Double charged heavy constituents of dark atoms and superheavy nuclear objects

We consider the model of composite dark matter assuming stable particles of charge $-2$ bound with primordial helium nuclei by Coulomb force in $O$He atoms. We study capture of such dark atoms in matter and propose a possibility of existence of stable $O$-enriched superheavy nuclei and $O$-nuclearites, in which heavy $O$-dark matter fermions are bound by electromagnetic forces with ordinary nuclear matter. $O$He atoms accumulation in stars and its possible effect in stellar evolution is also considered, extending the set of indirect probes for composite dark matter.


I. INTRODUCTION
There is overwhelming evidence for the presence of a dark matter (DM) in the Universe [1] and together with most popular, but still elusive weakly interacting massive particle (WIMP) [2], there exist numerous theoretical models including axions, sterile neutrinos, primordial black holes [3][4][5], strongly interacting massive particles and superweakly interacting particles (see Refs. [6][7][8] for review and references). Even electromagnetically interacting massive particle (EIMP) candidates are possibly hidden in neutral atomlike states. Dark OHe atoms, in which hypothetical −2 charged particles are bound with primordial helium nuclei, occupy a special place on this list. Such models involve only one free parameter of new physics -the mass of −2 charged EIMPs -so many features of this type of dark matter can be described by the known nuclear and atomic physics.
In 2005, Glashow [9] proposed a kind of EIMP model, according to which stable teraquarks U (of mass of the order of tera-electron-volts and of electric charge +2/3) form a U U U baryon bound with tera-electrons E of charge −1 in the neutral (U U U EE) atom.
However, the primordial He formed in the big bang nucleosynthesis captures all the free E in positively charged (HeE) + ions, preventing a required suppression of the positively charged particles that can bind with electrons in atoms of anomalous hydrogen. In general, stable single charged EIMPs form anomalous hydrogen either directly binding with ordinary electrons (+1 charged EIMPs), or indirectly (−1 charged EIMPs) forming first +1 charge ion with primordial helium and then anomalous hydrogen with ordinary electrons [10]. Therefore, anomalous hydrogen overproduction excludes any significant amount of stable single charged EIMPs.
Nevertheless, there are several models that predict stable double charged particles without stable single charged particles. In particular, the hypothesis of the heavy stable quark of the fourth family may provide a solution, if an excess ofŪ antiquarks with charge (−2/3) is generated in the early Universe. ExcessiveŪ antiquarks then formŪŪŪ antibaryons with the electric charge −2, which are captured by He forming O −− He ++ (OHe) atoms [11] right after the appearance of the He nuclei in the big bang nucleosynthesis. This hypothesis has found implementations in the model of almost commutative geometry as well as in models of walking technicolor and has been extensively discussed in the literature; see Refs. [12][13][14][15][16][17][18] and references therein. The model is particularly predictive since the only parameter that one needs to know is the mass of the O-particle. The model can explain the observed excess of the positronium annihilation line in the galactic bulge and excessive fraction of high-energy cosmic-ray positrons, if the mass of this particle does not exceed 1.3 TeV, challenging the direct test of this explanation in searches for stable double charged particles at the LHC [19].
Charge conservation implies the existence of +2 charged particle O ++ together with O −− .
To avoid overproduction of anomalous isotopes by O ++ , OHe-dominated dark matter should be asymmetric with strongly suppressed +2 charged particles. In the walking technicolor model [20,21], due to sphaleron transitions, such excess is related to the baryon excess, giving the observed dark matter/baryon matter density ratio for a reasonable choice of parameters.
In the early Universe when temperature fell below 1 keV, the rate of expansion started to exceed the rate of energy and momentum transfer from plasma to OHe gas (see, e.g., Ref. [14] for review and references). As a result, OHe decoupled from plasma and radiation and played the role of dark matter on the matter-dominated stage. Before decoupling from plasma and radiation, OHe density fluctuations convert in sound waves. It leads to the suppression of small-scale fluctuations. Thereby OHe dark matter was called warmer than cold dark matter for an OHe mass about 1 TeV, typical for cold dark matter particles [15]. The averaged baryonic density in the course of structure formation and in galaxies is sufficiently low making baryonic matter at large scales transparent for OHe. So, for a galaxy with mass M = 10 10 M and radius R = 10 23 cm, nσR = 8 · 10 −5 1, where n = M/4πR 3 and σ = 2 · 10 −25 cm 2 is the geometrical cross section for OHe collisions. For that reason, in the period of formation of the first objects, OHe does not follow the condensation of baryonic matter, so the OHe model avoids constraints from the cosmic microwave background [22] and formation of the first stars [23]. In galaxies and galaxy clusters, OHe behaves like collisionless gas avoiding constraints from Bullet Cluster observations [24]. Only dense matter objects like stars or planets are opaque for it. The protostellar cloud with the solar mass becomes opaque for OHe when it contracts within 8·10 15 cm. Correspondingly, the protoplanet cloud of the mass of the Earth becomes opaque when it contracts to 10 13 cm.
Because of the nuclear interaction cross section of elastic collisions with terrestrial matter, OHe is slowed down to thermal velocity in the matter of underground detectors. It leads to negligible nuclear recoil in OHe collisions with nuclei in direct-detection experiments.
Positive results of DAMA/NaI and DAMA/LIBRA and negative results of other groups are explained in the OHe model by annual modulation of the rate of low-energy binding of OHe with intermediate mass nuclei [12][13][14]. Open problems of this explanation related with the existence and role of the dipole potential barrier in OHe-nucleus interaction are discussed in Refs. [15][16][17][18].
On the other hand, various hypotheses of the existence of superheavy nuclei with the atomic numbers essentially higher than that of ordinary atomic nuclei have been explored.
In 1971, Migdal suggested the possibility of superdense nuclei glued by a pion condensate [25][26][27][28]. Lee and Wick conjectured σ-condensate superheavy nuclei [29,30]. Bodmer proposed collapsed quark nuclei [31]. Reference [32] demonstrated that the interior of a nucleus with a charge Z 1/e 3 , e is the charge of the electron, = c = 1, is electrically neutral and Refs. [28,33,34] suggested the possibility of existence of nuclei stars of the atomic number Witten [37] suggested the possible existence of quark nuggets, constructed from up, down, and strange quarks, with the atomic number between (3 · 10 2 − 10 3 ) ≤ A ≤ 10 57 , see Ref. [38], as candidates for the DM in the Universe. De Rujula and Glashow [39] called these stable drops "nuclearites" and discussed conditions for their feasible detection in terrestrial conditions. They have also discussed charged massive particles (CHAMPs) [40]. They argued that negative CHAMPs may bind to protons in superheavy isotopes. Superheavy nuclei and nuclearites may exist in the Galaxy as debris from the big bang, supernovae explosions, star collisions, and other astrophysical catastrophes. Numerous subsequent works focused on the consideration of the strange stars as a new family of compact stars. Besides that, exotic matter like the pion condensates and the quark matter in various phases may exist in the interiors of some neutron stars [41][42][43][44]. The other side of the problem is the possible influence of dark matter captured by stars on the stellar structure and evolution.
In particular, it can lead to observable effects in neutron stars [45]. The energy of such a constructed O-nuclearite is Here, the first term is the volume energy of the atomic nucleus, the next two terms describe the electromagnetic energy, and is the kinetic energy of the O-fermions of the mass m O ; V = −eφ is the potential well for the electron in the field of the positive charge (e > 0, φ > 0), and on the other hand, it is the potential well also for the protons in the field of the negative charge of O-particles, n O = p 3 F,O /(3π 2 ), n p = n n = p 3 F,p /(3π 2 ), p F,p 2m N |V |; see Ref. [32]. The contribution of E O kin is tiny, provided m O m N , where m N is the nucleon mass (following Ref. [11], in our estimations, we assume m O TeV), and can be neglected along with the nuclear surface term arising due to a redistribution of the charge in a narrow diffuseness layer.
The charge distribution can be found from the Poisson equation For an individual self-gravitating O-nuclearite to remain in a self-bounded state the nucleon density should be n < (2−2.5)n 0 since for realistic equations of state at such baryon densities the energy of the isosymmetric nuclear matter (at the switched-off Coulomb term) remains negative; see Fig. 1 in Ref. [49]. Assuming for a rough estimate that the internal pressure is Note that the local density of a nonluminous mass in the galaxies is ρ DM (3 − 7) · 10 −25 g/cm 3 [50]. We further assume that ρ DM ρ OHe and that interactions of OHe with ordinary matter are dominantly elastic. However, if the O-particle enters inside an ordinary nucleus, it is energetically profitable for it to remain there, making the nucleus superheavy.
where Ω 3 is the neutron-star volume; ρ OHe (r) is the ambient OHe mass density; n b (r) is the Near the boundary of the neutron-star crust core, n ∼ n 0 and n n n p , n H = 0. Typically [53], v esc ∼ v(r ∼ R) ∼ p F,n /m N ∼ 10 5 km/s for n n n ∼ n 0 , and thus ξ b ∼ 1,v 250 km/s, and thereby B b 1. Then, Eq. (5) simplifies as The maximum value for σ OHe,n is πR 2 /N n , and we are able to estimate a maximum number The formation of an OH − ion in proton capture by O −− may lead to another potential problem for the OHe scenario. The abundance of such ions is severely constrained by searches for stable charged massive particles and anomalous isotopes in sea water [54][55][56][57][58][59].
Production of such ions in the early Universe is strongly suppressed, since all the free O −− are captured by primordial helium before proton capture becomes possible. However, in the Galaxy, OHe destructions in stars and in cosmic rays can release free O −− , which can be captured by protons, forming OH − ions and an anomalous −2 charged component of cosmic rays. In principle, the capture of such components by Earth can lead to a dangerous amount of anomalous isotopes in sea water, but the corresponding analysis, involving detailed study of OHe evolution in the Galaxy, goes beyond the scope of the present work.
Putting aside these problems, we turn here to the extension of studies of possible effects of OHe in nuclear matter and astrophysical conditions. We proposed the possibility of the existence of stable O-nuclearites and discussed various mechanisms for their formation.
Observation of O-nuclearites, in which dark matter is bound with the normal nuclear matter, would be an important event that could provide us additional information on the possibility of the existence of dark OHe atoms of dark matter and their properties.