Narrow Results

Taking into account the different forms of the Coulomb-hadron interference phase and the possible spin-flip contribution the new analysis of the experimental data of the proton–antiproton elastic scattering at 3.8<p_L<6.0 GeV/c and small momentum transfer is carried out. It is shown that the size of the spin-flip amplitude can be determined from the form of the differential cross-sections at small-t, and the deviation of ρ(s, t) obtained from the examined experimental data of the scattering from the analysis¹, based on the dispersion relations, is conserved in all examined assumptions. The analysis of the proton–proton elastic scattering at 9<p_L<70 GeV/c also shows the impact of the examined effects on the form of the differential cross-sections.

In this paper, we examine, in the ’t Hooft renormalization scheme, the analytic running coupling ${\bar{\alpha }}_t(Q^2)$ in QCD, using the two-loop $\beta$-function with positive expansion parameters ${\beta }_0$ and ${\beta }_1$. An exact integral representation is derived for this causal coupling, which is fully expressed in terms of the imaginary part of the Lambert function $W$. This integral form manifestly accounts for the universal value of the infrared limit ${\bar{\alpha }}_t(Q^2=0)=4\pi /{\beta }_0$.

The construction of positronium decay amplitudes is handled through the use of dispersion relations. In this way, emphasis is put on basic QED principles: gauge invariance and soft-photon limits (analyticity).

A firm grounding is given to the factorization approaches, and some ambiguities in the spin and energy structures of the positronium wave function are removed. Nonfactorizable amplitudes are naturally introduced. Their dynamics are described, especially regarding the enforcement of gauge invariance and analyticity through delicate interferences. The important question of the completeness of the present theoretical predictions for the decay rates is then addressed. Indeed, some of those nonfactorizable contributions are unaccounted for by NRQED analyses. However, it is shown that such new contributions are highly suppressed, being of .

Finally, a particular effective form factor formalism is constructed for parapositronium, allowing a thorough analysis of binding energy effects and analyticity implementation.

A simple method to compute QED bound state properties is presented, in which binding energy effects are treated nonperturbatively. It is shown that to take the effects of all ladder Coulomb photon exchanges into account, one can simply perform the derivative of standard QED amplitudes with respect to the external momentum. For example, the derivative of the light-by-light scattering amplitude gives an amplitude for orthopositronium decay to three photons where any number of Coulomb photon exchanges between the e⁺e^- is included.

Various applications are presented. From them, it is shown that binding energy must be treated nonperturbatively in order to preserve the analyticity of positronium decay amplitudes.

Interesting perspectives for quarkonium physics are briefly sketched.

A new model for the QCD analytic running coupling, which incorporates the effects due to the π meson mass, is proposed. The properties of this invariant charge in spacelike and timelike regions are examined. Its main distinctive features are a finite infrared limiting value, which depends on the pion mass, and the "plateau–like" behavior in the deep infrared domain of the timelike region.

We give a brief review of the theoretical description of low energy pion-pion scattering by the combined use of Chiral Perturbation Theory and Roy equations, an update of the Regge parametrization of ππ cross sections at high energies, and a short discussion of the scalar radius of the pion.

The standard model of strong interactions invokes the quantum chromodynamics (QCD) of quarks and gluons interacting within a fluid. At sufficiently small length scales, the effective interactions between the color charged particles within the fluid are thought to be weak. Short distance asymptotic freedom provides the perturbation theory basis for comparisons between QCD theory and laboratory high energy scattering experiments. It is here shown that the asymptotically free vacuum has negative dissipation implicit in the color electrical conductivity. Negative dissipation implies an asymptotically free QCD negative temperature excited state amplifier unstable to decay. The qualitative experimental implications of this instability are explored.

We review how the use of recent precise data on kaon decays together with forward dispersion relations (FDR) and Roy's equations allow us to determine the sigma resonance pole position very precisely, by using only experimental input. In addition, we present preliminary results for a modified set of Roy-like equations with only one subtraction, that show a remarkable improvement in the precision around the σ region. We also improve the matching between the parametrizations at low and intermediate energy of the S0 wave, and show that the effect of this on the sigma pole position is negligible.

Once subtracted dispersion relations with imposed crossing symmetry condition are applied in description of the ππ D- and F-wave amplitudes. We show that these equations impose strong constraints on experimental data and model amplitudes.

We study a toy model for an interacting scalar field theory in which the fundamental excitations are confined in the sense of having unphysical, positivity-violating propagators, a fact tracing back to a decomposition of these in propagators with complex conjugate mass poles (the so-called i-particles). Similar two-point functions show up in certain approaches to gluon or quark propagators in Yang–Mills gauge theories. We investigate the spectrum of our model and show that suitable composite operators may be constructed having a well-defined Källén–Lehmann spectral representation, thus allowing for a particle interpretation. These physical excitations would correspond to the "mesons" of the model, the latter being bound states of two unphysical i-particles. The meson mass is explicitly estimated from the pole emerging in a resummed class of diagrams. The main purpose of this paper is thus to explicitly verify how a real mass pole can and does emerge out of constituent i-particles that have complex masses.

To better understand the role of CDD poles in modern field theories, we investigate the effects of CDD poles on the $P_{33}$ channel in $\pi -n$ scattering. We use the non-crossing Chew–Low model for this investigation. The Chew–Low model is the simplest phenomenological model of $\pi -n$ scattering. In the no crossing limit, the $P_{33}$ channel can be easily solved and displays the predominate $\mathrm{\Delta }$ resonance. It has been shown that the denominator function, used in the $N∕D$ method of solution, is a generalized R-function. Our research centers on two investigations. The first is whether one can readily associate a CDD pole with the $\mathrm{\Delta }$ resonance. We find that one cannot, since the CDD pole forces the phases to disagree with the experimental values. The second investigation is into the nature of the redundant solutions one can generate by adding CDD pole to the denominator function. We find that the solutions with the added CDD pole cannot reproduce the phases of the original Chew–Low Model at low energies. Thus, there are no redundant solutions to this model. These results are contrary to what is generally assumed. We question the use of adding a CDD pole to produce resonances and the ideal that adding such poles do not effect the low energy phases.

Form factors are important low-energy quantities and an accurate knowledge of these sheds light on the strong interactions. A variety of methods based on general principles have been developed to use information known in different energy regimes to constrain them in regions where experimental information needs to be tested precisely. Here we review our recent work on the electromagnetic $\omega \pi$ form factor in a model-independent framework known as the method of unitarity bounds, partly motivated by the discrepancies noted recently between the theoretical calculations of the form factor based on dispersion relations and certain experimental data measured from the decay $\omega \to {\pi }^0{\gamma }^{\ast }$. We have applied a modified dispersive formalism, which uses as input the discontinuity of the $\omega \pi$ form factor calculated by unitarity below the $\omega \pi$ threshold and an integral constraint on the square of its modulus above this threshold. The latter constraint was obtained by exploiting unitarity and the positivity of the spectral function of a QCD correlator, computed on the spacelike axis by operator product expansion and perturbative QCD. An alternative constraint is obtained by using data available at higher energies for evaluating an integral of the modulus squared with a suitable weight function. From these conditions we derived upper and lower bounds on the modulus of the $\omega \pi$ form factor in the region below the $\omega \pi$ threshold. The results confirm the existence of a disagreement between dispersion theory and experimental data on the $\omega \pi$ form factor around 0.6 GeV, including those from NA60 published in 2016.

We explain the origin of the mass for the Nambu–Goldstone bosons when there is a chemical potential in the action which explicitly breaks the symmetry. The method is based on the number of independent histories for the interaction of the pair of Nambu–Goldstone bosons with the degenerate vacuum (triangle relations). The analysis suggests that under some circumstances, pairs of massive Nambu–Goldstone bosons can become a single degree of freedom with an effective mass defined by the superposition of the individual masses of each boson. Possible mass oscillations for the Nambu–Goldstone bosons are discussed.

The electric $({\alpha }_{\pi })$ and magnetic $({\beta }_{\pi })$ Compton polarizabilities of both the charged and the neutral pion are of fundamental interest in the low-energy sector of quantum chromodynamics (QCD). Pion polarizabilities affect the shape of the $\gamma \pi \to \gamma \pi$ Compton scattering angular distribution at back scattering angles and $\gamma \gamma \to \pi \pi$ absolute cross sections. Theory derivations are given for the $\gamma \pi \to \gamma \pi$ Compton scattering differential cross section, dispersion relations, and sum rules in terms of the polarizabilities. We review experimental charged and neutral polarizability studies and theoretical predictions. The ${\pi }^0$ polarizabilities were deduced from DESY Crystal Ball $\gamma \gamma \to {\pi }^0{\pi }^0$ data, but with large uncertainties. The charged pion polarizabilities were deduced most recently from (1) radiative pion Primakoff scattering ${\pi }^{-}Z\to {\pi }^{-}Z\gamma$ at CERN COMPASS, (2) two-photon pion pair production $\gamma \gamma \to {\pi }^{+}{\pi }^{-}$ at SLAC Mark II, and (3) radiative pion photoproduction $\gamma p\to \gamma {\pi }^{+}n$ from the proton at MAMI in Mainz. A stringent test of chiral perturbation theory (ChPT) is possible based on comparisons of precision experimental charged pion polarizabilities with ChPT predictions. Only the CERN COMPASS charged pion polarizability measurement has acceptably small uncertainties. Its value ${\alpha }_{{\pi }^{\pm }}-{\beta }_{{\pi }^{\pm }}=(4.0\pm 1.8)\times 10^{-4}{\text{fm}}^3$ agrees well with the two-loop ChPT prediction ${\alpha }_{{\pi }^{\pm }}-{\beta }_{{\pi }^{\pm }}=(5.7\pm 1.0)\times 10^{-4}{\text{fm}}^3$, strengthening the identification of the pion with the Goldstone boson of chiral symmetry breaking in QCD.

We consider a two-parameter family of Drinfeld twists generated from a simple Jordanian twist further twisted by 1-cochains. Twists from this family interpolate between two simple Jordanian twists. Relations between them are constructed and discussed. It is proved that there exists a one-parameter family of twists identical to a simple Jordanian twist. The twisted coalgebra, star product and coordinate realizations of the $\kappa$-Minkowski noncommutative space–time are presented. Real forms of Jordanian deformations are also discussed. The method of similarity transformations is applied to the Poincaré–Weyl Hopf algebra and two types of one-parameter families of dispersion relations are constructed. Mathematically equivalent deformations, that are related to nonlinear changes of symmetry generators and linked with similarity maps, may lead to differences in the description of physical phenomena.

In this study, thermo-elastic and lattice dynamic properties of XMgAl (X = Li, Na) half-Heusler compounds are investigated using density functional theory implemented in WIEN2k and Quantum ESPRESSO codes. Generalized gradient approximation (GGA) as an exchange correlation function has been used in Kohn–Sham equations. Firstly, the structure of these Heusler compounds is optimized and then these optimized parameters are used to find three elastic constants $C_{11}$, $C_{12}$ and $C_{44}$ for $C_{1b}$ type structures. Three elastic constants are then used to determine different elastic moduli like bulk modulus, shear modulus, Young’s modulus and other mechanical parameters like Pugh’s ratio, Poisson’s ratio, anisotropic ratio, sound velocities, Debye temperature and melting temperature. On behalf of these mechanical parameters, the brittle/ductile nature and isotropic/anisotropic behavior of the materials has been studied. Different regions of vibrational modes in the materials are also discussed on behalf of Debye temperature calculations. The vibrational properties of the half-Heusler compounds are computed using Martins–Troullier pseudo potentials implemented in Quantum ESPRESSO. The phonon dispersion curves and phonon density of states in first Brillion zone are obtained and discussed. Reststrahlen band of LiMgAl is found greater than NaMgAl.

Studies of the structure of excited baryons are key factors to the N* program at Jefferson Lab (JLab). Within the first year of data taking with the Hall B CLAS12 detector following the 12 GeV upgrade, a dedicated experiment will aim to extract the N* electrocouplings at high photon virtualities Q². This experiment will allow exploration of the structure of N* resonances at the highest photon virtualities ever achieved, with a kinematic reach up to Q² = 12 GeV². This high-Q² reach will make it possible to probe the excited nucleon structures at distance scales ranging from where effective degrees of freedom, such as constituent quarks, are dominant through the transition to where nearly massless bare-quark degrees of freedom are relevant. In this document, we present a detailed description of the physics that can be addressed through N* structure studies in exclusive meson electroproduction. The discussion includes recent advances in reaction theory for extracting N* electrocouplings from meson electroproduction off protons, along with Quantum Chromodynamics (QCD)-based approaches to the theoretical interpretation of these fundamental quantities. This program will afford access to the dynamics of the nonperturbative strong interaction responsible for resonance formation, and will be crucial in understanding the nature of confinement and dynamical chiral symmetry breaking in baryons, and how excited nucleons emerge from QCD.

In this paper, a thorough analysis is conducted to examine the propagation characteristics of SH surface waves in a layered medium with a nanoscale piezoelectric guiding layer deposited on an isotropic elastic substrate. Specifically, a two-dimensional analytical model is established, within which the effects of strain gradient, electric field gradient, inertia gradient, and flexoelectricity are considered, as well as interfacial imperfections at the interface between the piezoelectric guiding layer and the elastic substrate, which are characterized by spring models. Within the framework of the variational principle, the governing equations, boundary conditions, and continuity conditions at the interface are derived. Based on these equations, the dispersion relations for SH surface waves are deduced and numerically solved for both the electrically open-circuit and electrically short-circuit cases. A comprehensive investigation of the dispersion relations for the fundamental mode of SH surface waves is subsequently provided, with a detailed discussion on the influence of critical factors. The developed theoretical model, encompassing various size effects observed in nano-scale structures, enables a more precise prediction of surface wave propagation behavior, thereby enhancing the design and application of surface acoustic wave devices.

Chemical reactions occur everywhere in both natural and artificial systems. Some of the reactions occur during the flow of a fluid (such a process is referred to as a reactive flow). Given the hazardous nature of some reactive flows, computer simulations (rather than physical experiments) are necessary for ascertaining or enhancing our understanding of such systems. The process of simulation involves mathematical and numerical modeling of the reactive flows. Mathematical models for reactive flow problems are complicated partial differential equations that often lack exact solutions, thus, numerical solutions are employed. Numerical methods must preserve almost all the relevant properties of the problem for accuracy reasons. Dispersion relations are important properties of wave propagation problems and numerical methods that satisfy them are called dispersion preserving methods. Furthermore, stiff transport models are wave propagation problems that cannot be solved efficiently with explicit methods. However, fully implicit methods are computationally expensive. A combination of implicit and explicit methods called implicit–explicit methods is usually employed to efficiently resolve stiffness. An example of problems of interest in this regard are the advection–diffusion–reaction (ADR) models. In this discussion, spectral analysis is performed on two implicit–explicit methods to ascertain their dispersion preserving abilities in order to determine their suitability for simulating general stiff reactive flow problems. The analysis shows that both implicit–explicit methods are dispersion preserving, however, one particular method is more suitable for general wave propagation problems.

A performance index is defined for linear wave dispersion property. The index measures the capability of a water wave model to simulate irregular wave transformation over general topography.

Optimization of this index leads to:

(1) the optimum vertical distribution functions for the nonlinear mild slope equations given by Isobe (1994) for different number of vertical distribution functions,

(2) the optimum values of wave numbers to be used for the fully dispersive nonlinear wave model given by Nadaoka et al. (1994) for different number of vertical distribution functions,

(3) the optimum values of the wave number to be used for the time dependent mild slope equation given by Kirby (1984).

All optimized parameters are given as functions of the dimensionless peak frequency of the energy spectrum. Comparisons among the optimized models are given.