Related papers: Finite Energy Sum Rules with Legendre Polynomial K…
We derive explicit expressions for the sum rules of the eigenvalues of inhomogeneous strings with arbitrary density and with different boundary conditions. We show that the sum rule of order $N$ may be obtained in terms of a diagrammatic…
Dispersive sum rules constitute long-standing tools for extracting hadron features from QCD. We estimate the systematic uncertainties induced by assuming quark-hadron duality and improve the accuracy of the resulting predictions by…
In a finite volume, resonances and multi-hadron states are identified by discrete energy levels. When comparing the results of lattice QCD calculations to scattering experiments, it is important to have a way of associating the energy…
The up and down quark masses are determined from an optimized QCD Finite Energy Sum Rule (FESR) involving the correlator of axial-vector divergences, to five loop order in Perturbative QCD (PQCD), and including leading non-perturbative QCD…
Energy-dependent sum rules are useful tools in many fields of physics. In nuclear physics, they typically involve an integration of the response function over the nuclear spectrum with a weight function composed of integer powers of the…
With the experimental observation of several credible candidates for multiquark hadrons, the latter states re-entered the focus of interest of theoretical strong-interaction physics. Proper treatment of hadronic bound states by quantum…
A finit periodic $\delta-\delta'$ comb was solved by the help of both classical approach based on a direct solving of a Sr\"{odinger} equation and a quantum wave impedance method. It was demonstrated that the violation of a periodicity…
We consider a simple model of large-Nc QCD defined by a spectrum consisting of an infinite set of equally spaced zero-width vector resonances. This model is an excellent theoretical laboratory for investigating certain approximation schemes…
We obtain function field analogues of recent energy bounds on modular square roots and modular inversions and apply them to bounding some bilinear sums and to some questions regarding smooth and square-free polynomials in residue classes.
We construct QCD sum rules for nonperturbative studies without assuming the quark-hadron duality for the spectral density at low energy on the hadron side. Instead, both resonance and continuum contributions to the spectral density are…
The saturation of QCD chiral sum rules of the Weinberg-type is analyzed using ALEPH and OPAL experimental data on the difference between vector and axial-vector correlators (V-A). The sum rules exhibit poor saturation up to current energies…
We develop a cut finite element method for a second order elliptic coupled bulk-surface model problem. We prove a priori estimates for the energy and $L^2$ norms of the error. Using stabilization terms we show that the resulting algebraic…
Recent developments and selected topics in low-energy QCD are summarized, from chiral effective field theory to systems with strange and charm quarks, from lattice QCD to precision experiments.
We introduce a hybrid method to couple continuous Galerkin finite element methods and high-order finite difference methods in a nonconforming multiblock fashion. The aim is to optimize computational efficiency when complex geometries are…
This work is a study of polynomial compositions having a fixed number of terms. We outline a recursive method to describe these characterizations, give some particular results and discuss the general case. In the final sections, some…
Infinite sets of sum rules involving the excitations of infinite nuclear matter are derived using only completeness, the current algebra implicit in QCD, and relativistic covariance. The sum rules can be used for isospin-asymmetric nuclear…
Studies of quarkonium spectral functions at finite temperature, based on an approach combining QCD sum rules and the maximum entropy method are briefly reviewed. QCD sum rules for heavy quarkonia incorporate finite temperature effects in…
We apply QCD Finite Energy Sum Rules to the scalar-isoscalar current to determine the lightest $u \bar{u} + d \bar{d}$ meson in this channel. We use `pinch-weights' to improve the reliability of the QCD predictions and reduce the…
Uses of QCD sum rules for heavy flavoured hadrons are discussed. "Standard" applications such as the determination of the $b$, $c$ quark masses, the calculation of $f_B$, $f_D$ and of the heavy-to-light form factors are overviewed.…
It is shown how the QCD sum rules can be applied for the investigation of the density dependence of the nucleon parameters. These characteristics can be expressed through the expectation values of QCD operators in nuclear matter. In certain…