1,143 research outputs found
Three-Fermion Bound States on the Light Front
We investigate the stability of the relativistic three-fermion system with a
zero-range force in the light front form. In particular, introducing an
invariant cut-off, we study the dependence of the bound state on the coupling
strength also for cases where the two-fermion system is unbound. The
relativistic Thomas collapse is discussed by solving the fully coupled integral
equation system. Furthermore, we explicitly investigate the ground state mass
of the three-fermion system and compare to previous simplified calculations.Comment: 23 pages, 6 figure
Three different approaches to the same interaction: the Yukawa model in nuclear physics
After a brief discussion of the meaning of the potential in quantum
mechanics, we examine the results of the Yukawa model (scalar meson exchange)
for the nucleon-nucleon interaction in three different dynamical frameworks:
the non-relativistic dynamics of the Schrodinger equation, the relativistic
quantum mechanics of the Bethe-Salpeter and Light-Front equations and the
lattice solution of the Quantum Field Theory, obtained in the quenched
approximation.Comment: 17 pages, 9 figures. Dedicated to Professor Henryk Witala at the
occasion of his 60th birthday. Submitted in Few-Body System
Regularization of fermion self-energy and electromagnetic vertex in Yukawa model within light-front dynamics
In light-front dynamics, the regularization of amplitudes by traditional
cutoffs imposed on the transverse and longitudinal components of particle
momenta corresponds to restricting the integration volume by a non-rotationally
invariant domain. The result depends not only on the size of this domain (i.e.,
on the cutoff values), but also on its orientation determined by the position
of the light-front plane. Explicitly covariant formulation of light front
dynamics allows us to parameterize the latter dependence in a very transparent
form. If we decompose the regularized amplitude in terms of independent
invariant amplitudes, extra (non-physical) terms should appear, with spin
structures which explicitly depend on the orientation of the light front plane.
The number of form factors, i.e., the coefficients of this decomposition,
therefore also increases. The spin-1/2 fermion self-energy is determined by
three scalar functions, instead of the two standard ones, while for the elastic
electromagnetic vertex the number of form factors increases from two to five.
In the present paper we calculate perturbatively all these form factors in the
Yukawa model. Then we compare the results obtained in the two following ways:
(i) by using the light front dynamics graph technique rules directly; (ii) by
integrating the corresponding Feynman amplitudes in terms of the light front
variables. For each of these methods, we use two types of regularization: the
transverse and longitudinal cutoffs, and the Pauli-Villars regularization. In
the latter case, the dependence of amplitudes on the light front plane
orientation vanishes completely provided enough Pauli-Villars subtractions are
made.Comment: 29 pages, 6 figures, to be published in Physical Review
Two-fermion relativistic bound states in Light-Front Dynamics
In the Light-Front Dynamics, the wave function equations and their numerical
solutions, for two fermion bound systems, are presented. Analytical expressions
for the ladder one-boson exchange interaction kernels corresponding to scalar,
pseudoscalar, pseudovector and vector exchanges are given. Different couplings
are analyzed separately and each of them is found to exhibit special features.
The results are compared with the non relativistic solutions.Comment: 40 pages, to be published in Phys. Rev. C, .tar.gz fil
Projecting the Bethe-Salpeter Equation onto the Light-Front and back: A Short Review
The technique of projecting the four-dimensional two-body Bethe-Salpeter
equation onto the three-dimensional Light-Front hypersurface, combined with the
quasi-potential approach, is briefly illustrated, by placing a particular
emphasis on the relation between the projection method and the effective
dynamics of the valence component of the Light-Front wave function. Some
details on how to construct the Fock expansion of both i) the Light-Front
effective interaction and ii) the electromagnetic current operator, satisfying
the proper Ward-Takahashi identity, will be presented, addressing the relevance
of the Fock content in the operators living onto the Light-Front hypersurface.
Finally, the generalization of the formalism to the three-particle case will
be outlined.Comment: 16 pages, macros included. Mini-review to be printed in a regular
issue of Few-Body Systems devoted to the Workshop on "Relativistic
Description of Two- and Three-body Systems in Nuclear Physics" ECT* Trento,
19 - 23 October 200
Three-boson relativistic bound states with zero-range interaction
For the zero-range interaction providing a given mass M_2 of the two-body
bound state, the mass M_3 of the relativistic three-boson state is calculated.
We have found that the three-body system exists only when M_2 is greater than a
critical value M_c approximately 1.43 m (m is the constituent mass). For
M_2=M_c the mass M_3 turns into zero and for M_2<M_c there is no solution with
real value of M_3.Comment: 7 pages, 4 figure
Electromagnetic form factors in the light-front formalism and the Feynman triangle diagram: spin-0 and spin-1 two-fermion systems
The connection between the Feynman triangle diagram and the light-front
formalism for spin-0 and spin-1 two-fermion systems is analyzed. It is shown
that in the limit q+ = 0 the form factors for both spin-0 and spin-1 systems
can be uniquely determined using only the good amplitudes, which are not
affected by spurious effects related to the loss of rotational covariance
present in the light-front formalism. At the same time, the unique feature of
the suppression of the pair creation process is maintained. Therefore, a
physically meaningful one-body approximation, in which all the constituents are
on their mass-shells, can be consistently formulated in the limit q+ = 0.
Moreover, it is shown that the effects of the contact term arising from the
instantaneous propagation of the active constituent can be canceled out from
the triangle diagram by means of an appropriate choice of the off-shell
behavior of the bound state vertexes; this implies that in case of good
amplitudes the Feynman triangle diagram and the one-body light-front result
match exactly. The application of our covariant light-front approach to the
evaluation of the rho-meson elastic form factors is presented.Comment: corrected typos in the reference
Hamiltonian light-front field theory within an AdS/QCD basis
Non-perturbative Hamiltonian light-front quantum field theory presents
opportunities and challenges that bridge particle physics and nuclear physics.
Fundamental theories, such as Quantum Chromodynmamics (QCD) and Quantum
Electrodynamics (QED) offer the promise of great predictive power spanning
phenomena on all scales from the microscopic to cosmic scales, but new tools
that do not rely exclusively on perturbation theory are required to make
connection from one scale to the next. We outline recent theoretical and
computational progress to build these bridges and provide illustrative results
for nuclear structure and quantum field theory. As our framework we choose
light-front gauge and a basis function representation with two-dimensional
harmonic oscillator basis for transverse modes that corresponds with
eigensolutions of the soft-wall AdS/QCD model obtained from light-front
holography.Comment: To appear in the proceedings of Light-Cone 2009: Relativistic
Hadronic and Particle Physics, July 8-13, 2009, Sao Jose dos Campos, Brazi
Light Front Formalism for Composite Systems and Some of Its Applications in Particle and Relativistic Nuclear Physics
Light front formalism for composite systems is presented. Derivation of
equations for bound state and scattering problems are given. Methods of
constructing of elastic form factors and scattering amplitudes of composite
particles are reviewed. Elastic form factors in the impulse approximation are
calculated. Scattering amplitudes for relativistic bound states are
constructed. Some model cases for transition amplitudes are considered. Deep
inelastic form factors (structure functions) are expressed through light front
wave functions. It is shown that taking into account of transverse motion of
partons leads to the violation of Bjorken scaling and structure functions
become square of transverse momentum dependent. Possible explanation of the
EMC-effect is given. Problem of light front relativization of wave functions of
lightest nuclei is considered. Scaling properties of deuteron, and
light front wave functions are checked in a rather wide energy range.Comment: Review paper, Submitted to Phys. Rep., 89 pages, 23 figure
Pair term in the Electromagnetic Current within the Front-Form Dynamics: Spin-0 Case
The frame and scale dependence of the pair-term contribution to the
electromagnetic form factor of a spin-zero composite system of two-fermions is
studied within the Light Front. The form factor is evaluated from the
plus-component of the current in the Breit frame, using for the first time a
nonconstant, symmetric ansatz for the Bethe-Salpeter amplitude. The frame
dependence is analyzed by allowing a nonvanishing plus component of the
momentum transfer, while the dynamical scale is set by the masses of the
constituents and by mass and size of the composite system. A transverse
momentum distribution, associated with the Bethe-Salpeter amplitude, is
introduced which allows to define strongly and weakly relativistic systems. In
particular, for strongly relativistic systems, the pair term vanishes for the
Drell-Yan condition, while is dominant for momentum transfer along the
light-front direction. For a weakly relativistic system, fitted to the deuteron
scale, the pair term is negligible up to momentum transfers of 1(GeV/c). A
comparison with results obtained within the Front-Form Hamiltonian dynamics
with a fixed number of constituents is also presented.Comment: 25 pages + 7 figures; axodraw.sty included. To appear in Nucl. Phys.
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