic monopoles can be found in [28]. The masses of these monopoles can lie in the range of when moving along field lines. Parker’s limit gives a 2 constraint on the flux of supermassive magnetic TeV/c or higher. The lower limit for the mass of a monopoles in experiments on Earth: Dirac monopole was estimated quite long ago in [29] from the results of a (g – 2) experiment: mg = 11mμ ≈ <× −−−15 2 1 Fg 310cms. (4) 1.2mp. This (g – 2) experiment was conceived for an The reference limit for the flux of isolated supermas- accurate measurement of the sive monopoles gives (a new physics was searched for already in the 1960s). < −−−−15 2 2 1 Recall that monopolium, along positronium, has Fg 10 cm cp s . (5) two systems of levels consisting of ortho- and para- Parker’s remark could be a “blank shot”, because modifications related to the orientation of their spins. there must be “few” isolated monopoles at the present Thus, before annihilation magnetic charges with a epoch in the Universe. On the other hand, young neu- mass of 2.4 GeV/c2 could form an atomic system— tron stars (gamma-ray pulsars) could “leave the foot- monopolium (g+g–). In this atomic system the energy prints” of monopoles in regions with their highest of the Lα transition is about 1.8 GeV, while the energy concentration (for example, the Galactic center). of the ortho–para transition is about 282 keV. Here the We reiterate once again that all cosmological heavy energies were calculated by the similarity method with monopoles (1015–1016 GeV) in the leptogenesis period similar transitions in positronium (e+e–). It is also were immediately bound into a magnetic , interesting to estimate the Bohr radius of this magnetic

JOURNAL OF EXPERIMENTAL AND THEORETICAL PHYSICS Vol. 127 No. 4 2018 MAGNETIC MONOPOLES AND DARK MATTER 641 atom and to compare it with the Bohr radius of the there is no dual symmetry of Maxwell’s equations. hydrogen atom: According to Schwinger, it is present. Furthermore,

2 note once again that dions deserve greater attention, as B =≈ −12 does Schwinger’s entire magnetic world of the early rg 10 cm, mg2 Universe, in which Maxwell’s equations could be g (8) 2 dually symmetric:  − r B =≈×510cm.9 H 2 1 ∂D mee curlHD=+π 4j , div =πρ 4 , ( ∂ ee) There are several research works on monopolium ct (11) =−1 ∂B +π =πρ and all of them are associated with Vento’s papers [20, curlEB() 4jgg , div 4 . 31], but there is also one “old” paper [32]. Note that ct∂ the monopolium two-photon annihilation energy in our case is 2.4 GeV per each photon and precisely this 5. THE GAMMA-RAY EXCESS process should be discussed. Three-photon annihila- AT THE GALACTIC CENTER—THE tion in positronium is much less probable [16] and the ANNIHILATION OF MAGNETIC CHARGES situation must be similar in the case of monopolium. WITH ENERGIES IN THE GeV RANGE The production of monopoles with masses in the GeV range on accelerators is impossible, because the J/ψ Recently, the Fermi Gamma-Ray Space Telescope particle production cross section is larger than the detected a gamma-ray excess in the energy range 1–3 monopolium production cross section at least by an GeV from the region surrounding the center of our order of magnitude (the J/ψ particle mass is Galaxy [34], which can be interesting for us if this is 3.1 GeV/c2). This will be discussed in Section 7. assumed to be the annihilation of monopolium. The observed spectrum of the gamma-ray excess is broad- Schwinger [33] proposed to modify Dirac’s quanti- ° zation condition (2) in such a way that the monopole ened up to 10 GeV and extends at an angle of 5 toward quantum number k could take only even values. In this the Galactic center [35]. Furthermore, the distribu- case, the minimum value is k = 2 and here there is tion of in the spectrum is not smooth [36, 37]. some symmetry that “forces” us to go into earlier Such a gamma-ray spectrum could probably be epochs of evolution of the Universe. The relation formed by unresolved point sources, young neutron between the magnetic and electric charges then stars (millisecond pulsars), which together give the becomes g = 137e. In view of their exceptional impor- observed gamma-ray excess, i.e., a new population of tance for cosmology, we will repeat these trivial rela- sources the gamma-ray flux from which was below the tions here: detection threshold of the Fermi detectors is predicted here. One of the preliminary attempts to explain the g 2 gamma-ray excess was to assume the annihilation of α= =137, αα= 1, mme dark matter particles into Standard Model particles c (9) [38]. As it seems to us, a different physical model—the α m = 18769, cooperative effect from the annihilation of monop- α e olium in the magnetospheres of young gamma-ray i.e., in Schwinger’s world the situation differs radically pulsars, which is related to the inverse Compton from our electric world. The minimum mass of the effect, is more suitable for interpreting the gamma-ray magnetic charge in Schwinger’s symmetric world must excess at the Galactic center. Relativistic probably be exist in the magnetospheres of pulsars near the mag- netic poles, moving at small pitch angles to the radial mgem= (/)2 . In this case, Compton scattering can ge (10) broaden and shift the 2.4-GeV annihilation line. =≈≈ 2 18769mmep 10.24 9.6 GeV/ c . Assuming that ε/E ≪ 1, where ε is the energy of the Here, as in Dirac’s case, the classical magnetic mono- incident gamma-ray photon and E is the electron energy, the recoil upon scattering may be neglected pole radius is equal to the classical electron radius. ε Before the annihilation of Schwinger magnetic charges [39]. In our case, ≈ 2.4 GeV and the Thomson approximation can be used for electrons with E ≫ with a minimum mass of 9.6 GeV/c2, they could also + – 2.4GeV. If the emission is concentrated in a narrow form an atomic system—monopolium (g g ). In this cone of pitch angles to the radial magnetic field, θ ≫ atomic system the energy of the Lα transition is about 2 mec /E, then the energy of the scattered gamma-ray 7.2 GeV, while the energy of the ortho–para transition photon is is about 1.13 MeV. These transitions were also calcu- lated by the similarity method with similar transitions ε≈(1/3) εθ222 (Emc / ) . (12) in positronium. sc e ε ε Actually, there is a deeper connection between If we take sc ~ 4 ~ 10 GeV and an electron energy E ~ 2 Dirac’s and Schwinger’s views. According to Dirac, 20000mcc , then θ ~ 0.01°, i.e., we assume that the

JOURNAL OF EXPERIMENTAL AND THEORETICAL PHYSICS Vol. 127 No. 4 2018 642 BURDYUZHA scattering effects will lead to an effective broadening 6. HEAVY MAGNETIC MONPOLES and shift of the g+g– annihilation line up to 10 GeV, as WITH MASSES 1015–1016 GeV/c2 is observed. The above estimates were made here for Note that the authors of [42] understood that a pair an individual gamma-ray pulsar. of heavy magnetic charges of opposite signs could pro- It should also be noted that the density of mono- duce ultrahigh-energy cosmic rays upon annihilation. ρ Let us discuss the production of heavy magnetic poles must not close the Universe, ngmg < cr. In this monopoles in the early Universe. Many authors have case, the density of monopoles must be no more than already taken this path [10, 32, 43]. As has been noted 10–6 cm–3. This remark is also true for the monop- above, the early Universe is described by the diffusion olium concentration. An observable gamma-ray flux approximation, because λ < r0. The diffusion equation (10–7 photons cm–2 s–1) cannot be obtained without for a magnetic monopole was written out in this case invoking an anisotropy of at least one order of magni- in [10]. It is tude. This is a weak deviation from isotropy, but it is 2 unavoidable. This, in some sense, is a radiation pat- ∂∂nrt(,)D ∂ ⎡⎛2 nrt (,) g ⎞ ⎤ =+⎢⎥rnrt⎜⎟(,), (15) tern. Let us also dwell on the micro- and macroscopic ∂∂∂trrrrkT22⎣⎝ ⎠ ⎦ constraints. B where D ≈ (2/3)λv is the diffusion coefficient. While If the mean free path of monopoles in a plasma λ > investigating this equation, the authors of [10] point 2 out that the annihilation of GUT monopoles virtually r0, where r0 = g /kBT is the size at which the Coulomb attraction is significant, then free monopoles can be ends already at t ~ 10–5 s and, in this case, the present- day residual density of isolated magnetic monopoles annihilated. In the case of λ < r0, the diffusion approx- will be exceptionally low, n ~ 10–19 cm–3. This conclu- imation should be applied. Our estimate is r0 = g (68.5e)2/k T ≈ 2 × 10–12 cm at E = 100 GeV. The dif- sion reached by the authors of [10] is also consistent B with the assertion that most of the produced mono- fusion approximation is probably valid only in a very poles were bound into the simplest magnetic atom, early Universe and it does not work at present. We monopolium, already in a very early Universe. How- assert that the gamma-ray excess is the production and ever, whereas a mass of monopoles (5–10) × annihilation of magnetic charges with energies in the 1012 GeV/c2 was used in [10], most of the authors take GeV range in the superstrong magnetic fields of young 16 2 12 ~10 GeV/c for the masses of GUT monopoles (for a neutron stars at B ≥ 10 G in the Galactic center review, see [42]). region. In this case, the luminosity under monop- To the credit of our colleagues [44, 45], they noted olium two-photon annihilation is quite long ago that at early epochs heavy monopoles were paired to form heavy monopolium, although the =σ22420v =×− × LmcnNngggns(4 10 )(9 10 ) classic work on monopolium was performed 35 years ××(4 10−32 ) × 10 5 (2 × 10 19 )(3 × 10 38 ) × 10 7 (13) ago [32]. It is pointed out in this paper that the lifetime − of such a bound system increases cubically from the =×210ergs,36 1 initial diameter for SU(5) GUT monopoles. If the monopolium diameter is 10–13 cm, then its lifetime is where Ng is the total number of pairs of magnetic only 43 days. If, however, the monopolium diameter is charges in the magnetic column of a neutron star (3 × 10–9 cm, then its lifetime will be 1011 years. More reli- 38 7 10 ), nns is the number of young neutron stars (10 ), v able estimates were made in [44]. Here the paired pri- is the monopolium , and the monopolium mordial heavy monopoles could survive and, in the 19 –3 view of the authors, can be the sources of ultrahigh- density is ng = 2 × 10 cm . Here we used the annihi- σ –32 2 energy cosmic rays above the Greizen–Zatsepin– lation cross section = 4 × 10 cm calculated by us 10 in [40]. Nevertheless, the questions related to the Kuzmin (GZK) limit (5 × 10 GeV) after annihila- tion. The size of such a bound system depends strongly annihilation time of magnetic charges in the column on the distribution of the initial momentum p. An esti- of a young neutron star remain, but the “required” mate of this possible size is given in [44]: luminosity, probably, can be estimated. Such an esti- + – 2 mation of the e e annihilation line luminosity for the 4 ⎛⎞⎛⎞104 GeV =× −7 p m same column parameters and the same number of lc[cm] 5 10()⎜⎟⎜⎟ , (16) ⎜⎟⎜⎟14 neutron stars gives mc⎝⎠⎝⎠10 GeV H which lies in the range from 7 × 10–7 to 6 × 10–3 cm for =σ2381v ≈×−− LmcnNneeens310ergs. (14) Ωx/0.3 < 1. Here Ωx is the relative density of the Uni- verse and H is the Hubble constant. This estimate Note that the 511-keV positronium annihilation line coincides with the estimate from [32] and, probably, it was observed from the Galactic center quite long ago may not be doubted that a bound system of heavy by Russian scientists [41]. monopoles will survive to our days. Unfortunately,

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relic monopoles with a considerably shorter lifetime, 8. BASIC ASSERTIONS ABOUT of course, will not survive. THE DETECTION OF MAGNETIC MONOPOLES 7. WHY ARE MAGNETIC CHARGES NOT It follows from this paper that monopoles of vari- OBSERVED ON ACCELERATORS? ous masses can exist in the Universe: heavy (relic) monopoles (1015–1016 GeV/c2), monopoles of inter- Much effort was expended [46] to detect magnetic mediate masses (2.4, 9.6 GeV/c2), and, probably, light charges with m ≈ 2.4 GeV/c2 on accelerators. However, monopoles of leptonic masses. Of course, much effort here, probably, there was an “embarrassment”, should be expended on their detection. In 2015 because these magnetic charges are close in mass to researchers from the Nuclear Research Institute the vector resonance of the J/ψ particle whose mass is (Moscow) and the Joint Nuclear Research Institute 3.097 GeV/c2 [47]. During the J/ψ particle production (Dubna) as well as a number of Russian scientific its cross section is ~10–31 cm2, which is larger than the organizations involved in the Baikal Collaboration monopole production cross section, ~10–32 cm2 [40]. deployed and put into operation a unique experimen- This “blocks” the production of the latter (of course, tal cluster—the deep-water Dubna telescope the interaction Lagrangian should be written out and on Lake Baikal, in which the detection of heavy mag- analyzed for a rigorous assertion). Furthermore, in netic monopoles is also envisaged [23, 24]. Now view of the enormous force of attraction between mag- (2018) they have already three clusters under the com- netic charges of opposite signs (stronger than that mon name “Baikal GBD—Gigaton Volume Detec- between e+ and e– by a factor of 4692), they are imme- tor”. We made testable spectroscopic predictions with diately bound to form a magnetic atom—monop- regard to Dirac monopoles of intermediate masses. olium. Consequently, there have never been chances The two-photon annihilation of para-monopolium to detect Dirac magnetic monopoles with a mass of with an energy of about 2.4 GeV in the magneto- 2.4 GeV under terrestrial conditions in experiments on of young neutron stars (gamma-ray pulsars) as accelerators. They should be searched for in the cos- a cooperative effect can be responsible for the gamma- mos, where there are no hampering effects, or in an ray excess (1–3 GeV) at the center of our Galaxy atomic state (gamma-ray transitions during recombi- observed by the Fermi observatory. At an annihilation nation), or by “catching” them in a single state on a energy E ≈ 2.4 GeV the energy of the ortho–para tran- 4 circumterrestrial orbit. In other words, a cosmic sition in Dirac monopolium, by analogy with positro- + – experiment for the detection of magnetic charges is nium (e e ), can be Eortho–para ≈ 282 keV, while the needed. In the magnetospheres of gamma-ray pulsars energy of the Lα transition is about 1.8 GeV. For they, along with electron–positron pairs, can be pro- Schwinger monopolium with a mass of 2 × 9.6 GeV/c2 duced and immediately bound into pairs, i.e., form the energy of the ortho–para transition is about monopolium. However, the stationarity equations 1.13 MeV, while the energy of the Lα transition is about should also be solved here to make better estimates for 7.2 GeV. the concentration of magnetic charges. Note that such Vento’s works on magnetic monopoles [28, 30, 31] a problem has already been solved for e+e– pairs by the are related to the possible detection of the latter at the authors of [48]. They solved the kinetic equation for , but, as has already been the production of electron–positron pairs in pulsars noted, the J/ψ particle production hampers this pro- with huge magnetic fields: cess. Furthermore, an interesting and natural predic- ∂ tion in [28] is the presence of recombination radiation F +=div(FQv ) , (17) at the time of monopolium formation, but how to ∂t detect it at huge redshifts is a separate astrophysical where F is the distribution function of particles, v is problem. The question regarding light monopoles of their velocity, and Q is a special operator that takes leptonic masses is open, although the magnetic analog into account the generation of particles by photons. of the Standard Model has already been created in The solution of this equation should be repeated for [20]. magnetic charges. Schwinger magnetic atoms with a The interest in artificial magnetic monopoles mass of 2 × 9.6 GeV/c2 could also be formed in the detected in laboratories at ultralow temperatures [1–3, superstrong magnetic fields of pulsars, though with a 13] continues to increase. Here, we are dealing with lower probability, and these atoms together with Dirac the case where the current of magnetic monopoles magnetic atoms can be the components of dark mat- (zero-dimension topological defects) is observed as a ter, as has already been noted. From general physical result of magnetic frustration in spin ice. Actually, this considerations, there is a high probability in the for- is a “prosaic” situation where a macroscopic quantum mation of monopoles with small quantum numbers k, phenomenon, a magnetic field source, is observed but whether these general physical considerations are [49]. Magnetic monopoles in spin ice have already applicable to the quantum magnetodynamics of the been discussed in earlier papers [50, 51], but they were cosmos is still an open question. called quasi-particles at that time.

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Regarding Schwinger’s magnetic world, it is prob- huge magnetic forces could affect the physical pro- ably necessary to accept his view [11]. The magnetic cesses in the early Universe, but this “incantation”, world must necessarily be realized in a very early Uni- which is repeated in our paper in view of its excep- verse, because the magnetic interaction in this world is tional importance, requires a careful study. Here we stronger than the electric one by a factor of 18769 and, are talking about the influence of such magnetic forces of course, the footprint of such an asymmetry must on the generation of baryon asymmetry of the Uni- necessarily manifest itself. No matter how we cut a verse. In Schwinger’s world (early Universe) magnetic , its parts will always have different poles and it charges were immediately bound into magnetic atoms is impossible to get to isolated magnetic charges (monopolium), whence it follows that, formally, (monopoles), because the magnetic interaction in the divB = 0 in the present-day world. present-day world is stronger than the electric one by The status of experimental and theoretical research a factor of 4692.25. At present, a magnetic atom, on magnetic monopoles as of 2006 was given in [55]. 2 monopolium with a mass of 2 × 2.4 GeV/c , remains An older, but good review was published back in 1978 for spectroscopic observations of the footprints of the [56]. Studies of the problem of magnetic monopoles magnetic world, although magnetic atoms with a mass are continued with unprecedented persistence [57, of 2 × 9.6 GeV/c2 could also be formed in pulsars, but 58]. breaking by magnetic monopoles with a lower probability. Furthermore, there is also can be found in [59]; Kaluza–Klein monopoles and room for isolated magnetic charges in cosmic condi- their zero modes are discussed in [60]. And there is no tions. They can be blown out from young neutron doubt that the initiation of studies of magnetic mono- stars, as electrons and positrons. The stationarity poles in the cosmos is not far off. From our viewpoint, equations for the production, annihilation, and the gamma-ray excess at the Galactic center observed destruction of monopolium by gamma-ray photons by the Fermi telescope [34] can be the first footprint of should be solved here, but our knowledge for this is so the magnetic world. However, an independent spec- far very scanty. troscopic check, for example, the detection of atomic transitions (e.g., the Lα line) in monopolium before its 9. CONCLUSIONS annihilation, is required here. The author of [61] pro- posed a different definition of the magnetic charge It may be pertinent to recall our view of the early mass coming from the Born–Infeld electromagnetic Universe in order to somehow correlate the physical theory [62]. As has been mentioned, the relation processes associated with magnetic monopoles. The between the masses mg and me in the case where the following cosmological scenario could be realized at 2 2 classical radii rg and re are equal is mg = me(g /e ) and early epochs of evolution of the Universe: having tun- 2 neled by chance, the Universe passed from the oscil- then mg = 2.4 GeV/c . However, nature could choose lating regime to the Friedmann regime [52], probably, a different definition of the masses. As was shown by through a quasi-inflationary phase. Subsequently, Caruso [61], the relation between the charges in the there were leptogenesis, baryogenesis, and nucleosyn- Born–Infeld electromagnetic theory is different, mg = 2 2 3/4 2 thesis during its sharp cooling as it expanded. As has me(g /e ) , and then mg = 0.29 GeV/c . This point already been noted, Schwinger’s magnetic world was only strengthens our desire to detect magnetic charges. formed at the epoch of leptogenesis. In the early Uni- For completeness, note that the author of [63] thinks verse a high symmetry was lost and, of course, these that all dark matter particles are magnetic con- processes were accompanied by phase transitions. sisting of two Dirac monopoles. Our estimates give a When the symmetry was lost, light pseudo-Goldstone contribution of relic monopoles to the dark matter were formed, filling the entire volume (for us density at least at a level of 18%. these are dark matter particles). In the “dark” medium More details on the composition of dark matter can phase transitions occur as the temperature drops be found in our review [54]. For monopoles with ener- sharply, forming preferential scales. followed gies in the GeV range a good estimate for the density the block-phase structure prepared by phase transi- cannot yet been made (the uncertainty with pulsars). tions in the dark medium, forming the baryonic large- –6 –3 Our upper limit for their density is ng ≤ 10 cm , for scale structure of our Universe that we observe. Note relic monopoles with energies in the TeV range it is that in [53] we exploited a composite () model of –19 –3 elementary particles, in which the presence of three ng ~ 10 cm [10]. For survived relic monopoles in generations of elementary particles is natural and energies 1015–1016 GeV the density cannot differ which explains well some of the unsolved cosmologi- greatly from the estimates made by Zel’dovich and cal problems, in particular, the fractality. Khlopov [10]—it can be only smaller. Note also another important point in cosmology In addition to the Baikal GVD experiment, in that is absent in our paper [54]. During its birth the which it is possible to detect relic magnetic charges of Universe could probably have a larger number of very high energies (1015–1016 GeV), the Gamma-400 5 dimensions and the compactification of extra dimen- experiment that can detect individual spectral lines in sions must also have been of necessity. The presence of magnetic atoms during their recombination is being

JOURNAL OF EXPERIMENTAL AND THEORETICAL PHYSICS Vol. 127 No. 4 2018 MAGNETIC MONOPOLES AND DARK MATTER 645 prepared in Russia [64]. This is a complex, but very the debates on magnetic monopoles in spin ice and the important task. In contrast, we propose to carry out a referee of this review for useful remarks. cosmic experiment to detect magnetic charges onboard the International Space Station. Quite long ago, while investigating the motion of magnetic REFERENCES charges, the authors of [64] defined even the unit of 1. M. Ray, E. Ruokokoski, S. Kandel, et al., Nature (Lon- –1 don, U.K.) 505, 657 (2014). magnetic charge: 5μB Å , i.e., a new physical constant whose value was predicted in [17]. Probably, it makes 2. G. Chen, arXiv:1602.02230. sense to call the unit of magnetic charge “ehrenhaft” 3. N. P. Armitage, arXiv:1710.11226. to perpetuate the name of the Austrian physicist Ehr- 4. P. Curie, Seances Soc. Fr. Phys. 76, 1 (1894). enhaft, who apparently detected magnetic charges at 5. F. Ehrenhaft, J. Franklin Inst. 3, 235 (1942). the beginning of the past century (the publication on 6. R. Sizov, Sov. Phys. JETP 33, 737 (1971). this was later, in 1942 [5]). The proposal for perpetua- 7. B. Cabrera, Phys. Rev. Lett. 48, 1378 (1982). tion was made by our “disgraced” physicist Sizov. 8. L. D. Landau and E. M. Lifshitz, Course of Theoretical Furthermore, the authors of [65] point out that in spin Physics, Vol. 2: The Classical Theory of Fields (Nauka, ice of (Dy2Ti2O7) they observed a Moscow, 1973; Pergamon, Oxford, 1975), p. 91. deviation from Ohm’s law during the motion of mag- 9. A. D. Sakharov, JETP Lett. 44, 379 (1986). netic charges. Note that Schwinger in his review 10. Ya. B. Zel’dovich and M. Yu. Khlopov, Phys. Lett. B “A Magnetic Model of Matter” [11] has already intro- 79, 239 (1978). duced the unit of magnetic charge for dually charged 11. J. Schwinger, Science 165 (3895), 757 (1969). particles whose value is far from that announced in 12. L. Laperashvili and H. Nielsen, arXiv:hep-th/0311261. [65]. Furthermore, electromagnetic duality [66] in the Yang–Mills supersymmetric theory should be noted, 13. T. Ollikainen, K. Tiurev, A. Blinova, et al., arXiv:1611.07766v.2. in which a monopole condensate and even some spec- trum of dions is possible. Hence the ideas of interpret- 14. E. Ruokokoski, V. Pietila, and M. Mottonen, Phys. Rev. A , 063627 (2011). ing the experiments on artificial magnetic monopoles 84 in spin ice can arise [1–3, 13]. 15. I. A. Ryzhkin, J. Exp. Theor. Phys. 101, 481 (2005). 16. S. Bramwell, Talk on School Les Houches, August 30, Although our paper is devoted to searching for 2012. magnetic charges in the cosmos, we cannot but men- 17. C. Castelnovo, R. Moessner, and S. Sondhi, Ann. Rev. tion the present-day experiments aimed at searching Cond. Phys. 3, 35 (2012). for a new physics associated with the muon anomalous 18. A. Zvyagin, arXiv:1308.1014. magnetic moment aμ, the (g – 2) experiment. Amaldi [29] established a lower limit for the magnetic mono- 19. Zh. Loshak, Inzh. Fiz., No. 3, 12 (2014). pole mass from this experiment 55 years ago (see Sec- 20. H. Stumpf, Z. Naturforsch. A 67, 163 (2012). tion 4). And the (g - 2) experiments are now continued 21. P. B. Price, E. K. Shirk, W. Z. Osborne, et al., Phys. in several laboratories worldwide: in USA (Fermilab) Rev. Lett. 35, 487 (1975). and Japan (KEK, J-PARC) [67]. According to Dirac, 22. V. V. Burdyuzha and V. L. Kauts, Astrophys. J. Suppl. 92, 549 (1994). gμ = 2. It follows from the experiment that gμ = 2(1 + 23. G. V. Domogatsky, Phys. Usp. 54, 959 (2011). aμ). The present-day value for aμ is given in the review [68]: 24. A. D. Avrorin, arXiv:1512.01198. 25. M. K. Sullivan and D. Fryberger, arXiv:1707.05295; exp− 10 aμ =±±×(11659209.1 5.4 3.3) 10 . (18) arXiv:1511.02200. 26. P. A. M. Dirac, Proc. R. Soc. A 133, 60 (1931). The muon has no good explanation and so 27. E. N. Parker, Astrophys. J. , 383 (1970). far this is a hot point in physics, as are the latest exper- 160 iments with spin ice [69]. 28. V. Vento and V. Mantovani, arXiv:1306.4213. 29. E. Amaldi et al., CERN Report No. 63-13 (CERN, There is no doubt that the detected dynamics of 1963). artificial magnetic monopoles will find a wide techno- 30. V. Vento, arXiv:astro-ph/0511764. logical application in future (it has a conceptual signif- icance already now). Thus, the monopole saga initi- 31. V. Vento et al., Eur. Phys. J. C 56, 87 (2008). ated by Dirac 87 years ago [26] unfolds with new vigor. 32. C. T. Hill, Nucl. Phys. B 224, 469 (1983). By investigating magnetic charges and atoms consist- 33. J. Schwinger, Phys. Rev. D 12, 3105 (1975). ing of them in the cosmos, we step by step enter the far 34. W. Atwood et al., Astrophys. J. 697, 1071 (2009). and unexplored magnetic world. 35. S. Horiuchi, M. Kaplinghat, and A. Kwa, arXiv:1604.01402. 36. R. Bartels et al., Phys. Rev. Lett. 116, 051102 (2016). ACKNOWLEDGMENTS 37. S. Lee et al., Phys. Rev. Lett. 116, 051103 (2016). I thank I.A. Ryzhkin from the Institute of Solid 38. C. Boehm, M. Dolan, and Ch. McCabe, Phys. Rev. D State Physics of the Russian Academy of Sciences for 90, 023531 (2014).

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39. V. M. Charugin, Sov. Astron. 28, 67 (1984). 55. K. A. Milton, Rep. Progr. Phys. 69, 1637 (2006). 40. V. V. Burdyuzha, Astron. Lett. (in press). 56. D. Olive and P. Goddard, Rep. Prog. Phys. 41, 1357 41. R. Sunyaev, E. Churazov, M. Gilfanov et al., Astro- (1978). phys. J. Lett. 383, L49 (1991). 57. N. M. Barraz, Jr., J. M. Fonseca, and W. A. Moura- 42. R. A. Carrigan and W. P. Trower, Nature (London, Melo, Phys. Rev. D 76, 027701 (2007). U.K.) 305, 673 (1983). 58. M. Chaichian et al., Phys. Rev. D 79, 125029 (2009). 43. G. V. Domogatskii and I. M. Zheleznykh, Sov. J. Nucl. 59. C. Csaki et al., Phys. Rev. D 85, 04514 (2012); Phys. 10, 702 (1969). arXiv:1108.4415. 44. V. K. Dubrovich and N. A. Sushko, Astrofizika 46, 517 60. C. Csaki, Yu. Shirman, J. Terning, and M. Waterbury, (2003). Phys. Rev. Lett. 120, 071603 (2018); arXiv: 1708.03330. 45. V. K. Dubrovich and M. Yu. Khlopov, JETP Lett. 77, 61. F. Caruso, Rev. Brasil. Fis. 16, 188 (2013); 335 (2003). arXiv:1305.4810. 46. N. Craigie et al., Theory and Detection of Monopolesin 62. M. Born and L. Infeld, Nature (London, U.K.) 132, Gauge Theories (World Scientific, Singapore, 1986). 1004 (1933). 47. Particle Data Groups, (2016). 63. V. S. Netchitailo, J. High Energy Phys. 4 (1) (2018). 48. Ya. N. Istomin and D. N. Sobyanin, Astron. Lett. 33, 64. www.gamma400.lebedev.ru. 660 (2007). 65. S. T. Bramwell et al., Nature (London, U.K.) 461, 956 49. S. Nakosai and S. Onoda, arXiv:1801.03117. (2009). 50. C. Castelnovo, R. Moessner, and S. Sondhi, Nature 66. N. Seiberg and E. Witten, Nucl. Phys. B 426, 19 (1994). (London, U.K.) 451, 42 (2008). 67. S. R. Giblin, M. Twengström, L. Bovo, et al., http://g- 51. L. D. C. Jaubert and P. C. W. Holdsworth, 2.kek.jp. arXiv:1010.0970. 68. F. Jegerlehner, arXiv:1804.07409. 52. V. Burdyuzha, O. Lalakulich, Yu. Ponomarev, and 69. S. R. Giblin, M. Twengström, L. Bovo, et al., G. Vereshkov, Phys. Rev. D 55, R7340 (1997). arXiv:1804.08970. 53. V. V. Burdyuzha, Astron. Rep. 58, 353 (2014). 54. V. V. Burdyuzha, J. Exp. Theor. Phys. 124, 358 (2017). Translated by V. Astakhov

SPELL: 1. deconfinement, 2. , 3. magnetricity, 4. circumterrestrial, 5. compactification

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