Description of Heavy Quark Mass by Lippmann-Schwinger Equation

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

基于广义Lippmann-Schwinger方程的地震波场模拟算法与应用

In the last several decades, due to the fast development of computer, numerical simulation has been an indispensable tool in scientific research. Numerical simulation methods which based on partial difference operators such as Finite Difference Method (FDM) and Finite Element Method (FEM) have been widely used. However, in the realm of seismology and seismic prospecting, one usually meets with geological models which have piece-wise heterogeneous structures as well as volume heterogeneities between layers, the continuity of displacement and stress across the irregular layers and seismic wave scattering induced by the perturbation of the volume usually bring in error when using conventional methods based on difference operators. The method discussed in this paper is based on elastic theory and integral theory. Seismic wave equation in the frequency domain is transformed into a generalized Lippmann-Schwinger equation, in which the seismic wavefield contributed by the background is expressed by the boundary integral equation and the scattering by the volume heterogeneities is considered. Boundary element-volume integral method based on this equation has advantages of Boundary Element Method (BEM), such as reducing one dimension of the model, explicit use the displacement and stress continuity across irregular interfaces, high precision, satisfying the boundary at infinite, etc. Also, this method could accurately simulate the seismic scattering by the volume heterogeneities. In this paper, the concrete Lippmann-Schwinger equation is specifically given according to the real geological models. Also, the complete coefficients of the non-smooth point for the integral equation are introduced. Because Boundary Element-Volume integral equation method uses fundamental solutions which are singular when the source point and the field are very close，both in the two dimensional and the three dimensional case, the treatment of the singular kernel affects the precision of this method. The method based on integral transform and integration by parts could treat the points on the boundary and inside the domain. It could transform the singular integral into an analytical one both in two dimensional and in three dimensional cases and thus it could eliminate the singularity. In order to analyze the elastic seismic wave scattering due to regional irregular topographies, the analytical solution for problems of this type is discussed and the analytical solution of P waves by multiple canyons is given. For the boundary reflection, the method used here is infinite boundary element absorbing boundary developed by a pervious researcher. The comparison between the analytical solutions and concrete numerical examples validate the efficiency of this method. We thoroughly discussed the sampling frequency in elastic wave simulation and find that, for a general case, three elements per wavelength is sufficient, however, when the problem is too complex, more elements per wavelength are necessary. Also, the seismic response in the frequency domain of the canyons with different types of random heterogeneities is illustrated. We analyzed the model of the random media, the horizontal and vertical correlation length, the standard deviation, and the dimensionless frequency how to affect the seismic wave amplification on the ground, and thus provide a basis for the choice of the parameter of random media during numerical simulation.

Collective Perspective on Advances in Dyson-Schwinger Equation QCD

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Identification of the Mass and Stability Interval of Strong Potential in Heavy Mesons

In this paper, we have calculated the masses of mesons containing t-quark and their spins' coupling coefficients. This was achieved by solving Lippmann-Schwinger equation for the quark-antiquark bound state of heavy mesons in configuration space. Heavy meson masses submitted criteria for the strong nuclear interactive potential between two quarks. We investigated the stability of a few suitable potentials and offered the best of these potentials for heavy mesons.

Study of the (D)over-barN Interaction in a QCD Coulomb Gauge Quark Model

We study the (D) over barN interaction at low energies with a quark model inspired in the QCD Hamiltonian in Coulomb gauge. The model Hamiltonian incorporates a confining Coulomb potential extracted from a self-consistent quasiparticle method for the gluon degrees of freedom, and transverse-gluon hyperfine interaction consistent with a finite gluon propagator in the infrared. Initially a constituent-quark mass function is obtained by solving a gap equation and baryon and meson bound-states are obtained in Fock space using a variational calculation. Next, having obtained the constituent-quark masses and the hadron waves functions, an effective meson-nucleon interaction is derived from a quark-interchange mechanism. This leads to a short range meson-baryon interaction and to describe long-distance physics vector- and scalar-meson exchanges described by effective Lagrangians are incorporated. The derived effective (D) over barN potential is used in a Lippmann-Schwinger equation to obtain phase shifts. The results are compared with a recent similar calculation using the nonrelativistic quark model.

COMPLEX KOHN VARIATIONAL PRINCIPLE FOR 2-NUCLEON BOUND-STATE AND SCATTERING WITH THE TENSOR POTENTIAL

Complex Kohn variational principle is applied to the numerical solution of the fully off-shell Lippmann-Schwinger equation for nucleon-nucleon scattering for various partial waves including the coupled S-3(1), D-3(1), channel. Analytic expressions are obtained for all the integrals in the method for a suitable choice of expansion functions. Calculations with the partial waves S-1(0), P-1(1), D-1(2), and S-3(1)-D-3(1) of the Reid soft core potential show that the method converges faster than other solution schemes not only for the phase shift but also for the off-shell t matrix elements. We also show that it is trivial to modify this variational principle in order to make it suitable for bound-state calculation. The bound-state approach is illustrated for the S-3(1)-D-3(1) channel of the Reid soft-core potential for calculating the deuteron binding, wave function, and the D state asymptotic parameters. (c) 1995 Academic Press, Inc.

Short-distance part of the interaction of D mesons and nucleons

The short-distance part of the low energy interaction of D-mesons and nucleons is investigated in the context of a quark model. The quark model is based on Coulomb gauge QCD. The model contains a confining Coulomb potential and a transverse hyperfine interaction consistent with a finite gluon propagator in the infrared. The basic mechanism for the short-distance interaction between the D-mesons and nucleons is quark interchange. Using Resonating GroupMethod techniques an effective potential for the interaction between nucleons and D mesons can be obtained and used in a Lippmann-Schwinger equation to obtain differential cross-sections and phase shifts.

Heavy-light mesons scattering from nucleons: Quark-gluon and meson exchanges

We investigate the scattering of heavy-light K and D mesons by nucleons at low energies. The short-distance part of the interaction is described by quark-gluon interchange and the longdistance part is described by a one-meson-exchange model that includes the contributions of vector (ρ, ω) and scalar (σ) mesons. The microscopic quark model incorporates a confining Coulomb potential extracted from lattice QCD simulations and a transverse hyperfine interaction consistent with a finite gluon propagator in the infrared. The derived effective meson-nucleon potential is used in a Lippmann-Schwinger equation to obtain s-wave phase shifts. Our final aim is to set up a theoretical framework that can be extended to finite temperatures and baryon densities. © 2010 American Institute of Physics.

Three-Dimensional Low-Momentum Interaction in Two-Body Bound State Calculations

The deuteron binding energy and wave function are calculated by using the recently developed three-dimensional form of low-momentum nucleon-nucleon (NN) interaction. The homogeneous Lippmann-Schwinger equation is solved in momentum space by using the low-momentum two-body interaction, which is constructed from Malfliet-Tjon potential. The results for both, deuteron binding energy and wave function, obtained with low-momentum interaction, are compared with the corresponding results obtained with bare potential. © 2012 Springer-Verlag.

D̄N interaction in a color-confining chiral quark model

We investigate the low-energy elastic D̄N interaction using a quark model that confines color and realizes dynamical chiral symmetry breaking. The model is defined by a microscopic Hamiltonian inspired in the QCD Hamiltonian in Coulomb gauge. Constituent quark masses are obtained by solving a gap equation, and baryon and meson bound-state wave functions are obtained using a variational method. We derive a low-energy meson-nucleon potential from a quark-interchange mechanism whose ingredients are the quark-quark and quark-antiquark interactions and baryon and meson wave functions, all derived from the same microscopic Hamiltonian. The model is supplemented with (σ, ρ, ω, a0) single-meson exchanges to describe the long-range part of the interaction. Cross sections and phase shifts are obtained by iterating the quark-interchange plus meson-exchange potentials in a Lippmann-Schwinger equation. Once coupling constants of long-range scalar σ and a0 meson exchanges are adjusted to describe experimental phase shifts of the K+N and K0N reactions, predictions for cross sections and s-wave phase shifts for the D̄0N and D-N reactions are obtained without introducing new parameters. © 2013 American Physical Society.

Heavy Mesons Spectroscopy

In this paper, Lippmann-Schwinger equation is solved by using Martin and Cornel potentials to calculate bc̄ energy levels. The results for some energy levels which are not observable, such as those of tt̄ in its short half-life are also predicted. Our calculated energy levels are in good agreement with results of other groups. The stability interval for Yukawa-Linear potential is also studied by investigating the spectrum of eigenvalues. © 2013 Springer Science+Business Media New York.

Quebra da simetria de sabor na interação de mésons charmosos com o núcleon

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Dynamics of rotationally resolved multiphoton ionization processes in molecules

This dissertation presents the results of studies of several rotationally- resolved resonance enhanced multiphoton ionization (REMPI) processes in some simple molecular systems. The objective of these studies is to quantitatively identify the underlying dynamics of this highly state-specific process which utilizes the narrow bandwidth radiation of a laser to ionize a molecule by first preparing an excited state via multiphoton absorption and subsequently ionizing that state before it can decay. Coupled with high-resolution photoelectron spectroscopy, REMPI is clearly an important probe of molecular excited states and their photoioniza tion dynamics.

A key feature of our studies is that they are carried out using accurate Hartree-Fock orbitals to describe the photoelectron orbitals of the molecular ions. The use of such photoelectron orbitals is important in rotationally-resolved studies where the angular momentum coupling in the photoelectron orbital plays a significant role in the photoionization dynamics. In these studies the Hartree-Fock molecular molecular photoelectron orbitals are obtained by numerical solution of a Lippmann-Schwinger integral equation.

Studies reported here include investigations of (i) ionic rotational branching ratios and their energy dependence for REMPI via the A^2Σ^+(3sσ) and D^2Σ^+(3pσ)states of NO, (ii) the influence of angular momentum constraints on branching ratios at low photoelectron energies for REMPI via low-J levels of the resonant intermediate state, (iii) the strong dependence of photoelectron angular distributions on final ionic rotational state and on the alignment in REMPI of the A^2Σ^+ state of NO, (iv) vibrational state dependence of ionic rotational branching ratios arising from rapid orbital evolution in resonant states (E'^2Σ^+(3pσ) of CH), (v) the influence of rovibronic interactions on the rotational branching ratios seen in REMPI via the D^2Σ^+(3pσ) state of NO, and (vi) effects of laser intensity on the photoionization dynamics of REMPI.