Darkon dark matter, unparticle effects and collider physics

In this talk I report recent results on the simplest dark matter model, the Darkon model, and supersymmetric unparticle effects on dark matter, and some implications for coUider physics. I first discuss dark matter properties and collider signatures in the Darkon model, and then I discuss some implications for dark matter if a scalar unparticle is introduced to the MSSM.     

Graded Lie Algebra Generating of Parastatistical Algebraic Relations

A new kind of graded Lie algebra (We call it Z2,2 graded Lie algebra) is introduced as a framework for formulating parasupersymmetric theories. By choosing suitable Bose subspace of the Z2,2 graded Lie algebra and using relevant generalized Jacobi identities, we generate the whole algebraic structure of parastatistics.     

Infinite-Dimensional Analysis and Analytic Number Theory

We consider arithmetical aspects of analysis on Fock spaces (Boson Fock space, Fermion Fock space, and Boson–Fermion Fock space) with applications to analytic number theory.     

Description of the Superdeformed Bands of the Lutetium Isotopes

In the cases with and without a perturbation possessing the S0_sdg(5) (or SU_sdg(5)) symmetry in the supersymmetry scheme with many-body interactions, superdeformed bands in the odd-A Lu isotopes ^163,165,167Lu are investigated. Quantitatively good results of γ-ray energies and dynamical moments of inertia are obtained in both of the two cases. It shows that the supersymmetry scheme with many-body interactions has almost the same power to describe the triaxial superdeformed bands as to the other superdeformed bands.     

Beyond the standard model: Working group report

This report summarises the work done in the ‘Beyond the Standard Model’ working group of the Sixth Workshop on High Energy Physics Phenomenology (WHEPP-6) held at the Institute of Mathematical Sciences, Chennai, Jan 3–15, 2000. The participants in this working group were: R Adhikari, B Ananthanarayan, K P S Balaji, Gour Bhattacharya, Gautam Bhattacharyya, Chao-Hsi Chang (Zhang). D Choudhury, Amitava Datta, Anindya Datta, Asesh K Datta, A Dighe, N Gaur, D Ghosh, A Goyal, K Kar, S F King, Anirban Kundu, U Mahanta, R N Mohapatra, B Mukhopadhyaya, S Pakvasa, P N Pandita, M K Parida, P Poulose, G Raffelt, G Rajasekaran, S Rakshit, Asim K Ray, A Raychaudhuri, S Raychaudhuri, D P Roy, P Roy, S Roy, K Sridhar and S Vempati.     

New physics effects from B meson decays

In this talk, we point out some of the present and future possible signatures of physics beyond the Standard Model from B-meson decays, taking R-parity conserving and violating supersymmetry as illustrative examples. An expanded version is available on hep-ph archive.     

用超对称性和形不变性方法求解环形振子的能谱和波函数

运用超对称性和形不变性方法计算环形振子的能量本征值和本征波函数.所得到的能谱公式与用费曼路径积分方法得到的严格解完全一致.     

New Theory of Periodic Systems by Supersymmetric Quantum Mechanics on Finite Interval

We show that the mechanism of gap formation has a resonance nature. The special real solutions were discovered which have knot distribution with a period coinciding with that of potential at all energies of the whole gap interval. In terms of these solutions resonance gap appearance gets the most direct explanation: ever repeating influence of the potential upon wave function results in exponential increase (decrease) of the wave amplitudes in the forbidden zones. Periodical continuation of exactly solvable models of SUSY QM on finite interval gives rise to algorithms of fixing zone properties - shifting chosen boundaries of spectral bands.     

FRW minisuperspace with local N=4 supersymmetry and self‐interacting scalar field

A supersymmetric FRW model with a scalar supermultiplet and generic superpotential is analysed from a quantum cosmological perspective. The corresponding Lorentz and supersymmetry constraints allow to establish a system of first order partial differential equations from which solutions can be obtained. We show that this is possible when the superpotential is expanded in powers of a parameter λ?1. At order λ⁰ we find the general class of solutions, which include in particular quantum states reported in the current literature. New solutions are partially obtained at order λ¹, where the dependence on the superpotential is manifest. These classes of solutions can be employed to find states for higher orders in λ. Our analysis further points to the following: (i) supersymmetric wave functions can only be found when the superpotential has either an exponential behaviour, an effective cosmological constant form or is zero; (ii) If the superpotential behaves differently during other periods, the wave function is trivial ( = 0, i.e., no supersymmetric states). We conclude this paper discussing how our FRW minisuperspace (with N = 4 supersymmetry and invariance under time‐reparametrization) can be relevant concerning the issue of supersymmetry breaking.     

Four-loop verification of an algorithm for summing Feynman diagrams in the N=1 supersymmetric electrodynamics

By calculating some four-loop diagrams in the N=1 supersymmetric electrodynamics regularized by higher derivatives, we verify a method for summing Feynman diagrams based on using Schwinger-Dyson equations and Ward identities. In particular, for the diagrams considered, we prove the correctness of an additional identity for Green’s functions not reduced to the gauge Ward identity. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 147, No. 2, pp. 290–302, May, 2006.