Symmetry Limit Research Articles

Light dark matter and the electroweak phase transition in the NMSSM

We analyze the stability of the vacuum and the electroweak phase transition in the NMSSM close to the Peccei-Quinn symmetry limit. This limit contains light Dark Matter (DM) particles with a mass significantly smaller than the weak scale and also light CP-even and CP-odd Higgs bosons. Such light particles lead to a consistent relic density and facilitate a large spin-independent direct DM detection cross section, that may accommodate the recently reported signatures at the DAMA and CoGeNT experiments. Studying the one-loop effective potential at finite temperature, we show that when the lightest CP-even Higgs mass is of the order of a few GeV, the electroweak phase transition tends to become first order and strong. The inverse relationship between the direct-detection cross-section and the lightest CP-even Higgs mass implies that a cross-section of the order of 10$^{-41}$ cm$^2$ is correlated with a strong first order phase transition.

Dirac equation for generalized Pöschl-Teller scalar and vector potentials and a Coulomb tensor interaction by Nikiforov-Uvarov method

Approximate analytical solutions of spin and pseudospin symmetry limits of Dirac equation are reported for the generalized Pöschl-Teller scalar and vector potentials and a Coulomb tensor interaction by Nikiforov-Uvarov method. On the contrary to the cumbersome numerical procedures, the analytical approach followed here can be followed even by the undergraduate students.

Phenomenological and microscopic cluster models. I. The geometric mapping

The geometrical mapping of algebraic nuclear cluster models is investigated within the coherent state formalism. Two models are considered: the Semimicroscopic Algebraic Cluster Model (SACM) and the Phenomenological Algebraic Cluster Model (PACM), which is a special limit of the SACM. The SACM strictly observes the Pauli exclusion principle while the PACM does not. The discussion of the SACM is adapted to the coherent state formalism by introducing the new SO(3) dynamical symmetry limit and third-order interaction terms in the Hamiltonian. The potential energy surface is constructed in both models and it is found that the effects of the Pauli principle can be simulated by higher-order interaction terms in the PACM. The present study is also meant to serve as a starting point for investigating phase transitions in the two algebraic cluster models.

Light-cone wave functions of heavy baryons

We present a classification of the three-quark light-cone distribution amplitudes (LCDAs) for ground-state heavy baryons with the spin parities JP = 1/2 + and JP = 3/2 + in QCD in the heavy-quark symmetry limit and calculate several lowest moments of LCDAs based on QCD sum rules. We propose simple model functions for the heavy-baryon distribution amplitudes and analyze their dependence on the energy scale.

Constraints on the large-xd/uratio from electron-nucleus scattering atx>1

Recently the ratio of neutron to proton structure functions ${F}_{2}^{n}/{F}_{2}^{p}$ was extracted from a phenomenological correlation between the strength of the nuclear EMC effect and inclusive electron--nucleus cross section ratios at $x>1$. Within conventional models of nuclear smearing, this ``in-medium correction'' (IMC) extraction constrains the size of nuclear effects in the deuteron structure functions, from which the neutron structure function ${F}_{2}^{n}$ is usually extracted. The IMC data determine the resulting proton $d/u$ quark distribution ratio, extrapolated to $x=1$, to be $0.23\ifmmode\pm\else\textpm\fi{}0.09$ with a 90% confidence level. This is well below the SU(6) symmetry limit of $1/2$ and significantly above the scalar diquark dominance limit of 0.

Relativistic Morse Potential and Tensor Interaction

In this paper, by applying the Pekeris approximation, we present solutions of the Dirac equation for the Morse potential including a Coulomb-like tensor potential with arbitrary spin-orbit coupling number κ under spin and pseudospin symmetry limits. The generalized parametric Nikiforov–Uvarov method is used to obtain energy eigenvalues and corresponding eigenfunctions in their closed forms. We show that tensor interaction removes degeneracies between spin and pseudospin doublets. Some numerical results are given, too.

Triaxial shapes in the interacting vector boson model

A new dynamical symmetry limit of the two-fluid interacting vector boson model (IVBM), defined through the chain $\text{Sp}(12,R)\ensuremath{\supset}\text{U}(3,3)\ensuremath{\supset}{\text{U}}^{*}(3)\ensuremath{\bigotimes}\text{SU}(1,1)\ensuremath{\supset}{\text{SU}}^{*}(3)\ensuremath{\supset}\text{SO}(3)$, is introduced. The SU${}^{*}$(3) algebra considered in the present paper closely resembles many properties of the SU${}^{*}$(3) limit of the interacting boson model-2, which have been shown by many authors geometrically to correspond to the rigid triaxial model. The influence of different types of perturbations on the SU${}^{*}$(3) energy surface, in particular the addition of a Majorana interaction and an O(6) term to the model Hamiltonian, is studied. The effect of these perturbations results in the formation of a stable triaxial minimum in the energy surface of the IVBM Hamiltonian under consideration. Using a schematic Hamiltonian that possesses a perturbed SU${}^{*}$(3) dynamical symmetry, the theory is applied for the calculation of the low-lying energy spectrum of the nucleus ${}^{192}$Os. The theoretical results obtained agree reasonably with the experimental data and show a very shallow triaxial minimum in the energy surface for the ground state in ${}^{192}$Os, suggesting that the proposed dynamical symmetry might be appropriate for the description of the collective properties of different nuclei, exhibiting triaxial features.

Phenomenological and semimicroscopic cluster models and their phase transitions

Two algebraic cluster models of nuclear structure which use the same Hamiltonian are explored: a Phenomenological Algebraic Cluster Model (PACM), and a Semi-microscopic Algebraic Cluster Model (SACM). The PACM does not incorporate the Pauli exclusion principle, while the SACM does. The Hamiltonian considered is an admixture of three dynamical symmetries; the SU(3), SO(4), and SO(3), with weighting of each determined by parameters. The classical potential is constructed using coherent states, and the model Hilbert space of the SACM is constructed in such a way as to include all shell model states which correspond to the cluster structure of interest. Phase transitions and their orders are investigated for each model, and parameter phase diagrams are presented, wherein it is found that consideration of the Pauli principle has significant consequences. Also shown are fits of Hamiltonian parameters for a nucleus of 2 spherical clusters, when moving between the symmetry limits.

Perturbative pseudospin symmetry limit with linear spin-orbit potential

The pseudospin symmetry (PSS) limits which conserve substantial spin-orbit splitting are investigated. It is found that while the strength of the spin-orbit potential as well as the spin-orbit splitting increase, the pseudospin doublets, e.g., 2p3/2 and 1f5/2 states, are always degenerate. Furthermore, by examining the perturbation corrections to the single-particle energies, the perturbative nature of the proposed PSS limits is also discussed.

Perturbative interpretation of relativistic symmetries in nuclei

Perturbation theory is used systematically to investigate the symmetries of the Dirac Hamiltonian and their breaking in atomic nuclei. Using the perturbation corrections to the single-particle energies and wave functions, the link between the single-particle states in realistic nuclei and their counterparts in the symmetry limits is discussed. It is shown that the limit of S-V=const and relativistic harmonic oscillator (RHO) potentials can be connected to the actual Dirac Hamiltonian by the perturbation method, while the limit of S+V=const cannot, where S and V are the scalar and vector potentials, respectively. This indicates that the realistic system can be treated as a perturbation of spin-symmetric Hamiltonians, and the energy splitting of the pseudospin doublets can be regarded as a result of small perturbation around the Hamiltonian with RHO potentials, where the pseudospin doublets are quasidegenerate.

EXACTLY COMPLETE SOLUTIONS OF THE DIRAC EQUATION WITH PSEUDOHARMONIC POTENTIAL INCLUDING LINEAR PLUS COULOMB-LIKE TENSOR POTENTIAL

In this paper, we present exact solutions of the Dirac equation with the pseudoharmonic potential including linear as well as Coulomb-like tensor potential with arbitrary spin–orbit coupling number κ under spin and pseudospin symmetry limits. The Nikiforov–Uvarov method is used to obtain energy eigenvalues and corresponding eigenfunctions in closed forms. We show that tensor interaction removes degeneracies between spin and pseudospin doublets. Some numerical results are also given.

Basis-independent methods for the two-Higgs-doublet model. III. TheCP-conserving limit, custodial symmetry, and the oblique parametersS,T,U

In the Standard Model, custodial symmetry is violated by the hypercharge U(1) gauge interactions and the Yukawa couplings, while being preserved by the Higgs scalar potential. In the two-Higgs doublet model (2HDM), the generic scalar potential introduces new sources of custodial symmetry breaking. We obtain a basis-independent expression for the constraints that impose custodial symmetry on the 2HDM scalar potential. These constraints impose CP-conservation on the scalar potential and vacuum, and in addition add one extra constraint on the scalar potential parameters. We clarify the mass degeneracies of the 2HDM that arise as a consequence of the custodial symmetry. We also provide a computation of the "oblique" parameters (S, T, and U) for the most general CP-violating 2HDM in the basis-independent formalism. We demonstrate that the 2HDM contributions to T and U vanish in the custodial symmetry limit, as expected. Using the experimental bounds on S and T from precision electroweak data, we examine the resulting constraints on the general 2HDM parameter space.

DIRAC EQUATION FOR A COULOMB SCALAR, VECTOR AND TENSOR INTERACTION

There is now motivating experimental evidence for relativistic symmetries in nuclei and hadrons, namely pseudospin and spin symmetry limits of the Dirac equation besides the old theoretical backgrounds. The most fundamental ingredients in such studies are definitely the wave functions and energy eigenvalues. Here, having in mind the importance of the Coulomb term as well as the degeneracy-removing role of tensor interaction, we obtain the exact solutions to the problem for Coulomb scalar, vector and tensor terms in both spin and pseudospin symmetry limits. We see that, contrary to many other common cumbersome techniques, the problem is simply solved via the methodology of supersymmetric quantum mechanics.

Occurrence of strain nonuniformity in thin‐walled cylinders subjected to constant axial compressive force and cyclic torsion

Hysteretic behaviour numerical analysis has been carried out for elastic–plastic thin‐walled cylinders subjected to a constant axial compressive force and cyclic torsion. It is shown that various deformation modes appear, which are different from those under constant axial contraction, and that those modes cause rapid growth of strain nonuniformity. Also branching analysis for the same model has been performed according to symmetry limit theory and the predicted multiple branching behaviour is compared with the hysteretic behaviour.

Solution of Dirac Equation with Killingbeck Potential by Using Wave Function Ansatz Method under Spin Symmetry Limit

The Dirac equation is solved for Killingbeck potential. Under spin symmetry limit, the energy eigenvalues and the corresponding wave functions are obtained by using wave function ansatz method.

Supersymmetric study of the pseudospin symmetry limit of the Dirac equation for a pseudoharmonic potential

We exactly determine the eigenfunctions and eigenvalues of the Dirac equation in the presence of a pseudoharmonic potential for the pseudospin symmetry that is known to have wide applications in the field of theoretical nuclear physics. We see that the problem is simply solved using the methodology of supersymmetric quantum mechanics.

Approximate Pseudospin Solutions of the Dirac Equation with the Eckart Potential Including a Coulomb-Like Tensor Potential

We solve the Dirac equation with the Eckart potential including a Coulomb-like tensor potential under pseudospin symmetry limit with arbitrary spin-orbit coupling quantum number κ by using the Nikiforov-Uvarov method. We have obtained closed forms of eigenfunctions, energy eigenvalues and compared our results with other present data.

Fast analysis of isoflavones by high-performance liquid chromatography using a column packed with fused-core particles

The recent development of fused-core technology in HPLC columns is enabling faster and highly efficient separations. This technology was evaluated for the development of an fast analysis method for the most relevant soy isoflavones. A step-by-step strategy was used to optimize temperature (25–50 °C), flow rate (1.2–2.7 mL/min), mobile phase composition and equilibration time (1–5 min). Optimized conditions provided a method for the separation of all isoflavones in less than 5.8 min and total analysis time (sample-to-sample) of 11.5 min. Evaluation of chromatographic performance revealed excellent reproducibility, resolution, selectivity, peak symmetry and low limits of detection and quantification levels. The use of a fused-core column allows highly efficient, sensitive, accurate and reproducible determination of isoflavones with an outstanding sample throughout and resolution. The developed method was validated with different soy samples with a total isoflavone concentration ranging from 1941.53 to 2460.84 μg g −1 with the predominant isoflavones being isoflavone glucosides and malonyl derivatives.

Exact pseudospin symmetry solution of the Dirac equation for spatially-dependent mass Coulomb potential including a Coulomb-like tensor interaction via asymptotic iteration method

In this Letter, the Dirac equation is exactly solved for spatially-dependent mass Coulomb potential including a Coulomb-like tensor potential under pseudospin symmetry limit by using asymptotic iteration method with arbitrary spin–orbit coupling number κ. The energy eigenvalues and corresponding eigenfunctions are obtained and some numerical results are given.

Distinguishing two kinds of scalar mesons from heavy meson decays

In the SU(3) symmetry limit, semileptonic $D^+\to Sl^+\nu$ and $B^-\to Sl^-\bar\nu$ decays, with $S=a_0(980)$, $f_0(980)$ and $f_0(600)$, are found to obey different sum rules in the $\bar qq$ and the tetra-quark descriptions for scalar mesons. Thus these sum rules can distinguish the two scenarios for light scalar mesons model-independently. This method also applies to the $\bar B^0\to J/\psi(\eta_c) S$ decays. Two kinds of SU(3) symmetry breaking effects are found to be under control, which will not spoil our method. The branching fractions of the $D^+\to Sl^+\nu$, $B^-\to Sl^-\bar\nu$ and $\bar B^0\to J/\psi(\eta_c) S$ decays roughly have the order $10^{-4}$, $10^{-5}$ and $10^{-6}$, respectively. The ongoing BES-III and the forthcoming Super B experiments are able to measure these channels and accordingly to provide detailed information of the scalar meson inner structure.