Covariant Light-front Dynamics Research Articles

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.

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

Renormalized Non-Perturbative Scalar and Fermion Models in Covariant Light-Front Dynamics

Within the framework of the covariant formulation of light-front dynamics, we develop a general non-perturbative renormalization scheme, based on the Fock decomposition of the state vector and its truncation. The explicit dependence of our formalism on the orientation of the light front, defined by a light-like four-vector ω, is essential in order to analyze the structure of the counterterms needed to renormalize the theory. We illustrate our framework for scalar and fermion models.

Renormalized nonperturbative fermion model in covariant light-front dynamics

Within the framework of the covariant formulation of light-front dynamics, we develop a nonperturbative renormalization scheme in the fermion model supposing that the composite fermion is a superposition of the ``bare'' fermion and a fermion+boson state. We first assume the constituent boson to be spinless. Then we address the case of gauge bosons in the Feynman and in the light-cone gauges. For all these cases the fermion state vector and the necessary renormalization counterterms are calculated analytically. It turns out that, in light-front dynamics, to restore the rotational invariance, an extra counterterm is needed, having no analogue in the Feynman approach. For gauge bosons the results obtained in the two gauges are compared with each other. In general, the number of spin components of the two-body $(\mathrm{fermion}+\mathrm{boson})$ wave function depends on the gauge. But due to the two-body Fock space truncation, only one nonzero component survives for each gauge. And moreover, the whole solutions for the state vector, found for the Feynman and light-cone gauges, are the same (except for the normalization factor). The counterterms are, however, different.

Stability of two-fermion bound states in the explicitly covariant light-front dynamics

The covariant light-front equations have been solved exactly for a two fermion system with different boson exchange ladder kernels. We present a method to study the cutoff dependence of these equations and to determine whether they need to be regularized or not. Results are presented for scalar and pseudo-scalar exchange. This latter furthermore exhibits some strange particularities which will be discussed.

Two-fermion bound states in the explicitly covariant light-front dynamics

We develop a general method to construct two relativistic fermions bound states with a given $J^{\pi}$, in the framework of the explicitly covariant light-front dynamics.

Relativistic bound states in the Yukawa model

The bound state solutions of two fermions interacting by a scalar exchange are obtained in the framework of the explicitly covariant light-front dynamics. The stability with respect to cutoff of the J$^{\pi}$=$0^+$ and J$^{\pi}$=$1^+$ states is studied. The solutions for J$^{\pi}$=$0^+$ are found to be stable for coupling constants $\alpha={g^2\over4\pi}$ below the critical value $\alpha_c\approx 3.72$ and unstable above it. The asymptotic behavior of the wave functions is found to follow a ${1\over k^{2+\beta}}$ law. The coefficient $\beta$ and the critical coupling constant $\alpha_c$ are calculated from an eigenvalue equation. The binding energies for the J$^{\pi}$=$1^+$ solutions diverge logarithmically with the cutoff for any value of the coupling constant. For a wide range of cutoff, the states with different angular momentum projections are weakly split.

Transition form factors and probabilities of the semileptonic decays of B and D mesons within covariant light-front dynamics

Electroweak form factors for the decays of heavy B and D mesons are considered within the covariant formulation of light-front dynamics. With the aid of this approach, it is possible to separate the physical and unphysical contributions to the form factors. An analytic expression is obtained for gluon corrections to the electroweak vertex of the vector and the vector-axial quark current, and it is shown that, for constructing a quantitative description of available experimental data, it is important to take into account such corrections to the decay widths of heavy hadrons. The effect of contact interaction on the transition form factors is analyzed, and the importance of taking into account contact interaction for 0− → 1− transitions is demonstrated numerically. The elements |Vbc|, |Vbu|, |Vcs|, and |tVcd| of the Cabibbo-Kobayashi-Maskawa matrix are determined from an analysis of the entire body of data on 0− → 0− and 0− → 1− semileptonic decays. Within the experimental errors, the results obtained in this way are intrinsically consistent and comply with world-averaged data.

Explicitly covariant light-front dynamics and relativistic few-body systems

The wave function of a composite system is defined in relativity on a space–time surface. In the explicitly covariant light-front dynamics, reviewed in the present article, the wave functions are defined on the plane ω· x=0, where ω is an arbitrary four-vector with ω 2=0. The standard non-covariant approach is recovered as a particular case for ω=(1, 0, 0,−1) . Using the light-front plane is of crucial importance, while the explicit covariance gives strong advantages emphasized through all the review. The properties of the relativistic few-body wave functions are discussed in detail and are illustrated by examples in a solvable model. The three-dimensional graph technique for the calculation of amplitudes in the covariant light-front perturbation theory is presented. The structure of the electromagnetic amplitudes is studied. We investigate the ambiguities which arise in any approximate light-front calculations, and which lead to a non-physical dependence of the electromagnetic amplitude on the orientation of the light-front plane. The elastic and transition form factors free from these ambiguities are found for spin 0, 1 2 and 1 systems. The formalism is applied to the calculation of the relativistic wave functions of two-nucleon systems (deuteron and scattering state), with particular attention to the role of their new components in the deuteron elastic and electrodisintegration form factors and to their connection with meson exchange currents. Straightforward applications to the pion and nucleon form factors and the ρ−π transition are also made.