Solving ground eigenvalue and eigenfunction of spheroidal wave equation at low frequency by supersymmetric quantum mechanics method

The spheroidal wave functions are found to have extensive applications in many branches of physics and mathematics. We use the perturbation method in supersymmetric quantum mechanics to obtain the analytic ground eigenvalue and the ground eigenfunction of the angular spheroidal wave equation at low frequency in a series form. Using this approach, the numerical determinations of the ground eigenvalue and the ground eigenfunction for small complex frequencies are also obtained.

Constructing(2+1)-dimensional N=1 supersymmetric integrable systems from the Hirota formalism in the superspace

The N = 1 supersymmetric extensions of two integrable systems,a special negative Kadomtsev–Petviashvili（NKP）system and a（2＋1）-dimensional modified Korteweg–de Vries（MKd V） system,are constructed from the Hirota formalism in the superspace.The integrability of both systems in the sense of possessing infinitely many generalized symmetries are confirmed by extending the formal series symmetry approach to the supersymmetric framework.It is found that both systems admit a generalization of W∞type algebra and a Kac-Moody–Virasoro type subalgebra.Interestingly,the first one of the positive flow of the supersymmetric NKP system is another N = 1 supersymmetric extension of the（2＋1）-dimensional MKd V system.Based on our work,a hypothesis is put forward on a series of（2＋1）-dimensional supersymmetric integrable systems.It is hoped that our work may develop a straightforward way to obtain supersymmetric integrable systems in high dimensions.

Supersymmetric Sawada-Kotera-Ramani Equation: Bilinear Approach

In this paper, using the Hirota＇s bilineax method, we consider the N = 1 supersymmetric Sawada-Kotera- Ramani equation and obtain the Bazcklund transformation of it. Its one- and two-supersoliton solutions axe obtained and N-supersoliton solutions for N ≥ 3 are given under the condition kiξj = kjξi.

Supersymmetric Electroweak Corrections to the Decay of the Heavy Chargino into the Light Chargino and Z Boson

The supersymmetric electroweak corrections to the partial width of the decay x2+ → Z0x1-+, including thecontributions from the third generation quarks and squarks, are presented within the minimal supersymmetric standardmodel. With the reasonable parameters sets, which open this decay channel kinematically, the relative corrections canreach the value of ～ -6%. Therefore they should be taken into consideration for the precise experimental measurementat future colliders.

Pseudospin symmetric solutions of the Dirac equation with the modified Rosen-Morse potential using Nikiforov-Uvarov method and supersymmetric quantum mechanics approach

Employing the Pekeris-type approximation to deal with the pseudo-centrifugal term,we analytically study the pseudospin symmetry of a Dirac nucleon subjected to equal scalar and vector modified Rosen-Morse potential including the spin-orbit coupling term by using the Nikiforov-Uvarov method and supersymmetric quantum mechanics approach.The complex eigenvalue equation and the total normalized wave functions expressed in terms of Jacobi polynomial with arbitrary spin-orbit coupling quantum number k are presented under the condition of pseudospin symmetry.The eigenvalue equations for both methods reproduce the same result to affirm the mathematical accuracy of analytical calculations.The numerical solutions obtained for different adjustable parameters produce degeneracies for some quantum number.

N = 4 Supersymmetric Morse Oscillator and Its Spectrum-Generating Algebra

In this paper N = 4 supersymmetry of generalized Morse oscillators in one dimension is studied. Both bound states and scattering states of its four superpartner Hamiltonians are analyzed by using unitary irreducible representations of the noncompact Lie algebra su(1,1). The spectrum-generating algebra governing the Hamiltonian of the N = 4 supersymmetric Morse oscillator is shown to be connected with the realization of Lie superalgebra osp(1,2)or B(0,1) in terms of the variables of a supersymmetric two-dimensional harmonic oscillator.

A new supersymmetric classical Boussinesq equation

In this paper, we obtain a supersymmetric generalization for the classical Boussinesq equation. We show that the supersymmetric equation system passes the Painlevé test and we also calculate its one- and two-soliton solutions.

Painlevé integrability of the supersymmetric Ito equation

A supersymmetric version of the Ito equation is proposed by extending the independent and dependent variables for the classic Ito equation.To investigate the integrability of the N = 1 supersymmetric Ito(sIto) equation, a singularity structure analysis for this system is carried out.Through a detailed analysis in two cases by using Kruskal’s simplified method, the sIto system is found to pass the Painlevé test, and thus is Painlevé integrable.

SUPERSYMMETRIC INVARIANCE AND UNIVERSAL CENTRAL EXTENSIONS OF LIE SUPERTRIPLE SYSTEMS

In this article, we discuss some properties of a supersymmetric invariant bilinear form on Lie supertriple systems. In particular, a supersymmetric invariant bilinear form on Lie supertriple systems can be extended to its standard imbedding Lie superalgebras. Furthermore, we generalize Garland＇s theory of universal central extensions for Lie supertriple systems following the classical one for Lie superalgebras. We solve the problems of lifting automorphisms and lifting derivations.

Generalized symmetries of an N=1 supersymmetric Boiti–Leon–Manna–Pempinelli system

The formal series symmetry approach （FSSA）, a quite powerful and straightforward method to establish infinitely many generalized symmetries of classical integrable systems, has been successfully extended in the supersymmetric framework to explore series of infinitely many generalized symmetries for supersymmetric systems. Taking the N = 1 supersymmetric Boiti-Leon-Manna-Pempinelli system as a concrete example, it is shown that the application of the extended FSSA to this supersymmetric system leads to a set of infinitely f（t）. Some interesting special cases of symmetry algebras are commutativity of higher order generalized symmetries. many generalized symmetries with an arbitrary function presented, including a limit case f（t） = 1 related to the

Solving Generalized Non-degenerate Two-Mode Two-Photon Jaynes-Cummings Model by Supersymmetric Unitary Transformation

Based on supersymmetric quantum mechanics theory, we introduced a supersymmetric unitary transfor mation to diagonalize the Hamiltonian of non-degenerate two-mode two-photon Jaynes-Cummings models which include any forms of intensity-dependent coupling, field-dependent detuning, and field nonlinearity. Its eigenvalue, eigenstates,and time evolution of state vector are obtained.

The Top-Charm Associated Production Within the R-Parity Violating Supersymmetric Model in Photon-Proton Collisions

The top-charm associated production with the effects from both B- and L-violating interactions in TeVscale photon-proton collisions is investigated in the framework of Rp minimal supersymmetric standard model. Withinthe bounds on the relevant R-parity violating couplings, the total cross section will reach the order of 10 fb in some partsof the parameter space.

Supersymmetric WKB Approximation of Anharmonic Potential V（r）=ar^2＋br^-4＋cr^-6

This article uses the supersymmetric WKB approximation to obtain the approximate energy levels and wave functions of the anharmonic potential V（r） = ar^2 ＋ br^-4 ＋ cr^-6 in order to tesify the correctness between [Phys. Left. A 170 （1992） 335] and the paper written by M. Landtman [Phys. Left. A 175 （1993） 147].

Supersymmetric Quantum Mechanics and SUSY Dependent SU(2) Symmetry for a Spin-1/2 Charged Particle in a Magnetic Field

We find that in a supersymmetric quantum mechanics （SUSY QM） system, in addition to supersymmetric algebra, an associated SU（2） algebra can be obtained by using semiunitary （SUT） operator and projection operator, and the relevant constants of motion can be constructed. Two typical quantum systems are investigated as examples to demonstrate the above finding. The first example is the quantum system of a nonrelativistic charged particle moving in x-y plane and coupled to a magnetic field along z-axis. The second example is provided with the Dirac particle in a magnetic field. Similarly there exists an SUτ（2） SUσ（2） symmetry in the context of the relativistic Pauli Hamilt onian squared. We show that there exists also an SU（2） symmetry associated with the supersvmmetrv of the Dirac particle.

The Top－Charm Associated Production Within the R－Parity Violating Supersymmetric Model in Photon－Proton Collisions

The top-charm associated production with the effects from both B- and L-violating interactions in TeV scale photon-proton collisions is investigated in the framework of minimal supersymmetric standard model. Within the bounds on the relevant R-parity violating couplings, the total cross section will reach the order of 10 fb in some parts of the parameter space.

Mass Spectrum in the Minimal Supersymmetric 3-3-1 Model

We consider the minimal supersymmetric extension of the 3-3-1 model. We study the mass spectrum of this model in the fermionic and gauge bosons sectors without the antisextet. We also present some phenomenological consequences of this model at colliders such as Large Hadron Collider (LHC) and International Linear Collider (ILC).

R-Parity Violation Effects on b_1 → bχ_1~0 in Minimal SupersymmetricStandard Model

We investigate in detail the effects of R-parity lepton number violation onthe decay b_1 → bχ_1~0 in the R-parity violating minimal supersymmetric standard model (R_p-MSSM)under the present experimental constraints on R_p parameters. In our numerical calculations weconsider two cases of input parameters of the squark and slepton sectors, M_(squark) 【 M_(slepton)and M_(squark) 】 M_(slepton), for comparison. The results show that the relative R-parity violatingcorrection is not very sensitive to the mass of the lightest neutralino bχ_1~0 the degenerateR-parity violating coupling parameter λ′_2 but strongly depends on M_(squark), M_(slepton) tan βand tie degenerate R-parity violating coupling parameter λ′_1. The relative correction is about -4～ 3% and can exceed -6% in some region of parameter space. Therefore, precise experiment analyseson the decay b_1 → bχ_1~0 may provide a probe of the R-parity violation.

Effects of Complex Parameters on t→ch^0 in Supersymmetric QCD

We investigate the leading SUSY-QCD contributions to the branch ratio (BR) oft→ch~0 within the context of the minimal supersymmetric standard model (MSSM) with complex parameters,assuming more generally that there is a misalignment between the squark and quark that leads to a flavor non-diagonal squark mass matrix.We introduce complex phases only in μ and At,namely φ_μ and φ_(Aq),for simplicity,and study the dependence of the BR of t→ch~0 on these phase parameters.Our calculations show that these CP-violation phases and the flavor mixing parameter λ influence the BR oft→ch~0 considerably,and the effect induced by φ_(At) is much larger than that by φ_μ and φ_(Ac(?)u.For different values of the complex parameters μ and A_t that are set in this paper,the BR of t -+ ch~ is in the range of 10~(-7)～10~(-6),depending mainly on the value of the trilinear coupling A_t.

Generating of Conditionally Exactly Soluble Potentials by Method of Supersymmetric Quantum Mechanics

This paper suggests a systematic method based on supersymmetric quantum mechanics for generating conditionally exactly soluble potentials, and uses the variational supersymmetric WKB method to obtain the approximate values of the energy spectrum of the whole class.

eμ Production in R-Parity Violating Supersymmetric Model at Hadron Colliders

We investigate the lepton flavor violating productions pp/pp→eμ ＋ X in the framework of the R-parity violating （RPV） supersymmetric model at the Tevatron and the CERN large hadron collider （LHC）. We present the total cross sections including the next-to-leading order （NLO） QCD corrections and the contribution from gluon-gluon fusion subprocess. Our numerical results show that the one-loop QCD corrections significantly increase the tree-level cross sections, and the variation of K factor is in the range between 1.28 （1.32） and 1.79 （1.58） at the Tevatron （LHC）. We find that the QCD correction from the one-loop gluon-gluon fusion subprocess is remarkable at the LHC and should be taken into account.