Related papers: $R$-matrices for Elliptic Calogero-Moser Models
We apply a recently introduced reduction procedure based on the embedding of non-crystallographic Coxeter groups into crystallographic ones to Calogero-Moser systems. For rational potentials the familiar generalized Calogero Hamiltonian is…
Based on current experimental results, such as neutrino oscillations and the neutrinoless double beta decays (i.e. data from Super Kamiokande, KamLAND, SNO, etc.), the neutrino mixing matrix can be adequately determined. Though there are…
We show that a Calogero-Sutherland type model with anharmonic interactions of fourth and sixth orders leads to the matrix model corresponding to the branched polymers. We also show that by suitably modifying this model one can also obtain…
The asymptotic kinematic limits of S-matrices are dominated by large logarithms which, roughly speaking, fall into two categories: those which are controlled by a renormalization group (RG) scale, which we may think of as logs involving…
We propose a predictive lepton model under a modular $S_4$ symmetry, where the neutrino mass matrix arises from a radiative seesaw at one-loop level. The tree-level mass matrix is forbidden by well-assigned modular weights, which also play…
A model describing N particles on a line interacting pairwise via an elliptic function potential in the presence of an external field is partially solved in the quantum case in a totally algebraic way. As an example, the ground state and…
The present work extends scotogenic and its modular $\mathcal{A}_4$ variation a step forward and demonstrates scotogenic modular $\mathcal{A}_4$ non-supersymmetric realization. To achieve this non-holomorphic modular symmetries come to…
We present a class of models with radiative neutrino mass and stable dark-matter candidates. Neutrino mass is generated by a one-loop diagram with the same topography as Ma's 2006 proposal (which used an inert scalar-doublet and singlet…
In this work we use matrix models to study the problem of strength distributions. This is motivated by noticing near exponential fall offs of strengths in calculated magnetic dipole excitations. We emphasize that the quality of the…
We describe classical top-like integrable systems arising from the quantum exchange relations and corresponding Sklyanin algebras. The Lax operator is expressed in terms of the quantum non-dynamical $R$-matrix even at the classical level,…
We present a model based on the A4 non-abelian discrete symmetry leading to a predictive five-parameter neutrino mass matrix and providing a stable dark matter candidate. We found an interesting correlation among the atmospheric and the…
In the case of two generation neutrinos, the energy-scale dependence of the lepton-flavor mixing matrix with Majorana phase can be governed by only one parameter r, which is the ratio between the diagonal elements of neutrino mass matrix.…
We investigate models of charged lepton and neutrino masses and lepton mixing based on broken modular symmetry. The matter fields in these models are assumed to transform in irreducible representations of the finite modular group $\Gamma_4…
We study an energy-scale dependence of the lepton-flavor-mixing matrix in the minimal supersymmetric standard model with the effective dimension-five operators which give the masses of neutrinos. We analyze the renormalization group…
A new method is proposed for fitting non-relativistic binary-scattering data and for extracting the parameters of possible quantum resonances in the compound system that is formed during the collision. The method combines the well-known…
Suppose $X$ and $Y$ are $p\times n$ matrices each with mean $0$, variance $1$ and where all moments of any order are uniformly bounded as $p,n \to \infty$. Moreover, the entries $(X_{ij}, Y_{ij})$ are independent across $i,j$ with a common…
We present a new type of integrable one-dimensional many-body systems called a one-parameter Calogero-Moser (CM) system. In the discrete level, the Lax pairs with a parameter are introduced and, of course, the discrete-time equations of…
The discrete non-Abelian symmetry $A_4$, valid at some high-energy scale, naturally leads to degenerate neutrino masses, without spoiling the hierarchy of charged-lepton masses. Realistic neutrino mass splittings and mixing angles (one of…
We consider scalar-tensor theories and reconstruct their potential U(\Phi) and coupling F(\Phi) by demanding a background LCDM cosmology. In particular we impose a background cosmic history H(z) provided by the usual flat LCDM…
We consider the problem of determining the limiting spectral distribution for random matrices whose row distributions are permitted to have limited dependence. We assume mild moment conditions and give an extension of the…