scholarly journals Hadrons as QCD Bound States

2022 ◽  
Vol 258 ◽  
pp. 10002
Author(s):  
Paul Hoyer
Keyword(s):  
Hyperfine Splitting ◽  
Bound States ◽  
Homogeneous Solution ◽  
Bound State ◽  
Perturbative Expansion ◽  
Wave Functions ◽  
Binding Potential ◽  
Fock States ◽  
Confining Potential ◽  
Universal Scale

Bound state perturbation theory is well established for QED atoms. Today the hyperfine splitting of Positronium is known to 𝒪 (α7 log α). Whereas standard expansions of scattering amplitudes start from free states, bound states are expanded around eigenstates of the Hamiltonian including a binding potential. The eigenstate wave functions have all powers of α, requiring a choice in the ordering of the perturbative expansion. Temporal (A0 = 0) gauge permits an expansion starting from valence Fock states, bound by their instantaneous gauge field. This formulation is applicable in any frame and seems promising even for hadrons in QCD. The 𝒪(αs0) confining potential is determined (up to a universal scale) by a homogeneous solution of Gauss’ law.

QUARK MODEL WITH A REGULARIZED BREIT POTENTIAL

2009 ◽  
Vol 18 (03) ◽  
pp. 729-745 ◽  
Author(s):  
JIRIMUTU ◽  
HAI-JUN WANG ◽  
WEI-NING ZHANG ◽  
CHEUK-YIN WONG
Keyword(s):  
Quark Model ◽  
Long Range ◽  
Bound States ◽  
Bound State ◽  
Wave Functions ◽  
Confining Potential

The Breit interaction contains terms that are singular in nature and cannot be used non-perturbatively for quark–antiquark bound state studies. We regularize the Breit interaction by subtraction such that the interaction is not singular at the origin but the intermediate and long-range parts of the interaction remain unchanged. With the regularized quark–antiquark potential and the confining potential, the solution of [Formula: see text] bound states are therefore stable possessing wave functions that can be used for future applications in other study of scattering and reaction problems.

RETARDATION EFFECTS IN COVARIANT THREE-DIMENSIONAL BOUND STATE WAVE FUNCTIONS

2005 ◽  
Vol 14 (06) ◽  
pp. 931-947 ◽  
Author(s):  
F. PILOTTO ◽  
M. DILLIG
Keyword(s):  
Bound States ◽  
Three Dimensional ◽  
Bound State ◽  
Relative Energy ◽  
Wave Functions ◽  
Three Dimensions ◽  
State Wave ◽  
Scalar Diquark ◽  
Bound State Wave Function ◽  
Retardation Effects

We investigate the influence of retardation effects on covariant 3-dimensional wave functions for bound hadrons. Within a quark-(scalar) diquark representation of a baryon, the four-dimensional Bethe–Salpeter equation is solved for a 1-rank separable kernel which simulates Coulombic attraction and confinement. We project the manifestly covariant bound state wave function into three dimensions upon integrating out the non-static energy dependence and compare it with solutions of three-dimensional quasi-potential equations obtained from different kinematical projections on the relative energy variable. We find that for long-range interactions, as characteristic in QCD, retardation effects in bound states are of crucial importance.

THE BETHE–SALPETER EQUATION APPROACH TO BOUND STATE: SCALAR–FERMION CASE AND SCALAR–SCALAR CASE

2007 ◽  
Vol 22 (39) ◽  
pp. 2979-2992 ◽  
Author(s):  
JIAO-KAI CHEN ◽  
ZHENG-XIN TANG ◽  
QING-DONG CHEN
Keyword(s):  
Bound States ◽  
Bound State ◽  
Wave Functions ◽  
Scalar Case ◽  
Equation Approach

The general form of the Bethe–Salpeter wave functions for bound states comprising one scalar constituent and one fermion, or two scalars is presented. Using the reduced Salpeter equation obtained, we can work out the effective nonrelativistic potentials. And one new version of reduced Bethe–Salpeter equation is proposed by extending Gross approximation.

scholarly journals MASS SPECTRUM OF THE JP=1/2- AND 3/2- PENTAQUARK ANTIDECUPLETS IN THE PERTURBATIVE CHIRAL QUARK MODEL

2005 ◽  
Vol 14 (07) ◽  
pp. 995-1015 ◽  
Author(s):  
T. INOUE ◽  
V. E. LYUBOVITSKIJ ◽  
TH. GUTSCHE ◽  
AMAND FAESSLER
Keyword(s):  
Mass Spectrum ◽  
Quark Model ◽  
Single Particle ◽  
Ground State ◽  
Bound State ◽  
Wave Functions ◽  
Chiral Quark Model ◽  
Confining Potential ◽  
Full Mass Spectrum ◽  
Basic Configuration

We study the recently discovered Θ+ baryon in the context of the perturbative chiral quark model. The basic configuration of the Θ+ is a pentaquark bound state, where the single particle wave functions are the ground state solutions of a confining potential. We classify the resulting pentaquark multiplets as the JP=1/2- and 3/2- flavor SU (3) antidecuplet. The full mass spectrum of the multiplets is determined by including the meson and gluon cloud contributions, which induce flavor SU (3) breaking. The resulting 3/2- antidecuplet is about 185 MeV heavier than the 1/2- one, mainly because of the semi-perturbative gluon effects. We assign the observed Θ+ baryon as a member of the 1/2- antidecuplet and discuss in particular its relation to the recent experimental signal for a Ξ-- baryon.

scholarly journals Generalized relativistic wave equations with intrinsic maximum momentum

2014 ◽  
Vol 29 (15) ◽  
pp. 1450080 ◽  
Author(s):  
Chee Leong Ching ◽  
Wei Khim Ng
Keyword(s):  
Bound States ◽  
Wave Equations ◽  
Scalar Potential ◽  
Bound State ◽  
Relativistic Wave Equations ◽  
Wave Functions ◽  
Relativistic Wave ◽  
One Dimensional ◽  
Nonperturbative Effect ◽  
Klein Gordon

We examine the nonperturbative effect of maximum momentum on the relativistic wave equations. In momentum representation, we obtain the exact eigen-energies and wave functions of one-dimensional Klein–Gordon and Dirac equation with linear confining potentials, and the Dirac oscillator. Bound state solutions are only possible when the strength of scalar potential is stronger than vector potential. The energy spectrum of the systems studied is bounded from above, whereby classical characteristics are observed in the uncertainties of position and momentum operators. Also, there is a truncation in the maximum number of bound states that is allowed. Some of these quantum-gravitational features may have future applications.

scholarly journals EXACT-PROPAGATOR INSTANTANEOUS BETHE–SALPETER EQUATION FOR QUARK–ANTIQUARK BOUND STATES

2006 ◽  
Vol 21 (21) ◽  
pp. 1657-1673 ◽  
Author(s):  
ZHI-FENG LI ◽  
WOLFGANG LUCHA ◽  
FRANZ F. SCHÖBERL
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Bound States ◽  
Lattice Gauge Theory ◽  
Bound State ◽  
State Equation ◽  
Wave Functions ◽  
Quantum Field ◽  
Lattice Gauge ◽  
Instantaneous Approximation

Recently an instantaneous approximation to the Bethe–Salpeter formalism for the analysis of bound states in quantum field theory has been proposed which retains, in contrast to the Salpeter equation, as far as possible the exact propagators of the bound-state constituents, extracted nonperturbatively from Dyson–Schwinger equations or lattice gauge theory. The implications of this improvement for the solutions of this bound-state equation, i.e. the spectrum of the mass eigenvalues of its bound states and the corresponding wave functions, when considering the quark propagators arising in quantum chromodynamics are explored.

SEMI-RELATIVISTIC SOLUTIONS OF THE TWO-BODY SPINLESS SALPETER EQUATION UNDER THE WOODS–SAXON POTENTIAL AND THE PEKERIS APPROXIMATION

2013 ◽  
Vol 22 (06) ◽  
pp. 1350039 ◽  
Author(s):  
H. FEIZI ◽  
M. HOSEININAVEH ◽  
A. H. RANJBAR
Keyword(s):  
Particle Physics ◽  
Nuclear Physics ◽  
Bound States ◽  
State Energy ◽  
Bound State ◽  
Wave Functions ◽  
Shape Invariance ◽  
Energy Eigenvalues ◽  
Elementary Particle Physics ◽  
Pekeris Approximation

In this paper, by applying the Pekeris approximation and in the frame of Supersymmetric Quantum Mechanics (SUSYQM), the semi-relativistic solutions of the two-body spinless Salpeter equation are obtained analytically. For an interaction of nuclear form, we obtain the approximate bound-state energy eigenvalues and the corresponding wave functions using the shape invariance concept. The solutions are reported for any l state and some energy eigenvalues are given. These results are useful in elementary-particle physics and nuclear physics to obtain the bound states spectra of relativistic systems such as fermion–antifermion systems.

On noninertial effects inducing a confinement of a neutral particle to a hard-wall confining potential

Open Physics ◽  
2013 ◽  
Vol 11 (11) ◽  
Author(s):  
Knut Bakke
Keyword(s):  
Bound States ◽  
Magnetic Dipole Moment ◽  
Neutral Particle ◽  
Energy Levels ◽  
Bound State ◽  
Field Configuration ◽  
Hard Wall ◽  
Confining Potential ◽  
Noninertial Effects

AbstractIn this contribution, we discuss the confinement of a nonrelativistic spin-half neutral particle to a hard-wall confining potential induced by noninertial effects. We show that the geometry of the manifold plays the role of a hard-wall confining potential and yields bound state solutions. We also consider a neutral particle with a permanent magnetic dipole moment interacting with a field configuration induced by noninertial effects, and discuss the behaviour of the induced fields and obtain energy levels for bound states.

scholarly journals Bound states of Newton’s equivalent finite square well

2018 ◽  
Vol 33 (33) ◽  
pp. 1850195
Author(s):  
Amornthep Tita ◽  
Pichet Vanichchapongjaroen
Keyword(s):  
Energy Spectrum ◽  
Bound States ◽  
Infinite Order ◽  
State Energy ◽  
Order Differential Equation ◽  
Bound State ◽  
Wave Functions ◽  
Bound State Energy ◽  
Standard Quantum ◽  
Square Well

In this paper, a one-parameter family of Newton’s equivalent Hamiltonians (NEH) for finite square well potential is analyzed in order to obtain bound state energy spectrum and wave functions. For a generic potential, each of the NEH is classically equivalent to one another and to the standard Hamiltonian yielding Newton’s equations. Quantum mechanically, however, they are expected to be different from each other. The Schrödinger’s equation coming from each NEH with finite square well potential is an infinite order differential equation. The matching conditions, therefore, demand the wave functions to be infinitely differentiable at the well boundaries. To handle this, we provide a way to consistently truncate these conditions. It turns out as expected that bound state energy spectrum and wave functions are dependent on the parameter [Formula: see text] which is used to characterize different NEH. As [Formula: see text], the energy spectrum coincides with that from the standard quantum finite square well.

scholarly journals Bound states of dtμ, pdμ and t pμ mesomolecules

2019 ◽  
Vol 204 ◽  
pp. 05006 ◽  
Author(s):  
A. V. Eskin ◽  
V. I. Korobov ◽  
A. P. Martynenko ◽  
V. V. Sorokin
Keyword(s):  
Numerical Calculation ◽  
Bound States ◽  
Computer Code ◽  
Bound State ◽  
Wave Functions ◽  
Matrix Elements ◽  
Muonic Molecule ◽  
Gaussian Form ◽  
Stochastic Variational Method ◽  
The Matrix

The energy spectrum of excited bound states of muonic molecules ptμ, pdμ, and dtμ is calculated on the basis of the stochastic variational method. The basis wave functions of the muonic molecule are taken in the Gaussian form. The matrix elements of the Hamiltonian are calculated analytically. For numerical calculation, a computer code was written in the MATLAB system. As a result, the numerical values of bound state energies for excited P-states of muonic molecules ptμ, pdμ and dtμ were obtained.

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