Light-front Dynamics Research Articles

Neutron Transverse-Momentum Distributions and Polarized 3He within Light-Front Hamiltonian Dynamics

The possibility to extract the quark transverse-momentum distributions in the neutron from semi-inclusive deep inelastic electron scattering off polarized 3He is illustrated through an impulse approximation analysis in the Bjorken limit. The generalization of the analysis at finite momentum transfers in a Poincare' covariant framework is outlined. The definition of the light-front spin-dependent spectral function of a J=1/2 system allows us to show that within the light-front dynamics only three of the six leading twist T-even transverse-momentum distributions are independent.

Quark Transverse Momentum Distributions inside a nucleon : a Light-Front Hamiltonian Dynamics study

Through an impulse approximation analysis of single spin Sivers and Collins asymmetries in the Bjorken limit, the possibility to extract the quark transverse-momentum distributions in the neutron from semi-inclu- sive deep inelastic electron scattering off polarized 3He is illustrated. The analysis is generalized to finite momentum transfers in a light-front Poincare covariant framework, defining the light-front spin-dependent spectral func- tion of a J = 1/2 system. The definition of the light-front spin-dependent spectral function for constituent quarks in the nucleon allows us to show that, within the light-front dynamics, only three of the six leading twist T-even transverse-momentum distributions are independent.

Ab initiononperturbative calculation of physical observables in light-front dynamics: Application to the Yukawa model

We present a coherent and operational strategy to calculate in a nonperturbative way, physical observables in light-front dynamics. This strategy is based on the decomposition of the state vector of any compound system in Fock components, and on the covariant formulation of light-front dynamics, together with the so-called Fock sector dependent renormalization scheme. We apply our approach to the calculation of the electromagnetic form factors of a fermion in the Yukawa model, in the nontrivial three-body Fock space truncation, for rather large values of the coupling constant. We find that once the renormalization conditions are properly taken into account, the form factors do not depend---within our numerical accuracy---on the regularization scale when the latter is much larger than the physical masses. We then extend the Fock space by including antifermion degrees of freedom.

Structure properties of medium and heavy exotic nuclei

Investigations of important characteristics of the structure of nuclei near drip-lines in coordinate and momentum space have been performed. The charge form factors, charge and matter densities and the corresponding rms radii for even-even isotopes of Ni, Kr, and Sn are calculated in the framework of deformed self-consistent mean field Skyrme DDHF+BCS method. The resulting charge radii and neutron skin thicknesses of these nuclei are compared with available experimental data, as well as with other theoretical predictions. The formation of a neutron skin is analyzed in terms of various definitions. Its correlation with the nuclear symmetry energy is studied within the coherent density fluctuation model using the symmetry energy as a function of density within the Brueckner energy-density functional. The nucleon momentum distributions for the same isotopic chains of neutron-rich nuclei are studied in the framework of the same mean-field method, as well as of theoretical correlation methods based on light-front dynamics and local density approximation. The isotopic sensitivities of the calculated neutron and proton momentum distributions are investigated together with the effects of nucleon correlations and deformation of nuclei.

Light-Front Dynamics in Hadron Physics

Light-front dynamics(LFD) plays an important role in the analyses of relativistic few-body systems. As evidenced from the recent studies of generalized parton distributions (GPDs) in hadron physics, a natural framework for a detailed study of hadron structures is LFD due to its direct application in Minkowski space as well as its distinct feature of accounting for the vacuum fluctuations in quantum field theories. In the last few years, however, it has been emphasized that treacherous points such as LF singularities and zero-modes should be taken into account for successful LFD applications to hadron phenomenology. In this paper, we discuss a typical example of the contemporary relativistic hadron physics in which the fundamental issues should be taken into account for the successful application of LFD. In particular, we focus on the kinematic issue of GPDs in deeply virtual Compton scattering (DVCS). Although this fundamental issue has been glossed over in the literature, it must be taken care of for the correct analysis of DVCS data.

The Taylor–Lagrange scheme as a template for symmetry-preserving renormalization procedures

A general regularization/renormalization scheme based on intrinsic properties of quantum fields as operator-valued distributions with adequate test functions is presented. The paracompactness property of the Minkowskian or Euclidean manifolds permits a unique definition of fields through integrals over the manifold based on test functions which are partition of unity (PU). These test functions turn out to provide a direct Lorentz-invariant scheme to the extension procedure of singular distributions and possess the unique property of being equal to their Taylor remainder of any order. When expressed through Lagrange’s formulae, this remainder leads to specific procedures of extension in the UV and IR domains. These results, directly obtainable at the physical dimension D = 4, are found to depend on an arbitrary scale present in the definition of any PU test functions and relevant to the final RG-analysis of physical amplitudes. The method is of general character in that it comprises the well-known symmetry-preserving procedures of Bogoliubov–Parasiuk–Hepp–Zimmermann, Pauli–Villars subtractions at the level of propagators and dispersion relations. Symmetry preservation is indeed verified explicitly in simple QED/QCD gauge-boson contributions and in a covariant light-front dynamics treatment of the Yukawa model.

The pion wave function in covariant light-front dynamics

The structure of the pion wave function in the relativistic constituent quark model is investigated in the explicitly covariant formulation of light-front dynamics. We calculate the two relativistic components of the pion wave function in a simple one-gluon exchange model and investigate various physical observables: decay constant, charge radius, electromagnetic and transition form factors. We discuss the influence of the full relativistic structure of the pion wave function for an overall good description of all these observables, including both low and high momentum scales.

Two-body Current Operators and Deuteron Form Factors Within the Light-Front Hamiltonian Dynamics

The deuteron electromagnetic properties are investigated within the Light-Front Hamiltonian dynamics using one-body and two-body currents. The dynamical nature of the latter is generated within a Yukawa model from an analysis of the Light-Front current that acts on the three-dimensional valence component and fulfills the Ward–Takahashi identity. Preliminary results for the magnetic moment and the probability of the nonvalence component are shown.

Nonperturbative Renormalization in Light-Front Dynamics and Applications

We present a general framework to calculate the properties of relativistic compound systems from the knowledge of an elementary Hamiltonian. Our framework provides a well-controlled nonperturbative calculational scheme which can be systematically improved. The state vector of a physical system is calculated in light-front dynamics. From the general properties of this form of dynamics, the state vector can be further decomposed in well-defined Fock components. In order to control the convergence of this expansion, we advocate the use of the covariant formulation of light-front dynamics. In this formulation, the state vector is projected on an arbitrary light-front plane $\omega \cd x=0$ defined by a light-like four-vector $\omega$. This enables us to control any violation of rotational invariance due to the truncation of the Fock expansion. We then present a general nonperturbative renormalization scheme in order to avoid field-theoretical divergences which may remain uncancelled due to this truncation. This general framework has been applied to a large variety of models. As a starting point, we consider QED for the two-body Fock space truncation and calculate the anomalous magnetic moment of the electron. We show that it coincides, in this approximation, with the well-known Schwinger term. Then we investigate the properties of a purely scalar system in the three-body approximation, where we highlight the role of antiparticle degrees of freedom. As a non-trivial example of our framework, we calculate the structure of a physical fermion in the Yukawa model, for the three-body Fock space truncation (but still without antifermion contributions). We finally show why our approach is also well-suited to describe effective field theories like chiral perturbation theory in the baryonic sector.

Nonperturbative calculation of the anomalous magnetic moment in the Yukawa model within truncated Fock space

Within the covariant formulation of light-front dynamics, we calculate the state vector of a physical fermion in the Yukawa model. The state vector is decomposed in Fock sectors and we consider the first three ones: the single constituent fermion, the constituent fermion coupled to one scalar boson, and the constituent fermion coupled to two scalar bosons. This last three-body sector generates nontrivial and nonperturbative contributions to the state vector, which are calculated numerically. Field-theoretical divergences are regularized using Pauli-Villars fermion and boson fields. Physical observables can be unambiguously deduced using a systematic renormalization scheme we have developed previously. As a first application, we consider the anomalous magnetic moment of the physical fermion.

Taylor-Lagrange renormalization scheme, Pauli-Villars subtraction, and light-front dynamics

We show how the recently proposed Taylor-Lagrange renormalization scheme can lead to extensions of singular distributions which are reminiscent of the Pauli-Villars subtraction. However, at variance with the Pauli-Villars regularization scheme, no infinite mass limit is performed in this scheme. As an illustration of this mechanism, we consider the calculation of the self-energy in second order perturbation theory in the Yukawa model, within the covariant formulation of light-front dynamics. We show in particular how rotational invariance is preserved in this scheme.

GPD Extraction from DVCS in LFD

We discuss the issue of extracting the generalized parton distribution (GPD) from deeply virtual Compton scattering (DVCS). We focus our discussion on the fermion propagator between the two photons in the handbag diagram taking the well-known kinematics frequently used in the light-front dynamics (LFD). We compare the results between the full calculation of the tree level Compton scattering amplitude and the reduced calculation using the GPD formulation. We present the treacherous points in obtaining the agreement between the two results: one from the full calculation of the DVCS and the other from the reduced calculation of the GPD formulation. The utility of our calculation is also discussed.

Non-perturbative approach in truncated Fock space including antifermion

Non-perturbative approach which we develop is based on representation of the state vector as a set of Fock components. After truncation to a finite number of components, we come to a coupled-channel problem which is solved non-perturbatively, in light-front dynamics, without using any decomposition in degrees of the coupling constant. Previously [J.-F. Mathiot, V.A. Karmanov and A.V. Smirnov, Proc. of Sci., LC2008:024, 2008; arXiv:0812.1100[hep-ph] .], in Yukawa model, we took into account the Fock sectors corresponding to single fermion, a fermion coupled to one boson, and a fermion coupled to two bosons. Now we extend the Fock space and incorporate also the fermion-antifermion pair, i.e., the Fock sector with two fermions and one antifermion. An appropriate non-perturbative renormalization procedure is developed.

Taylor-Lagrange regularization scheme and light-front dynamics

The recently proposed renormalization scheme based on the definition of field operators as operator valued distributions acting on specific test functions is shown to be very convenient in explicit calculations of physical observables within the framework of light-front dynamics. We first recall the main properties of this procedure based on identities relating the test functions to their Taylor remainder of any order expressed in terms of Lagrange's formulae, hence the name given to this scheme. We thus show how it naturally applies to the calculation of state vectors of physical systems in the covariant formulation of light-front dynamics. As an example, we consider the case of the Yukawa model in the simple two-body Fock state truncation.

Taylor-Lagrange renormalization scheme: Application to light-front dynamics

The recently proposed renormalization scheme based on the definition of field operators as operator valued distributions acting on specific test functions is shown to be very convenient in explicit calculations of physical observables within the framework of light-front dynamics. We first recall the main properties of this procedure based on identities relating the test functions to their Taylor remainder of any order expressed in terms of Lagrange's formulas, hence the name given to this scheme. We thus show how it naturally applies to the calculation of state vectors of physical systems in the covariant formulation of light-front dynamics. As an example, we consider the case of the Yukawa model in the simple two-body Fock state truncation.

Momentum distributions in medium and heavy exotic nuclei

We study nucleon momentum distributions of even-even isotopes of Ni, Kr, and Sn in the framework of deformed self-consistent mean-field Skyrme HF+BCS method, as well as of theoretical correlation methods based on light-front dynamics and local density approximation. The isotopic sensitivities of the calculated neutron and proton momentum distributions are investigated together with the effects of pairing and nucleon-nucleon correlations. The role of deformation on the momentum distributions in even-even Kr isotopes is discussed. For comparison, the results for the momentum distribution in nuclear matter are also presented.

Equivalence of pion loops in equal-time and light-front dynamics

We demonstrate the equivalence of the light-front and equal-time formulations of pionic corrections to nucleon properties. As a specific example, we consider the self-energy $\ensuremath{\Sigma}$ of a nucleon dressed by pion loops, for both pseudovector and pseudoscalar $\ensuremath{\pi}NN$ couplings. We derive the leading and next-to-leading nonanalytic behavior of $\ensuremath{\Sigma}$ on the light front, and show explicitly their equivalence in the rest frame and infinite momentum frame in equal-time quantization, as well as in a manifestly covariant formulation.

Manifestation of Three-Body Forces in Three-Body Bethe–Salpeter and Light-Front Equations

Bethe-Salpeter and light-front bound state equations for three scalar particles interacting by scalar exchange-bosons are solved in ladder truncation. In contrast to two-body systems, the three-body binding energies obtained in these two approaches differ significantly from each other: the ladder kernel in light-front dynamics underbinds by approximately a factor of two compared to the ladder Bethe-Salpeter equation. By taking into account three-body forces in the light-front approach, generated by two exchange-bosons in flight, we find that most of this difference disappears; for small exchange masses, the obtained binding energies coincide with each other.

Scalar mesonf0(980)in heavy-meson decays

A phenomenological analysis of the scalar meson f{sub 0}(980) is performed that relies on the quasi-two-body decays D and D{sub s} {yields} f{sub 0}(980)P, with P = {pi}, K. The two-body branching ratios are deduced from experimental data on D or D{sub s} {yields} {pi}{pi}{pi}, K{sup -} K{pi} and from the f{sub 0}(980) {yields} {pi}{sup +}{pi}{sup -} and f{sub 0}(980) {yields} K{sup +}K{sup -} branching fractions. Within a covariant quark model, the scalar form factors for the transitions D and D{sub s} {yields} f{sub 0}(980) are computed. The weak D decay amplitudes, in which these form factors enter, are obtained in the naive factorization approach assuming a q{bar q} state for the scalar and pseudoscalar mesons. They allow to extract information on the f{sub 0}(980) wave function in terms of u{bar u}, d{bar d}, and s{bar s} pairs as well as on the mixing angle between the strange and nonstrange components. The weak transition form factors are modeled by the one-loop triangular diagram using two different relativistic approaches: covariant light-front dynamics and dispersion relations. We use the information found on the f{sub 0}(980) structure to evaluate the scalar and vector form factors in the transitions D and D{sub s} {yields}more » f{sub 0}(980), as well as to make predictions for B and B{sub s} {yields} f{sub 0}(980), for the entire kinematically allowed momentum range of q{sup 2}.« less

Recent Progress in Application of Light-Front Dynamics to HadronPhysics

Recent Progress in Application of Light-Front Dynamics to HadronPhysics