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We propose a generalized Kim-Shifman-Vainshtein-Zakharov-type axion framework in which colored fermions and scalars act as two-loop Majorana neutrino-mass mediators. The global Peccei-Quinn symmetry under which exotic fermions are charged solves the strong CP problem. Within our general proposal, various setups can be distinguished by probing the axion-to-photon coupling at helioscopes and haloscopes. We also comment on axion dark-matter production in the early Universe., Comment: 18 LaTeX pages; 4 figures. Minor changes in main text, references added and supplemental material added. Matches version published in PRL

In this article, we study the boundedness and several properties of the quaternion Wigner transform. Using the quaternion Wigner transform as a tool, we define the quaternion Weyl transform (QWT) and prove that the QWT is compact for a certain class of symbols in $L^{r}\left(\mathbb{R}^{4}, \mathbb{Q}\right)$ with $1 \leq r \leq 2.$ Moreover, it can not be extended as a bounded operator for symbols in $L^{r}\left(\mathbb{R}^{4},\mathbb{Q}\right)$ for $2

In this article, we study the injectivity of the spherical mean for continuous functions on the M\'{e}tivier group. The spherical mean is injective for $f(z, .)\in L^p(\mathbb{R}^m),~1\leq p \leq 2$ with tempered growth in $z$ variable. This result is also true for a class of functions in $L^p(\mathbb{C}^n),\,1\leq p\leq\infty$ without tempered growth. Further, we obtain a two-radii theorem for functions on the M\'{e}tivier group, which are tempered in $z$ variable and periodic in the centre variable., Comment: updated, 13 pages

Let $Z_{r, R}$ be the space of continuous functions on the annulus $B_{r, R}$ in $\mathbb C^n$ whose $\lambda$-twisted spherical mean, in the set up of the M\'{e}tivier group, vanishes over the spheres $S_s(z)\subset B_{r, R} $ with ball $B_r(0)\subseteq B_s(z).$ We characterize the spherical harmonic coefficients of functions in $Z_{r, R},$ eventually, in terms of polynomial growth, by which we infer support theorem. Further, we prove that non-harmonic complex cone and the boundary of a bounded domain are sets of injectivity for the $\lambda$-twisted spherical means., Comment: 18 pages

In this article, we define Weyl transform on second countable type - $I$ locally compact group $G,$ and as an operator on $L^2(G),$ we prove that the Weyl transform is compact when the symbol lies in $L^p(G\times \hat{G})$ with $1\leq p\leq 2.$ Further, for the Euclidean motion group and Heisenberg motion group, we prove that the Weyl transform can not be extended as a bounded operator for the symbol belongs to $L^p(G\times \hat{G})$ with $2

We propose simple scoto-seesaw models to account for dark matter and neutrino masses with spontaneous CP violation. This is achieved with a single horizontal $\mathcal{Z}_8$ discrete symmetry, broken to a residual $\mathcal{Z}_2$ subgroup responsible for stabilizing dark matter. CP is broken spontaneously via the complex vacuum expectation value of a scalar singlet, inducing leptonic CP-violating effects. We find that the imposed $\mathcal{Z}_8$ symmetry pushes the values of the Dirac CP phase and the lightest neutrino mass to ranges already probed by ongoing experiments, so that normal-ordered neutrino masses can be cornered by cosmological observations and neutrinoless double beta decay experiments., Comment: 15 pages, 8 Figures

This paper focuses on the pricing of continuous geometric Asian options (GAOs) under a multifactor stochastic volatility model. The model considers fast and slow mean reverting factors of volatility, where slow volatility factor is approximated by a quadratic arc. The asymptotic expansion of the price function is assumed, and the first order price approximation is derived using the perturbation techniques for both floating and fixed strike GAOs. Much simplified pricing formulae for the GAOs are obtained in this multifactor stochastic volatility framework. The zeroth order term in the price approximation is the modified Black-Scholes price for the GAOs. This modified price is expressed in terms of the Black-Scholes price for the GAOs. The accuracy of the approximate option pricing formulae is established, and the model parameter is also estimated by capturing the volatility smiles., Comment: 29 pages, 2 figures

In the option valuation literature, the shortcomings of one factor stochastic volatility models have traditionally been addressed by adding jumps to the stock price process. An alternate approach in the context of option pricing and calibration of implied volatility is the addition of a few other factors to the volatility process. This paper contemplates two extensions of the Heston stochastic volatility model. Out of which, one considers the addition of jumps to the stock price process (a stochastic volatility jump diffusion model) and another considers an additional stochastic volatility factor varying at a different time scale (a multiscale stochastic volatility model). An empirical analysis is carried out on the market data of options with different strike prices and maturities, to compare the pricing performance of these models and to capture their implied volatility fit. The unknown parameters of these models are calibrated using the non-linear least square optimization. It has been found that the multiscale stochastic volatility model performs better than the Heston stochastic volatility model and the stochastic volatility jump diffusion model for the data set under consideration., Comment: 15 pages, 3 pages

Since $(\mathbb{H}^n\rtimes U(n),U(n))$ is a Gelfand pair, an exact analogue of the Heisenberg group result due to Narayanan and Ratnakumar is not possible for the Heisenberg motion group. In this article, we prove that if the Weyl transform of a finitely supported integrable function on the Heisenberg motion group is non-zero only for finitely many Fourier-Wigner pieces and have finite rank, then the function must be zero. We also prove an analogue of the Heisenberg group result on the quaternion Heisenberg group. In the end, a quantitative interpretation of these results is described through strong annihilating pair for the Weyl transform., Comment: 18 pages

In this article, we prove that (unit sphere, non-harmonic cone) is a Heisenberg uniqueness pair for the symplectic Fourier transform on $\mathbb C^n.$ We derive that spheres as well as non-harmonic cones are determining sets for the spectral projections of the finite measure supported on the unit sphere. Further, we prove that if the Fourier transform of a finitely supported function on step two nilpotent Lie group is of arbitrary finite rank, then the function must be zero. The latter result correlates to the annihilating pair for the Weyl transform., Comment: updated

We have carried out theoretical investigations of electron correlation effects on the atomic properties of the Ca atom trapped inside an attractive spherically symmetric potential well of an endohedral fullerene C$_{60}$ cluster. Relativistic coupled-cluster (RCC) theory has been employed to obtain electron correlation energy, ionization potential and dipole polarizability of this atom. We have also performed calculations using the Dirac-Hartree-Fock (DF), relativistic second-order many-body perturbation theory (RMBPT(2) method) and relativistic random phase approximation (RRPA) to demonstrate propagation of the correlation effects in these properties. Our results are compared with the reported calculations employing multi-configuration Hartree-Fock (MCHF) method in Phys. Rev. A {\bf 87}, 013409 (2016). We found trends in correlation energy with respect to the potential depth are same, but magnitudes are very large in the relativistic calculations. We have also determined the differential and total cross-sections for elastic scattering of electrons from the free and confined Ca atoms using the electronic charge densities from the Dirac-Hartree core-potential (DFCP) and RCC methods to demonstrate role of potential depth in these properties., Comment: 10 pages, 4 tables and 3 figures