ISSN 1063-7761, Journal of Experimental and Theoretical Physics, 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, PARTICLES, FIELDS, GRAVITATION, AND ASTROPHYSICS Magnetic Monopoles and Dark Matter 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 Universe, in which magnetic charges (monopoles) and magnetic atoms (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-photon annihilation of magnetic charges as a cooperative effect from neutron 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 physicists “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. nature 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 grand unified theory). 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 electron and positrons, 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 physicist 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 baryon 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 spin 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- 638 MAGNETIC MONOPOLES AND DARK MATTER 639 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 spin ice, 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 magnets 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 charge 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 Hadron 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 monopole 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 Standard Model 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 magnetic monopole with charge g = 137e and its main peculiarity. Furthermore, we know well that a mass larger than 100 proton 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 positronium, but in the case of pos- Since g 1, accurate quantum-mechanical calcula- itronium this is the millimeter and radio bands.