Laser-induced optical activity in range of Rydberg autoionizing states of xenon

Optical activity of xenon atoms in the vacuum UV range induced by circularly polarized laser light is studied theoretically. The optical activity arises in the vicinity of the autoionizing state 5p ⁵(² P _1/2)8s′$ \left[ {\frac{1} {2}} \right]_1 $ \left[ {\frac{1} {2}} \right]_1 as a result of its coupling via the laser field with the discrete state 5p ⁵(² P _3/2)7p $ \left[ {\frac{1} {2}} \right]_1 $ \left[ {\frac{1} {2}} \right]_1 . Polarization variations of the vacuum UV radiation upon its propagation through the atomic medium are calculated, and the possibility of controlling this polarization is discussed. Manifestations of nonresonant coupling of the discrete state with the broad autoionizing state 5p ⁵(² P _1/2)6d′$ \left[ {\frac{1} {2}} \right]_1 $ \left[ {\frac{1} {2}} \right]_1 induced by the overlap of the Rydberg autoionizing series in xenon are studied.     

Spontaneous breakdown of $$ \mathcal{P}\mathcal{T} $$ symmetry in the complex Coulomb potential

The $ \mathcal{P}\mathcal{T} $ \mathcal{P}\mathcal{T} symmetry of the Coulomb potential and its solutions are studied along trajectories satisfying the $ \mathcal{P}\mathcal{T} $ \mathcal{P}\mathcal{T} symmetry requirement. It is shown that with appropriate normalization constant the general solutions can be chosen $ \mathcal{P}\mathcal{T} $ \mathcal{P}\mathcal{T} -symmetric if the L parameter that corresponds to angular momentum in the Hermitian case is real. $ \mathcal{P}\mathcal{T} $ \mathcal{P}\mathcal{T} symmetry is spontaneously broken, however, for complex L values of the form L = −1/2 + iλ. In this case the potential remains $ \mathcal{P}\mathcal{T} $ \mathcal{P}\mathcal{T} -symmetric, while the two independent solutions are transformed to each other by the $ \mathcal{P}\mathcal{T} $ \mathcal{P}\mathcal{T} operation and at the same time, the two series of discrete energy eigenvalues turn into each other’s complex conjugate.     

Finite-size scaling and power law relations for dipole-quadrupole interaction on Blume-Emery-Griffiths model

The Blume-Emery-Griffiths model with the dipole-quadrupole interaction ($ \ell = \frac{I} {J} $ \ell = \frac{I} {J} ) has been simulated using a cellular automaton algorithm improved from the Creutz cellular automaton (CCA) on the face centered cubic (fcc) lattice. The finite-size scaling relations and the power laws of the order parameter (M) and the susceptibility (χ) are proposed for the dipole-quadrupole interaction (ℓ). The dipole-quadrupole critical exponent δ_χ has been estimated from the data of the order parameter (M) and the susceptibility (χ). The simulations have been done in the interval $ 0 \leqslant \ell = \frac{I} {J}0 \leqslant 0.01 $ 0 \leqslant \ell = \frac{I} {J}0 \leqslant 0.01 for $ d = \frac{D} {J} = 0,k = \frac{K} {J} = 0 $ d = \frac{D} {J} = 0,k = \frac{K} {J} = 0 and $ h = \frac{H} {J} = 0 $ h = \frac{H} {J} = 0 parameter values on a face centered cubic (fcc) lattice with periodic boundary conditions. The results indicate that the effect of the ℓ parameter is similar to the external magnetic field (h). The critical exponent δ_ℓ are in good agreement with the universal value (δ _h = 5) of the external magnetic field.     

The p/π ratio pT dependence in the RHIC range of baryo-chemical potential

The BRAHMS measurement of proton-to-pion ratios in Au+Au and p+p collisions at $ \sqrt {s_{NN} } $ \sqrt {s_{NN} } = 62.4 GeV and $ \sqrt {s_{NN} } $ \sqrt {s_{NN} } = 200 GeV is presented as a function of transverse momentum and collision centrality within the pseudorapidity range 0 ≤ η ≤ 3. The baryo-chemical potential, μ _B , for the indicated data spans from μ _B ≈ 26 MeV ($ \sqrt {s_{NN} } $ \sqrt {s_{NN} } 200 GeV, η ≈ 0) to μ _B ∼ 260 MeV ($ \sqrt {s_{NN} } $ \sqrt {s_{NN} } = 62.4 GeV, η ≈ 3) [1]. The p/πratio measured for Au+Au system at $ \sqrt {s_{NN} } $ \sqrt {s_{NN} } 62.4 GeV, η ≈ 3 reaches astounding value of 8–10 at p _T > 1.5 GeV/c. For these energy and pseudorapidity interval no centrality dependency of p/π ratio is observed. Moreover, the baryon-to-meson ratio of nucleus-nucleus data are consistent with results obtained for p+p interactions.     

The masses of charged leptons and quarks from superposition self-interference of their Dirac fields

Without Higgs field interaction, accurate pole mass values are obtained for the charged leptons and quarks from a Z₃-symmetric linear superposition self-interference of the Dirac fields in the effective free-field Lagrangian. The charged lepton and quark pole masses evidence the discrete Z₃ symmetry, the theoretical-experimental deviations δm/m are $ \mathcal{O} $ \mathcal{O} (10⁻⁵) for all three charged leptons, and the quark pole masses are in very satisfactory overall agreement with the experimental data.     

Supersymmetric quantum mechanics living on topologically non-trivial Riemann surfaces

Supersymmetric quantum mechanics is constructed in a new non-Hermitian representation. Firstly, the map between the partner operators H ^(±) is chosen antilinear. Secondly, both these components of a super-Hamiltonian $ \mathcal{H} $ \mathcal{H} are defined along certain topologically non-trivial complex curves r ^(±)(x) which spread over several Riemann sheets of the wave function. The non-uniqueness of our choice of the map $ \mathcal{T} $ \mathcal{T} between ‘tobogganic’ partner curves r ⁽⁺⁾(x) and r ⁽⁻⁾(x) is emphasized.     

A Categorification of Quantum \widehat{sl_2}

In this paper, we categorify the algebraU_q(\widehat{sl_2}) with the same approach as in [A. Lauda, Adv. Math. (2010), arXiv:math.QA/0803.3652;
M. Khovanov, Comm. Algebra11 (2001) 5033]. The algebra \dot{U}=\dot{U}_q(\widehat{sl_2}) is obtained fromU_q(\widehat{sl_2}) by adjoining a collection of orthogonal idempotents 1_λ,λ \in P, in which P is the weight lattice ofU_q(\widehat{sl_2}). Under such construction the algebraU is decomposed into a direct sum \bigoplus_{\lambda\in P} 1_{\lambda'}{U} 1_λ. We set the collection of λ\in P as the objects of the categoryU, 1-morphisms fromλ toλ' are given by 1_λ' }k U1_λ, and 2-morphisms are constructed by some semilinear form defined onU. Hence we get a 2-category {\cal U} from the algebraU_q{(\widehat{sl_2})}.     

The property of maximal transcendentality in the N \mathcal{N} = 4 SYM

We show results for the universal anomalous dimension γ_uni(j) of Wilson twist-2 operators in the $ \mathcal{N} $ \mathcal{N} = 4 Supersymmetric Yang-Mills theory in the first three orders of perturbation theory. These expressions are obtained by extracting the most complicated contributions from the corresponding anomalous dimensions in QCD.     

q-Difference Realization of Uq(sl(M|N)) and Its Application to Free Boson Realization of Uq $$(\widehat{{\text{sl}}}(2|1))$$

We present a q-difference realization of the quantum superalgebra U_q(sl(M|N)), which includes Grassmann even and odd coordinates and their derivatives. Based on this result, we obtain a free boson realization of the quantum affine superalgebra U_q of an arbitrary level k.     

Twist deformations of the supersymmetric quantum mechanics

The $ \mathcal{N} $ \mathcal{N} -extended Supersymmetric Quantum Mechanics is deformed via an abelian twist which preserves the super-Hopf algebra structure of its Universal Enveloping Superalgebra. Two constructions are possible. For even $ \mathcal{N} $ \mathcal{N} one can identify the 1D $ \mathcal{N} $ \mathcal{N} -extended superalgebra with the fermionic Heisenberg algebra. Alternatively, supersymmetry generators can be realized as operators belonging to the Universal Enveloping Superalgebra of one bosonic and several fermionic oscillators. The deformed system is described in terms of twisted operators satisfying twist-deformed (anti)commutators. The main differences between an abelian twist defined in terms of fermionic operators and an abelian twist defined in terms of bosonic operators are discussed.     

Isospectrality of conventional and new extended potentials,second-order supersymmetry and role of $$ \mathcal{P}\mathcal{T} $$ symmetry

We develop a systematic approach to construct novel completely solvable rational potentials. Second-order supersymmetric quantum mechanics dictates the latter to be isospectral to some well-studied quantum systems. $ \mathcal{P}\mathcal{T} $ \mathcal{P}\mathcal{T} symmetry may facilitate reconciling our approach to the requirement that the rationally extended potentials be singularity free. Some examples are shown.     

The model-independent analysis indications for spectroscopy of scalar mesons. Proof for the K0* (900)

In a model-independent approach the data on ππ → ππ, K $ \bar K $ \bar K , ηη, ηη′ in the I ^G J ^PC = 0⁺0⁺⁺ channel and on the Kπ scattering in the $ I\left( {J^P } \right) = \frac{1} {2}\left( {0^ + } \right) $ I\left( {J^P } \right) = \frac{1} {2}\left( {0^ + } \right) channel are analyzed jointly for studying the status and QCD nature of the f ₀- and the K*₀-mesons. It is shown that in the 1500-MeV region, there are two states, wide (interpreted as a glueball) and narrow (q $ \bar q $ \bar q ). In the Kπ-scattering data analysis, the proof for the K*₀(900) is given.     

Confinement singularities in two-pion decays of mesons

We consider as an example the two-pion decay of the ρ meson, the ³ S ₁ q $ \bar q $ \bar q state of the constituent quarks—the decay being determined by the transition q $ \bar q $ \bar q → ππ contains information about confinement interactions. One can specify in this decay two types of transitions: (i) the bremsstrahlung radiation of a pion q → q + π (or $ \bar q $ \bar q → $ \bar q $ \bar q + π) with a subsequent fusion q $ \bar q $ \bar q → π, and (ii) the direct transition q $ \bar q $ \bar q → ππ. We demonstrate how in the amplitudes of the corresponding transitions the quark singularities have to disappear, i.e., what is the way the quark confinement at relatively short distances can be realized. We calculate and estimate the contributions of processes with bremsstrahlung radiation of the pion and of the direct transition q $ \bar q $ \bar q → ππ. The estimates demonstrate that the processes involving the direct transition q $ \bar q $ \bar q → ππ are necessary, but they cannot be determined unambiguously by the decay ρ(775) → ππ. We conclude that for the determination of the q $ \bar q $ \bar q → ππ transition more complete data on the resonance decays into the ππ channels are needed than those available at the moment.     

Measurement of the mass and width of the W boson

The mass and width of the W boson are measured using e⁺e^– → W⁺W^– events from the data sample collected by the OPAL experiment at LEP at centre-of-mass energies between 170 GeV and 209 GeV. The mass (m_W) and width (Γ_W) are determined using direct reconstruction of the kinematics of W⁺W^– → and W⁺W^– → events. When combined with previous OPAL measurements using W⁺W^– → events and the dependence on of the WW production cross-section at threshold, the results are determined to be

Anomalous dimensions of the Wilson operators in $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills theory

We present results for the universal anomalous dimension γ _uni(j) of Wilson twist-2 operators in the = 4 supersymmetric Yang-Mills theory in the first four orders of perturbation theory. The text was submitted by the authors in English.     

Maximal possible accretion rates for slim disks

It was proved in the previous work that there must be a maximal possible accretion rate $ \dot M_{max} $ \dot M_{max} for a slim disk. Here we discuss how the value of $ \dot M_{max} $ \dot M_{max} depends on the two fundamental parameters of the disk, namely the mass of the central black hole M and the viscosity parameter α. It is shown that $ \dot M_{max} $ \dot M_{max} increases with decreasing α, but is almost independent of M if $ \dot M_{max} $ \dot M_{max} is measured by the Eddington accretion rate $ \dot M_{Edd} $ \dot M_{Edd} , which is in turn proportional to M.     

New quasi-exactly solvable Hermitian as well as non-Hermitian $$ \mathcal{P}\mathcal{T} $$-invariant potentials

We start with quasi-exactly solvable (QES) Hermitian (and hence real) as well as complex $ \mathcal{P}\mathcal{T} $ \mathcal{P}\mathcal{T} -invariant, double sinh-Gordon potential and show that even after adding perturbation terms, the resulting potentials, in both cases, are still QES potentials. Further, by using anti-isospectral transformations, we obtain Hermitian as well as $ \mathcal{P}\mathcal{T} $ \mathcal{P}\mathcal{T} -invariant complex QES periodic potentials. We study in detail the various properties of the corresponding Bender-Dunne polynomials.     

Level crossings in complex two-dimensional potentials

Two-dimensional $ \mathcal{P}\mathcal{T} $ \mathcal{P}\mathcal{T} -symmetric quantum-mechanical systems with the complex cubic potential V ₁₂ = x ² + y ² + igxy ² and the complex Hénon-Heiles potential V _HH = x ² +y ² +ig(xy ² −x ³/3) are investigated. Using numerical and perturbative methods, energy spectra are obtained to high levels. Although both potentials respect the $ \mathcal{P}\mathcal{T} $ \mathcal{P}\mathcal{T} symmetry, the complex energy eigenvalues appear when level crossing happens between same parity eigenstates.     

Mechanism of the production of the <Emphasis Type="Italic">a</Emphasis><Subscript>0</Subscript>(980) resonance in the γγ → π<Superscript>0</Superscript>η reaction

High-statistics Belle data on the γγ → π⁰η reaction have been analyzed in order to reveal the mechanism of two-photon production and the nature of the a ₀(980) resonance. The solution obtained for the γγ → π⁰η amplitude is in agreement with the predictions of the chiral theory for the πη-scattering length; with the strong coupling of the a ₀(980) resonance with the πη, K $ \bar K $ \bar K , and πη′ channels; and with the key role of the a ₀(980) → (K $ \bar K $ \bar K + π⁰η + π⁰η′) → γγ rescattering mechanisms in the a ₀(980) → γγ decay. This picture is much in favor of the q ² $ \bar q $ \bar q ² nature of a ₀(980) resonance and is consistent with the properties of its partners, σ₀(600) and f ₀(980) resonances, in particular, with those manifested in the γγ → ππ reactions. The important role of vector exchanges in the formation of the nonresonant background in the γγ → π⁰η reaction has been revealed. Preliminary information on the π⁰η → π⁰η reaction has been obtained.