Analysis of the chargino and neutralino mass parameters at one-loop level

In the minimal supersymmetric standard model (MSSM) the masses of the neutralinos and charginos depend on the gaugino and higgsino mass parameters M, M' and . If supersymmetry is realized, the extraction of these parameters from future high energy experiments will be crucial to test the underlying theory. We present a consistent method for properly defining on-shell parameters at one-loop level and determining these from precision measurements. In addition, we show how a GUT relation for the parameters M and M' can be tested at one-loop level. The numerical analysis is based on a complete one-loop calculation. The derived analytic formulae are given in the appendix.Received: 7 April 2003, Published online: 23 June 2003     

Charge density plateaux and insulating phases in the $\mathsf{t-J}$ model with ladder geometry

We discuss the occurrence and the stability of charge density plateaux in ladder-like t-J systems (at zero magnetization M = 0) for the cases of 2- and 3-leg ladders. Starting from isolated rungs at zero leg coupling, we study the behaviour of plateaux-related phase transitions by means of first order perturbation theory and compare our results with Lanczos diagonalizations for t-J ladders (N = 2 × 8) with increasing leg couplings. Furthermore we discuss the regimes of rung and leg couplings that should be favoured for the appearance of the charge density plateaux.Received: 28 July 2003, Published online: 8 December 2003PACS: 71.10.Fd Lattice fermion models (Hubbard model, etc.) - 71.27. + a Strongly correlated electron systems; heavy fermions - 75.10.-b General theory and models of magnetic ordering - 75.10.Jm Quantized spin models     

Precursor diamagnetism above the superconducting transition in YNi_\mathsf{2}B_\mathsf{2}C

High-resolution SQUID magnetization measurements in a single crystal of YNi₂B₂C around the superconducting transition are reported. The diamagnetic magnetization -M _fl at constant field H as a function of temperature and isothermal magnetization curves -M _fl vs. H are used to derive insights on precursor phenomena approaching the bulk transition temperature K. The precursor diamagnetism is found strongly enhanced with respect to the conventional Ginzburg-Landau value for Gaussian fluctuations and the curves -M _fl vs. H exhibit an upturn with the field and hysteretic effects up to T ^* = 15.4 K. These results are interpreted in terms of a non-zero order parameter in superconducting droplets above the bulk T _c . These droplets are likely to be related to inhomogeneities resulting from small amount of boron to carbon substitutions.Received: 23 April 2003, Published online: 15 October 2003PACS: 74.40.+k Fluctuations (noise, chaos, nonequilibrium superconductivity, localization, etc.) - 74.20.De Phenomenological theories (two-fluid, Ginzburg-Landau, etc.) - 74.25.Ha Magnetic properties     

Collective electronic excitations in a semiconductor superlattice in the Landau and Wannier-Stark ladder regime

Using a mean-field approximation, we have developed a systematic treatment of collective electronic modes in a semiconductor superlattice (SL) in the presence of strong electric and magnetic fields parallel to the SL axis. The spectrum of collective modes with zero wavevector along the SL axis is shown to consist of a principle magnetoplasmon mode and an infinite set of Bernstein-like modes. For non-zero wavevector along the SL axis, in addition to the cyclotron modes, extra collective modes are found at the frequencies |Nω _c±Mω _s|, which we call cyclotron-Stark modes (ω _c and ω _s are respectively the cyclotron and Stark frequencies, N and M are integer numbers). The frequencies of the modes propagating in “oblique” direction with respect to the SL axis show oscillatory behavior as a function of electric field strength. All the modes considered have very weak spatial dispersion and they are not Landau damped. The specific predictions made for the dispersion relations of the collective excitations should be observable in resonant Raman scattering experiments. Received 29 August 2002 / Received in final form 25 February 2003 Published online 4 June 2003 RID="a" ID="a"e-mail: 612033@inbox.ru     

Method of Quantum Characters in Equivariant Quantization

 Let G be a reductive Lie group, g its Lie algebra, and M a G-manifold. Suppose 𝔸 _h (M) is a 𝕌 _h (g)-equivariant quantization of the function algebra 𝔸(M) on M. We develop a method of building 𝕌 _h (g)-equivariant quantization on G-orbits in M as quotients of 𝔸 _h (M). We are concerned with those quantizations that may be simultaneously represented as subalgebras in 𝕌^* _h (g) and quotients of 𝔸 _h (M). It turns out that they are in one-to-one correspondence with characters of the algebra 𝔸 _h (M). We specialize our approach to the situation g=gl(n,ℂ), M=End(ℂ ⁿ ), and 𝔸 _h (M) the so-called reflection equation algebra associated with the representation of 𝕌 _h (g) on ℂ ⁿ . For this particular case, we present in an explicit form all possible quantizations of this type; they cover symmetric and bisymmetric orbits. We build a two-parameter deformation family and obtain, as a limit case, the 𝕌(g)-equivariant quantization of the Kirillov-Kostant-Souriau bracket on symmetric orbits. Received: 28 April 2002 / Accepted: 3 October 2002 Published online: 24 January 2003 RID="*" ID="*" This research is partially supported by the Israel Academy of Sciences grant no. 8007/99-01. Communicated by L. Takhtajan     

Birkhoff Normal Form for Some Nonlinear PDEs

 We consider the problem of extending to PDEs Birkhoff normal form theorem on Hamiltonian systems close to nonresonant elliptic equilibria. As a model problem we take the nonlinear wave equation

Quantum-hydrodynamical picture of the massive Higgs boson

The phenomenon of spontaneous symmetry breaking admits a physical interpretation in terms of the Bose condensation process of elementary spinless quanta. In this picture, the broken-symmetry phase emerges as a real physical medium, endowed with a hierarchical pattern of scales, supporting two types of elementary excitations for : a massive energy branch , corresponding to the usual Higgs boson field, and a collective gapless branch . This is similar to the coexistence of phonons and rotons in superfluid ⁴He that, in fact, is usually considered the condensed-matter analog of the Higgs condensate. After previous work dedicated to the properties of the gapless phonon branch, in this paper we use quantum hydrodynamics to propose a physical interpretation of the massive branch. On the base of our results, M_H coincides with the energy gap for vortex formation and a massive Higgs boson is like a roton in superfluid ⁴He. Within this interpretation of the Higgs particle, there is no naturalness problem since M_H remains a naturally intermediate, fixed energy scale, even for an ultimate ultraviolet cutoff .Received: 24 November 2003, Published online: 29 January 2004     

Some remarks on -invariant Fedosov star products and quantum momentum mappings

In these notes we consider a slightly generalized Fedosov star product * on a symplectic manifold (M,ω), emanating from the fibrewise Weyl product and the triple (,Ω,s) consisting of a symplectic torsion free connection on M, a formal series ΩνZ²_dR(M)[[ν]] of closed two-forms on M, and a certain formal series s of symmetric contravariant tensor fields on M. We prove necessary and sufficient conditions for certain classical symmetries to become symmetries of the star product, only sufficient conditions having been published in special cases when this letter was written (note, however, the different proofs in [S. Gutt, J. Rawnsley, Natural star products on symplectic manifolds and quantum moment maps, 2003. math.SG/0304498 v1]). For a given symplectic vector field X on M, it is well known that (= is a sufficient condition for the Lie derivative to be a derivation of *. We prove that these conditions are in fact necessary ones, also providing a very simple proof for their being sufficient. Moreover, we prove a criterion that has first been presented by Gutt [S. Gutt, Star products and group actions, Contribution to the Bayrischzell Workshop, April 26–29, 2002] (see also [S. Gutt, J. Rawnsley, Natural star products on symplectic manifolds and quantum moment maps, 2003. math.SG/0304498 v1] for a different proof) and which specifies a necessary and sufficient condition for to be a quasi-inner derivation. The statement that this condition is a sufficient one dates back to Kravchenko [O. Kravchenko, Compos. Math. 123 (2000) 131]. Applying our results, we find necessary and sufficient criteria for a Fedosov star product to be -invariant and to admit a quantum Hamiltonian. Finally, supposing the existence of a quantum Hamiltonian, we present a cohomological condition on Ω that is equivalent to the existence of a quantum momentum mapping. In particular, our results show that the existence of a classical momentum mapping in general does not imply the existence of a quantum momentum mapping and thus give a negative answer to Xu’s question posed in [P. Xu, Commun. Math. Phys. 197 (1998) 167].     

Experimental evidence for narrow baryons in the mass range 1.0≤M≤1.46 GeV

The reaction pp → pπ⁺ X was studied at different incident energies around T _p = 2 GeV. Narrow baryonic structures were observed in the missing mass M _X and in the invariant mass M _pπ{+}. The masses of these structures are 1004, 1044, 1094, 1136, 1173, 1249, 1277, and 1384 MeV (and possibly 1339 MeV). Some of them were also observed at the same masses in the missing-mass spectra of the dp → ppX reaction although with a weaker signature. Many checks were performed to make sure that these structures were not produced by experimental artifacts. Several narrow small-amplitude peaks, were also extracted using already published photonucleon cross-sections. The small widths of all these results, and the stability of the observed structures, regardless of the experiment, were used to conclude that they are genuine baryons and not merely the consequence of dynamical rescatterings. These baryons cannot be associated with classical q³ quark configurations. We associate them with two colored-quark cluster configurations. Received: 3 July 2002 / Accepted: 30 January 2003 / Published online: 5 June 2003     

Passive Advection and the Degenerate Elliptic Operators <Emphasis Type="Italic">M</Emphasis><Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>

 We prove estimates for the stationary state n-point functions at zero molecular diffusivity in the Kraichnan model [13]. This is done by proving upper bounds for the heat kernels and Green's functions of the degenerate elliptic operators M _n that occur in the Hopf equations for the n-point functions. Received: 25 August 2001 / Accepted: 30 September 2002 Published online: 20 January 2003 Communicated by A. Kupiainen     

On <Emphasis Type="Italic">osp</Emphasis>(<Emphasis Type="Italic">M</Emphasis>∣2<Emphasis Type="Italic">n</Emphasis>) Integrable Open Spin Chains

We consider open spin chains based on osp(M2n) Yangians and solve the reflection equations for some classes of reflection matrices, including the diagonal ones. Having then integrable open spin chains, we write the analytical Bethe Ansatz equations. More details and references can be found in D. Arnaudon et al.: Nucl. Phys B 668 (2003) 469 and 687 (2004) 257.     

Phase Transitions in the Dynamics of Slow Random Monads

Let us have a finite set B (basin) with n>1 elements, which we call points, and a map M:B→B. Following Vladimir Arnold, we call such pairs (B,M) monads. Here we study a class of random monads, where the values of M(⋅) are independently distributed in B as follows: for all a,b∈B the probability of M(a)=a is s and the probability of M(a)=b, where a≠b, is (1−s)/(n−1). Here s is a parameter in [0,1].     

Configuration assignments of yrare high-spin structures in 126Cs

High-spin states in ¹²⁶Cs were populated in the reaction ¹¹⁶Cd(¹⁴N, 4n) at a beam energy of 65 MeV. About 50 new transitions were placed in a level scheme that consists of six rotational structures, three of which have been observed for the first time. The newly observed bands and a previously reported but uninterpreted band were assigned configurations based on their population, aligned angular momentum, energy signature splitting and B(M1)/B(E2) ratios (for the strongly coupled bands).Received: 16 September 2002, Revised: 10 March 2003, Published online: 1 July 2003PACS: 21.10.Re Collective levels - 27.60.+j      

Correction algorithm for finite sample statistics

Assume in a sample of size M one finds M_i representatives of species i with . The normalized frequency , based on the finite sample, may deviate considerably from the true probabilities p_i. We propose a method to infer rank-ordered true probabilities r_i from measured frequencies M_i. We show that the rank-ordered probabilities provide important informations on the system, e.g., the true number of species, the Shannon- and the Renyi-entropies.Received: 14 July 2003, Published online: 5 February 2004PACS: 02.50.-r Probability theory, stochastic processes, and statistics - 02.60.-x Numerical approximation and analysis - 07.05.Kf Data analysis: algorithms and implementation; data management     

Toward an experimental determination of possible vacuum regeneration for neutral flavoured mesons

The usual phenomenology of the complex formed by a neutral flavoured meson M⁰ and its antiparticle assumes the absence of vacuum regeneration in this complex. We propose experiments for determining the two amplitudes of (possibly non-zero) vacuum regeneration: (i) a comparison of the time dependence of decays of the M⁰ and into a channel which could be a CP-eigenstate (e.g., or ), or a general channel like ; (ii) a measurement of the ratio of the time-dependent transmutations, and ; (iii) a measurement of the ratio of the time-dependent probabilities for the production of and states, starting with a C-odd correlated state like the -meson. The proposed experiments are required to be as accurate as those for the known CP-violation effects in the complex. Received: 25 October 2002 / Revised version: 20 December 2002 / Published online: 7 March 2003 RID="a" ID="a" e-mail: guruv@phy.iitb.ac.in     

Resonance Theory for Schrödinger Operators

Given a family of isometries in a tracial von Neumann algebra M, a unital subalgebra B⊂M and a completely-positive map we define the free Fisher information of relative to B and η. Using this notion, we define the free dimension of relative to B, id. Let R be a measurable equivalence relation on a finite measure space X. Let M be the von Neumann algebra associated to R, and let be the canonical diffuse subalgebra. If are partial isometries arising from a treeing of this equivalence relation, then is equal to the cost of the equivalence relation in the sense of Gaboriau and Levitt. Received: 11 September 1999/Accepted: 10 November 2000     

A Small-Scale Density of States Formula

 Let (M,g) be a C ^∞ compact Riemann manifold with classical Hamiltonian, HC ^∞ (T ^* M). Assume that the corresponding -quantization P ₁ :=Op _ (H) is quantum completely integrable. We establish an -microlocal Weyl law on short spectral intervals of size ^2−ε;∀ε>0 for various families of operators P ₁ ^u ;uI containing P ₁ , both in the mean and pointwise a.e. for uI. The -microlocalization refers to a small tubular neighbourhood of a non-degenerate, stable periodic bicharacteristic γ⊂T ^* M−0. Received: 10 December 2001 / Accepted: 23 January 2003 Published online: 2 April 2003 RID="⋆" ID="⋆" Supported in part by an Alfred P. Sloan Research Fellowship and NSERC grant OGP01720280 Communicated by P. Sarnak     

Wigner Symbols and Combinatorial Invariants¶of Three-Manifolds with Boundary

In this paper we generalize the partition function proposed by Ponzano and Regge in 1968 to the case of a compact 3-dimensional simplicial pair (M, ∂M). The resulting state sum Z[(M, ∂M)] contains both Wigner 6j symbols associated with tetrahedra and Wigner 3jm symbols associated with triangular faces lying in ∂M. In order to show the invariance of Z[(M, ∂M)] under PL-homeomorphisms we exploit some results due to Pachner on the equivalence of n-dimensional PL-pairs both under bistellar moves on n-simplices in the interior of M and under elementary boundary operations (shellings and inverse shellings) acting on n-simplices which have some component in ∂M. We find, in particular, the algebraic identities – involving a suitable number of Wigner symbols – which realize the complete set of Pachner's boundary operations in n=3. The results established for the classical SU(2)-invariant Z[(M, ∂M)] are further extended to the case of the quantum enveloping algebra U _q (sl(2,ℂ)) (q a root of unity). The corresponding quantum invariant, M _q [(M, ∂M)], turns out to be the counterpart of the Turaev–Viro invariant for a closed 3-dimensional PL-manifold. To Giorgio Ponzano and Tullio Regge Received: 14 December 1998 / Accepted: 30 January 2000     

Hierarchical matrices in the see-saw mechanism,large neutrino mixing and leptogenesis

We consider the see-saw mechanism for hierarchical Dirac and Majorana neutrino mass matrices m _D and M _R, including the CP violating phases. Simple arguments about the structure of the neutrino mass matrix and the requirement of successful leptogenesis lead to the situation that one of the right-handed Majorana neutrinos is much heavier than the other two, which in turn display a rather mild hierarchy. It is investigated how for the neutrino mixing one small and two large mixing angles are generated. The mixing matrix element |U _e3|² is larger than 10^-3 and a characteristic ratio between the branching ratios of lepton flavor violating charged lepton decays is found. Successful leptogenesis implies sizable CP violation in oscillation experiments. As in the original minimal see-saw model, the signs of the baryon asymmetry of the universe and of the CP asymmetry in neutrino oscillations are equal and there is no connection between the leptogenesis phase and the effective mass as measurable in neutrinoless double beta decay.Received: 28 May 2003, Revised: 13 September 2003, Published online: 26 November 2003