Distinctive signatures for new particles in e+ e− annihilation and z-decay

New particles and new interactions reveal themselves most clearly where standard model contributions are negligibly small. A prominent example with this advantage is the one-lepton inclusive longitudinal structure function (W_L) in e⁺ e^? annihilation and Z-decay. We discuss general features of this approach and present structure functions for two types of new particles (heavy charged fermion, e.g. new sequential lepton or top quark; and supersymmetric scalar lepton, i.e. slepton), along with the (small) standard model “background”. The x-dependence of W_L provides a distinct signature of the identity of the new particle. Extensions of this approach are discussed.     

Projection of Wilson coefficients from deep inelastic leptoproduction data

We show in detail how the techniques of Nachtmann can be applied to the operator product expansion of two-vector (or vector minus axial vector) current in order to extract Wilson coefficients from the deep inelastic leptoproduction data. Included are new results for the G₁ and G₂ (spin dependent) and W₃ (parity violating) structure functions.     

Electronic structure and optical response in GaxAl1−xN solid alloys

A new method for the calculation of the electronic band structure for the Ga_xAl_1−xN solid alloys is proposed. We present the solid alloy structure as a superposition of two sublattices with the appropriate weighting factors. Both the ab initio norm-conserving pseudo-potential (PP) and LCAO methods give essential disagreement with the experimental data. Only the appropriate correction of the norm-conserving PP method by the orthogonalized LCAO wave functions essentially stabilizes the convergence procedure. To check the reliability of the proposed method we have carried out experimental investigations of the optical functions for two representatives of the investigated wurtzite solid alloys: Ga_xAl_1−xN (x = 0.85 and 0.65). Calculations were performed as a function of the energy cutoff as well as of the Slater screening parameter α. The optical functions at zero frequency give overestimated values compared with the experimental data. The best agreement with experiment can be achieved by using the orthogonalization procedure between the norm-conserving PP and LCAO wave functions. The latter ones help in understanding the solid alloy structure modulations in the compounds mentioned. The possibility is shown of achieving good agreement between the experimental and theoretical data.     

Time-Reversal symmetry violation and the structure of the superconducting order parameter of PrOs4Sb12

The antisymmetric two-electron wave functions corresponding to the symmetry of Cooper pairs are constructed for the symmetry group T _h of the PrOs₄Sb₁₂ superconductor and its subgroup D _2h . The dependence of the structure of these functions (the presence of point nodes) on the group of the wave vector and the multiplicity is investigated. The theoretical nodal structure obtained for the two-electron wave functions makes it possible to explain the experimentally observed structure of the superconducting order parameter of the PrOs₄Sb₁₂ compound (the presence of two phases with different nodal structures) by the time-reversal symmetry violation.     

Field theoretic approach to unstable critical dynamics: Initial stage renormalization

The formalism of initial stage renormalization is constructed and used to study the spinodal decomposition of time-dependent Ginzburg-Landau models. Scaling relations of correlation functions are derived and new critical exponents describing the effects of initial order parameters and external fields are identified. At early stages, the structure function satisfies the usual dynamic scaling ansatz and exponents for characteristic length scales are nothing but the inverse of the dynamic critical exponent. Critical exponents and the structure function are calculated explicitly to first order in ϵ=d_c−d.     

Anomalous cross section for photon-photon scattering in gauge theories

We consider the deep inelastic structure functions of the photon in an asymptotically free gauge theory. In contrast to the case of a hadronic target, we find that the shortdistance analysis determines the shape and magnitude and not merely the Q² dependence of the structure functions. The structure functions of the free quark theory are renormalized by finite, calculable factors. For example, at x = 0.1, we find that F₂ will, at large Q², exceed the free quark result by a factor 1.751, while for x = 0.5, F₂ is suppressed asymptotically, relative to the free quark theory, by a factor 0.964, and at x = 0.8, by a factor 0.611.     

Baryons in chiral SU(N)—QCD on the light-cone in 1 + 1-dimensions

We demonstrate that using bosonization techniques in 1+1-dimensional QCD in the chiral limit a unique definition of baryons is possible for finiteN _c despite the fact that mesons, baryons and anti-baryons are massless. The definition which is based on the construction of an SU(2)-algebra provides the basis for a new approach to investigate hadronic properties in the strong coupling limit. It is used to study the Fock-state decomposition and structure functions of baryons for various finite values ofN _c . The results are discussed in comparison to similar calculations based on discretized lightcone quantization.     

QCD analysis of structure functions in terms of Jacobi polynomials

A new method of QCD-analysis of singlet and nonsinglet structure functions based on their expansion in orthogonal Jacobi polynomials is proposed. An accuracy of the method is studied and its application is demonstrated using the structure functionF ₂(x, Q ²) obtained by the EMC Collaboration from measurements with an iron target.     

Long-wavelength excitations in a Bose gas at zero temperature

The long-wavelength excitations in a simple model of a dilute Bose gas at zero temperature are investigated from a purely microscopic viewpoint. The role of the interaction and the effects of the condensate are emphasized in a dielectric formulation, in which the response functions are expressed in terms of regular functions that do not involve an isolated single-interaction line nor an isolated single-particle line. Local number conservation is incorporated into the formulation by the generalized Ward identities, which are used to express the regular functions involving the density in terms of regular functions involving the longitudinal current. A perturbation expansion is then developed for the regular functions, producing to a given order in the perturbation expansion an elementary excitation spectrum without a gap and simultaneously response functions that obey local number conservation and related sum rules.Explicit results to the first order beyond the Bogoliubov approximation in a simple one-parameter model are obtained for the elementary excitation spectrum ω_k, the dynamic structure function $\text{S}$(k, ω), the associated structure function $\text{S}$_m(k), and the one-particle spectral function $\text{A}$(k, ω), as functions of the wavevector k and frequency ω. These results display the sharing of the gapless spectrum ω_k by the various response functions and are used to confirm that the sum rules of interest are satisfied. It is shown that ω_k and some of the $\text{S}$_m(k) are not analytic functions of k in the long wavelength limit. The dynamic structure function $\text{S}$(k, ω) can be conveniently separated into three parts: a one-phonon term which exhausts the f sum rule, a backflow term, and a background term. The backflow contribution to the static structure function $\text{S}$₀(k) leads to the breakdown of the one-phonon Feynman relation at order k³. Both $\text{S}$(k, ω) and $\text{A}$(k, ω) display broad backgrounds because of two-phonon excitations. Simple arguments are given to indicate that some of the qualitative features found for various physical quantities in the first-order model calculation might also be found in superfluid helium.     

QCD predictions for the Q2 dependence of quark and gluon fragmentation functions using Altarelli-Parisi type equations

In the leading logarithmic approximation, the fragmentation functions of quarks and gluons are investigated using Altarelli-Parisi type equations. Using a new method to make the Mellin transformation, the equation is solved. Analytic expressions for the fragmentation functions near z = 0 and z = 1 are also given. Finally, numerical results for the fragmentation functions D_q^π, D_q^K are presented for different Q².     

Origin of the Q 2-dependence of the DIS structure functions

We consider in detail Q ²-dependence of the DIS structure functions. Very often this dependence is claimed to be originated by the Q ²-dependence of the QCD coupling. This leads to the small-x asymptotics of the structure functions with Q ²-dependent intercepts. We demonstrate that the DGLAP parametrization α _s = α _s (Q ²) is an approximation valid in the region of large x (where 2pq can be approximated by Q ²) only, providing the factorization scale is also large. Outside this region, the DGLAP parametrization fails, so α _s should be replaced by an effective coupling which is independent of Q ² at small x. As a consequence, intercepts of the structure functions are independent of Q ² . Nevertheless, the small-x asymptotics of the structure functions explicitly depend on Q ² , even when the coupling does not depend on it. We also consider the structure functions at small Q ² and give a comment on power-Q ² corrections to the structure functions at large and small Q ² .     

Spin structure of the nucleon—status and recent results

After the initial discovery of the so-called “spin crisis in the parton model” in the 1980s, a large set of polarization data in deep inelastic lepton-nucleon scattering was collected at labs like SLAC, DESY and CERN. More recently, new high precision data at large x and in the resonance region have come from experiments at Jefferson Lab. These data, in combination with the earlier ones, allow us to study in detail the polarized parton densities, the Q² dependence of various moments of spin structure functions, the duality between deep inelastic and resonance data, and the nucleon structure in the valence quark region. Together with complementary data from HERMES, RHIC and COMPASS, we can put new limits on the flavor decomposition and the gluon contribution to the nucleon spin. In this report, we provide an overview of our present knowledge of the nucleon spin structure and give an outlook on future experiments. We focus in particular on the spin structure functions g₁ and g₂ of the nucleon and their moments.     

Resonances at slow electron collisions with zinc atoms and ions

The optical excitation functions of four spectral lines corresponding to the transitions from the 4¹ D ₂, 5³ S ₁, 4³ D _j, and 6¹ S ₀ levels of atomic Zn were investigated with an electron spectrometer of a new construction. For the first time, elastic scattering of slow electrons from the Zn ions at an angle close to 180° was studied. In the energy range under investigation (0–7 eV), both the optical excitation functions of atomic spectral lines and the differential cross section of elastic scattering manifested the resonant structure caused by the contribution of autoionization states of the atom.     

Conformal field theories and modular invariant partition functions for parafermion field theories

Parafermion conformal field theories with D_2N discrete symmetry are examined in detail. The structure of field space of parafermion field theories is studied with the help of a projection operator G. Characters of the representations of the twist sector of parafermion algebra and projected characters are given. A new class of modular invariant partition functions, therefore conformal field theories, for parafermion theories are found. We argue that the principal theories correspond to the generic critical SOS models of Andrew, Baxter and Forrest.     

The two-dimensional Falicov-Kimball model at finite temperatures: numerical studies

The finite temperature properties of the spinless Falicov-Kimball model are studied in two dimensions using small-cluster exact-diagonalization calculations. The resultant exact solutions are used to examine the f-state occupation (n _f), the specific heat (C) and the density of doubly occupied sites (d) as functions of temperature (τ), f-level energy (E _f) and the interaction strength U. A number of remarkable results are found. (i) In all cases nf and d are smooth functions of τ and E _f. No discontinuous transitions occur at finite temperatures. (ii) The specific-heat curves exhibit a broad single-peak structure of Shottky form (‖E _f‖ large), as well as a two-peak structure consisting of a sharp peak of Ising type followed by a broad peak of Shottky type (‖E _f‖ small). (iii) The specific-heat coefficient is extremely enhanced at low temperatures for some values of E _f. (iv) Depending on a range of parameters used, the system exhibits intermediate-valence behavior as well as some features of heavy-fermion behavior. The results are independent of the size of clusters for a wide range of parameters and can be used to interpret much of the experimental data of rare-earth compounds. Finally, the f-electron density-density correlation functions are calculated and the U-dependence of the critical temperature is discussed.     

Higher order QCD contributions to electron structure functions

We study deep inelastice ⁺ e ^? scattering with untagged throughgoing target electrons. The corresponding electron structure functions are not trivially related to photon structure functions. Both can be calculated in QCD perturbation theory but the first ones can be measured more easily. In studying next-to-leading log contributions to electron structure functions we find that the leading logQ ² approximation completely fails at present energies. This is due to different scales λ andm _e . A modified leading-log approximation is introduced. Higher order corrections to this approximation are small away fromx=0 or 1.     

Total Positivity Properties of Generalized Hypergeometric Functions of Matrix Argument

In multivariate statistical analysis, several authors have studied the total positivity properties of the generalized (₀ F ₁) hypergeometric function of two real symmetric matrix arguments. In this paper, we make use of zonal polynomial expansions to obtain a new proof of a result that these ₀ F ₁functions fail to satisfy certain pairwise total positivity properties; this proof extends both to arbitrary generalized ( _r F _s ) functions of two matrix arguments and to the generalized hypergeometric functions of Hermitian matrix arguments. In the case of the generalized hypergeometric functions of two Hermitian matrix arguments, we prove that these functions satisfy certain modified pairwise TP₂properties; the proofs of these results are based on Sylvester's formula for compound determinants and the condensation formula of C. L. Dodgson [Lewis Carroll] (1866).     

Eigenvalues, eigenfunctions, and surface states in finite periodic systems

Using a simple approach that requires neither the Bloch functions nor the reciprocal lattice, new, compact, and rigorous analytical formulas are derived for an accurate evaluation of resonant energies, resonant states, energy eigenvalues and eigenfunctions of open and bounded n-cell periodic systems with arbitrary 1D potential shapes, provided the single cell transfer matrix is given. These formulas are applied to obtain the energy spectra and wave functions of a number of simple but representative open and bounded superlattices. We solve the fine structure in bands and exhibit unambiguously that the true eigenfunctions do no not fulfill the periodicity property |Ψ_μ,ν (z + l_c)|² = |Ψ_μ,ν (z)|², with l_c the single cell length. We show that the well known surface states and surface energy levels come out naturally. We analyze the surface repulsion effect and calculate exactly the surface energy levels for different potential discontinuities an the ends.