Through the Looking-Glass: Alice's Adventures in Mirror World

We briefly review the concept of a parallel `mirror' world which has the same particle physics as the observable world and couples to the latter by gravity and perhaps other very weak forces. The nucleosynthesis bounds demand that the mirror world should have a smaller temperature than the ordinary one. By this reason its evolution should substantially deviate from the standard cosmology as far as the crucial epochs like baryogenesis, nucleosynthesis etc. are concerned. In particular, we show that in the context of certain baryogenesis scenarios, the baryon asymmetry in the mirror world should be larger than in the observable one. Moreover, we show that mirror baryons could naturally constitute the dominant dark matter component of the Universe, and discuss its cosmological implications.Comment: Published in Ian Kogan Memorial Collection "From Fields to Strings: Circumnavigating Theoretical Physics", Eds. M. Shifman et al., World Scientific, Singapore, vol. 3, pp. 2147-2195. 49pp., 8 Figure

Unified picture of the particle and sparticle masses in SUSY GUT

The horizontal symmetry $U(3)_H$ can greatly help in solving the flavor problems in the supersymmetric grand unification. We consider the $SU(5)\times U(3)_H$ model and show that it leads to the remarkable relations between the fermion mass matrices and the soft SUSY breaking terms. Dangerous supersymmetric contributions to the flavor-changing phenomena are naturally suppressed. The possible extensions to the $SO(10)\times U(3)_H$ model are also outlined.Comment: Latex, 5 pages - some more discussions adde

Marriage between the baryonic and dark matters

The baryonic and dark matter fractions in the universe can be both generated by the same baryogenesis mechanism, simultaneously and with comparable amounts, if dark matter is constituted by the baryons of the mirror world, a parallel hidden sector with the same (or similar) microphysics as that of the observable world.Comment: 8 pages, invited talk at the "Dark Side of the Universe" DSU 2006, Madrid, 19-24 June 200

Neutron-antineutron Oscillation and Baryonic Majoron: Low Scale Spontaneous Baryon Violation

We discuss a possibility that baryon number $B$ is spontaneously broken at low scales, of the order of MeV or even smaller, so that the neutron-antineutron oscillation can be induced at the experimentally accessible level. An associated Goldstone particle, baryonic majoron, can have observable effects in neutron to antineutron transitions in nuclei or dense nuclear matter. By extending baryon number to $B-L$ symmetry, baryo-majoron can be identified with the ordinary majoron associated with the spontaneous breaking of lepton number, with interesting implications for neutrinoless $2\beta$ becay with the majoron emission, etc. We also discuss a hypothesis suggesting that baryon number maybe spontaneously broken by the QCD itself via the six-quark condensates.Comment: 8 pages, 5 figure

Neutron--Antineutron Oscillations: Discrete Symmetries and Quark Operators

We analyze status of ${\bf C}$, ${\bf P}$ and ${\bf T}$ discrete symmetries in application to neutron-antineutron transitions breaking conservation of baryon charge ${\cal B}$ by two units. At the level of free particles all these symmetries are preserved. This includes ${\bf P}$ reflection in spite of the opposite internal parities usually ascribed to neutron and antineutron. Explanation, which goes back to the 1937 papers by E. Majorana and by G. Racah, is based on a definition of parity satisfying ${\bf P}^{2}=-1$, instead of ${\bf P}^{2}=1$, and ascribing ${\bf P}=i$ to both, neutron and antineutron. We apply this to ${\bf C}$, ${\bf P}$ and ${\bf T}$ classification of six-quark operators with $|\Delta {\cal B} |=2$. It allows to specify operators contributing to neutron-antineutron oscillations. Remaining operators contribute to other $|\Delta {\cal B} |=2$ processes and, in particular, to nuclei instability. We also show that presence of external magnetic field does not induce any new operator mixing the neutron and antineutron provided that rotational invariance is not broken.Comment: 8 pages, 2 figures. arXiv admin note: text overlap with arXiv:1506.0509