International Journal of Modern Physics A

We present an overview of scenarios where the observed Dark Matter (DM) abundance consists of Feebly Interacting Massive Particles (FIMPs), produced nonthermally by the so-called freeze-in mechanism. In contrast to the usual freeze-out scenario, frozen-in FIMP DM interacts very weakly with the particles in the visible sector and never attained thermal equilibrium with the baryon–photon fluid in the early Universe. Instead of being determined by its annihilation strength, the DM abundance depends on the decay and annihilation strengths of particles in equilibrium with the baryon–photon fluid, as well as couplings in the DM sector. This makes frozen-in DM very difficult but not impossible to test. In this review, we present the freeze-in mechanism and its variations considered in the literature (dark freeze-out and reannihilation), compare them to the standard DM freeze-out scenario, discuss several aspects of model building, and pay particular attention to observational properties and general testability of such feebly interacting DM.

Cosmic strings in the early universe have received revived interest in recent years. In this paper, we derive these structures as topological defects from singular distributions of the quintessence field of dark energy. Our emphasis is placed on the topological charge of tangled cosmic strings, which originates from the Hopf mapping and is a Chern–Simons action possessing strong inherent tie to knot topology. It is shown that the Kauffman bracket knot polynomial can be constructed in terms of this charge for unoriented knotted strings, serving as a topological invariant much stronger than the traditional Gauss linking numbers in characterizing string topology. Especially, we introduce a mathematical approach of breaking-reconnection which provides a promising candidate for studying physical reconnection processes within the complexity-reducing cascades of tangled cosmic strings.

The causal perturbation theory is an axiomatic perturbative theory of the S-matrix. This formalism has as its essence the following axioms: causality, Lorentz invariance and asymptotic conditions. Any other property must be showed via the inductive method order-by-order and, of course, it depends on the particular physical model. In this work we shall study the normalizability of the generalized quantum electrodynamics in the framework of the causal approach. Furthermore, we analyze the implication of the gauge invariance onto the model and obtain the respective Ward–Takahashi–Fradkin identities.

In order to investigate various decay channels of the Higgs boson $h$ or the hypothetical dilaton, we consider a neutral particle $X$ with zero spin and arbitrary $CP$ parity. This particle can decay into two off-mass-shell $Z$ bosons ($Z_1^{\ast }$ and $Z_2^{\ast }$) decaying to identical fermion–antifermion pairs ($f\bar{f}$): $X\to Z_1^{\ast }{Z}_2^{\ast }\to f\bar{f}f\bar{f}$. We derive analytical formulas for the fully differential width of this decay and for the fully differential width of $h\to Z_1^{\ast }{Z}_2^{\ast }\to 4\ell$ ($4\ell$ stands for $4e$, $4\mu$, or $2e2\mu$). Integration of these formulas yields some Standard Model histogram distributions of the decay $h\to Z_1^{\ast }{Z}_2^{\ast }\to 4\ell$ which are compared with corresponding Monte Carlo simulated distributions obtained by ATLAS and with ATLAS experimental data.

The (1+1) scalar quantum mechanics on the de Sitter space–time is outlined focusing on the momentum-energy statistics and the propagation of the packets that minimize the uncertainty relation between energy and momentum.

In our work, we study the texture zeros of $m_{\nu }$ in the minimal extended type-I seesaw (MES) with incorporating one extra gauge singlet field “$S$”. The MES models deal with the Dirac neutrino mass matrix $(M_D)$, the right-handed Majorana mass matrix $(M_R)$ and the sterile neutrino mass matrix $(M_S)$. We carry out the mapping of all possible zero textures of $M_D$, $M_R$ and $M_S$ for phenomenologically predictive cases having total eight zeros of $M_D$ and $M_R$ studied in the literature. With this motivation, we consider (a) $(4+4)$ scheme, (b) $(5+3)$ scheme and (c) $(6+2)$ scheme, where the digits of a pair represent the number of zeros of $M_D$ and $M_R$, respectively along with the one zero and two zero textures of $(M_S)$. There are a large number of possibilities of zeros of fermion mass matrices but the implementation of $S_3$ transformations reduces it to a very minimum number of basic structures. Interestingly out of four allowed one zero textures of $m_{\nu }$ without sterile neutrino, only three cases ($m_{e\tau }=0$, $m_{\mu \mu }=0$ and $m_{\tau \tau }=0$) are allowed in MES mechanism for the $(4+4)$ and $(5+3)$ schemes. We find some correlations for different combination of $M_D$, $M_R$ and $M_S$ on enforcement of zeros. We examined all the correlations under the recent neutrino oscillation data and find that only $m_{\tau \tau }=0$ survives while both $m_{e\tau }=0$ and $m_{\mu \mu }=0$ are ruled out. Interestingly the one zero textures inherently represent the inverted hierarchy of the mass ordering of light neutrinos. No two zero textures of $m_{\nu }$ survive in MES although there are a number of allowed structures phenomenologically. The allowed texture zeros are finally realized using a discrete Abelian flavor symmetry group $Z_7$ with the extension of standard model to include some scalar fields.

Using generalised geometry we study the action of U-duality acting in three and four dimensions on the bosonic fields of 11-dimensional supergravity. We compare the U-duality symmetry with the T-duality symmetry of double field theory and see how the $SL(2)\otimes SL(3)$ and $SL(5)$ U-duality groups reduce to the $SO(2,2)$ and $SO(3,3)$ T-duality symmetry groups of the type IIA theory. As examples we dualise M2-branes, both black and extreme. We find that uncharged black M2-branes become charged under U-duality, generalising the Harrison transformation, while extreme M2-branes will become new extreme M2-branes. The resulting tension and charges are quantised appropriately if we use the discrete U-duality group $E_d(Z)$.

In this paper, we investigate nonrelativistic anti-Snyder model in momentum representation and obtain quantum mechanical eigenvalues and eigenfunctions. Using this framework, first, in one dimension, we study a particle in a box and the harmonic oscillator problems. Then, for more investigations, in three dimensions, the quantum mechanical eigenvalues and eigenfunctions of a free particle problem and the radius of the neutron star are obtained.