Tree-level contributions to the rare decays , , and in the Standard Model

The tree-level contributions to the rare decays , , and are analyzed and compared to those occurring in , , and . It is shown that these purely long-distance contributions, arising from the exchange of a charged lepton, can be significant in B⁺ decays for an intermediate τ, potentially blurring the distinction between the modes used to extract B⁺→τ⁺ν_τ and those used to probe the genuine short-distance and FCNC transitions. Numerically, the tree-level contributions are found to account for 98%, 12% and 14% of the total , , and rates, respectively.     

Counting BPS operators in SYM

The free field partition function for a generic U(N) gauge theory, where the fundamental fields transform in the adjoint representation, is analysed in terms of symmetric polynomial techniques. It is shown by these means how this is related to the cycle polynomial for the symmetric group and how the large N result may be easily recovered. Higher order corrections for finite N are also discussed in terms of symmetric group characters. For finite N, the partition function involving a single bosonic fundamental field is recovered and explicit counting of multi-trace quarter BPS operators in free super-Yang–Mills discussed, including a general result for large N. The partition function for quarter BPS operators in the chiral ring of super-Yang–Mills is analysed in terms of plane partitions. Asymptotic counting of BPS primary operators with differing R-symmetry charges is discussed in both free super-Yang–Mills and in the chiral ring. Also, general and explicit expressions are derived for SU(2) gauge theory partition functions, when the fundamental fields transform in the adjoint, for free field theory.     

High-power continuous-wave operation of a diode-pumped laser at

The continuous-wave laser properties of an efficient diode-pumped Nd:GdVO₄ crystal operating at formed with a simple plane-concave cavity have been studied. With the incident pump power of 21 W, an output power of 6.9 W was obtained, giving an optical conversion efficiency of 32.8% and a slope efficiency of 35.3%. The laser characterization of two different Nd³⁺-doped concentration of Nd:GdVO₄ crystals were studied.     

Fabrication of polyaniline/ heterojunction structure using plasma enhanced polymerization technique

The work reports on the fabrication of a p–n heterojunction structure comprised of polyaniline (PANI) and TiO₂ nanoparticles. PANI was deposited by plasma enhanced polymerization on TiO₂ thin film substrates. The structural and the crystalline properties demonstrated the coherence and the substantive interaction of the plasma polymerized PANI molecules with the TiO₂ nanoparticle thin film. The UV–Vis studies of PANI/TiO₂ thin film supported the internalization of PANI with TiO₂ nanoparticles due to π–π^* transition of the phenyl rings with the lone pair electrons () of the nitrogen atom present in the PANI molecules. The I–V characteristics of the PANI/TiO₂ heterojunction structure were obtained in the forward and the reverse biased at applied voltage ranging from −1 V to +1 V with a scan rate of 2 mV/s. The proficient current in the PANI/TiO₂ heterojunction structure was attributed to the well penetration of PANI molecules into the pores of the TiO₂ nanoparticle thin film. The I–V characteristics ensured an efficient charge movement at the junction of PANI/TiO₂ interface and thus, behaved as a typical ohmic system.     

Multiplication for solutions of the equation

Linear first-order systems of partial differential equations (PDEs) of the form f=Mg, where M is a constant matrix, are studied on vector spaces over the fields of real and complex numbers. The Cauchy–Riemann equations belong to this class. We introduce on the solution space a bilinear *-multiplication, playing the role of a nonlinear superposition principle, that allows for algebraic construction of new solutions from known solutions. The gradient equation f=Mg is a simple special case of a large class of systems of PDEs, admitting a *-multiplication of solutions. We prove that any gradient equation has the exceptional property that the general analytic solution can be expressed as *-power series of certain simple solutions.     

First-principles calculations on elasticity of under pressure

First-principles calculations of the crystal structure and the elastic properties of OsN₂ have been carried out with the plane-wave pseudopotential density functional theory method. The calculated values are in very good agreement with experimental data as well as with some of the existing model calculations. The dependence of the elastic constants c_ij, the aggregate elastic moduli (B,G,E), Poisson’s ratio, and the elastic anisotropy on pressure has been investigated. Moreover, the variation of the Debye temperature and the compressional and shear elastic wave velocities with pressure P up to 60 GPa at 0 K have been investigated for the first time.     

Some observations related to intermittency and multifractality in Si and C-nucleus collisions at

An attempt is made to study the existence of dynamical fluctuations of relativistic particles using the methods of modified multifractal moments, G_q, and scaled factorial moments, F_q, in terms of new scaled variable X(η) suggested by Bialas and Gazdzicki. For this purpose analyses of experimental and UrQMD data involving interactions of ²⁸Si and ¹²C nuclei at with nuclear emulsion are used. The variation of lnG_q and lnF_q with lnM in pseudorapidity (η) phase space reveals power law behaviour. The values of slopes, τ_q and _q determined from the analyses of G_q and F_q moments are discussed. The generalized fractal dimensions, D_q, determined from the above methods are found to decrease with the order of the moments, q, indicating multifractality in multiparticle production. It is also observed that the spectral function f(α_q) for heavier projectile is much broader than for lighter beam due to larger number of participating nucleons present in heavier projectile.     

superconformal Newton–Hooke algebra and many-body mechanics

A representation of the conformal Newton–Hooke algebra on a phase space of n particles in arbitrary dimension which interact with one another via a generic conformal potential and experience a universal cosmological repulsion or attraction is constructed. The minimal superconformal extension of the Newton–Hooke algebra and its dynamical realization in many-body mechanics are studied.     

Anomalous dimension with wrapping at four loops in SYM

In this paper we give all the details of the calculation that we presented in our previous paper [F. Fiamberti, A. Santambrogio, C. Sieg, D. Zanon, Wrapping at four loops in SYM, arXiv: 0712.3522], concerning the four-loop anomalous dimension of the Konishi descendant tr(ZZ−ZZ) in the SU(2) sector of the planar SYM theory. We explicitly consider all the wrapping diagrams that we compute using an superspace approach and Gegenbauer polynomial x-space techniques.     

Islanding mechanism and band edges in InAs/GaAs nanostructures

Within the continuum elasticity theory, we investigate the substrate orientation effects on the Stranski–Krastanov (SK) growth mode and the band edges in InAs/GaAs nanostructures. Attending to the first part of the study, we estimate the transition thickness and the accumulated stress for substrate orientations (1 1 3) and (1 1 5) and we compare with the values obtained previously in InAs/GaAs (0 0 1) nanostructures. Assuming a coherent behavior at the substrate/film interface in the investigated substrate orientations, we consider a sigmoidal-type function for the dependence of the lattice parameter on the height. To evaluate the transition thickness, a minimization of the total free energy density with the slope is made. Similar to the orientation (0 0 1), in (1 1 3) and (1 1 5)-oriented substrates, two different stability regimes for the total free-energy density as well as for the accumulated stress are obtained. These regimes are directly related to the two stages of the SK growth mode. Although the relief strain mechanisms seem similar in all orientations, a delay in the 2D–3D phase transition is induced for high Miller indexes of the substrate. The non-rigid substrate approximation applied in InAs/GaAs nanostructures yields successful results for the transition thicknesses; the fraction of strained substrate being greater in InAs/GaAs (1 1 3). On the other hand, within our model, quantum dots formation is predicted for InAs/GaAs (1 1 1) heterostructures. Attending to the second, we find for all substrate orientations investigated, the strain-induced shifts lower the energies of the conduction band edges, while they raise the energies of the heavy- and light-holes band edges. In addition, the energy shifts are less significant for orientation (1 1 3), where the compressive stresses are smaller.     

Existence of different intermediate Hamiltonians in type A -fold supersymmetry

Type A -fold supercharge admits a one-parameter family of factorizations into product of first-order linear differential operators due to an underlying symmetry. As a consequence, a type A -fold supersymmetric system can have different intermediate Hamiltonians corresponding to different factorizations. We derive the necessary and sufficient conditions for the latter system to possess intermediate Hamiltonians for the case. We then show that whenever it has (at least) one intermediate Hamiltonian, it can admit second-order parasupersymmetry and a generalized 2-fold superalgebra. As an illustration, we construct a set of generalized Pöschl–Teller potentials of this kind.     

: A quantitative measure of NMR signal receiving efficiency

Recognizing that the sensitivity of NMR is influenced by factors such as conductance and dielectric constant of the sample, we propose the receiving efficiency to characterize how efficiently the NMR signal can be observed from a unit transverse magnetization in a sample under optimal probe tuning and matching conditions. Conveniently, the relative receiving efficiency can be defined as the ratio of the NMR signal induced by a unit transverse magnetization in a sample of interest and a reference solution. Based on the reciprocal relationship between excitation and observation in NMR, the relative receiving efficiency can be correlated with the 90° pulse length (τ₉₀). In the special case of perfect probe tuning (impedance matched to 50 Ω), is inversely proportional to τ₉₀. Application of the NMR receiving efficiency in quantitative analysis potentially enables a single external concentration reference for almost any sample, eliminating the need to know its exact chemical composition or detailed electromagnetic properties.     

Infrared safe observables in super Yang–Mills theory

The infrared structure of MHV gluon amplitudes in planar limit for super Yang–Mills theory is considered in the next-to-leading order of PT. Explicit cancellation of the infrared divergencies in properly defined cross-sections is demonstrated. The remaining finite parts for some inclusive differential cross-sections in planar limit are calculated analytically. In general, contrary to the virtual corrections, they do not reveal any simple structure.     

Strong coupling for planar SYM theory: An all-order result

We propose a scheme for determining a generalised scaling function, namely the Sudakov factor in a peculiar double scaling limit for high spin and large twist operators belonging to the sl(2) sector of planar SYM. In particular, we perform explicitly the all-order computation at strong 't Hooft coupling regarding the first (contribution to the) generalised scaling function. Moreover, we compare our asymptotic results with the numerical solutions finding a very good agreement and evaluate numerically the non-asymptotic contributions. Eventually, we illustrate the agreement and prediction on the string side.     

Elliptic quantum group , Hopf algebroid structure and elliptic hypergeometric series

We propose a new realization of the elliptic quantum group equipped with the H-Hopf algebroid structure on the basis of the elliptic algebra . The algebra has a constructive definition in terms of the Drinfeld generators of the quantum affine algebra and a Heisenberg algebra. This yields a systematic construction of both finite- and infinite-dimensional dynamical representations and their parallel structures to . In particular we give a classification theorem of the finite-dimensional irreducible pseudo-highest weight representations stated in terms of an elliptic analogue of the Drinfeld polynomials. We also investigate a structure of the tensor product of two evaluation representations and derive an elliptic analogue of the Clebsch–Gordan coefficients. We show that it is expressed by using the very-well-poised balanced elliptic hypergeometric series .     

Large spin corrections in SYM : Still a linear integral equation

Anomalous dimension and higher conserved charges in the sl(2) sector of SYM for generic spin s and twist L are described by using a novel kind of non-linear integral equation (NLIE). The latter can be derived under typical situations of the SYM sectors, i.e. when the scattering need not depend on the difference of the rapidities and these, in their turn, may also lie on a bounded range. Here the non-linear (finite range) integral terms, appearing in the NLIE and in the dimension formula, go to zero as s→∞. Therefore they can be neglected at least up to the O(s⁰) order, thus implying a linear integral equation (LIE) and a linear dimension/charge formula respectively, likewise the ‘thermodynamic’ (i.e. infinite spin) case. Importantly, these non-linear terms go faster than any inverse logarithm power (lns)⁻ⁿ, n>0, thus extending the linearity validity.