Light-front Formalism Research Articles

Electroweak properties of the π, K and K*(892) in the three forms of relativistic kinematics

The electromagnetic form factors, charge radii and decay constants of π, K and K*(892) are calculated using the three forms of relativistic kinematics: instant form, point form and (light) front form. Simple representations of the mass operator together with single-quark currents are employed with all the forms. Making use of previously fixed parameters, together with the constituent-quark mass for the strange quark, a reasonable reproduction of the available data for form factors, charge radii and decay constants of π, ρ, K and K*(892) is obtained in front form. With the instant form a similar description, but with a systematic underestimation of the vector meson decay constants is obtained using two different sets of parameters, one for π and ρ and another one for K and K*(892). The point form produces a poor description of the data.

Manifestations of the vector anomaly in covariant and light-front calculations of the anomalous magnetic moment ofW±bosons

In the calculation of the anomalous magnetic moment of ${W}^{\ifmmode\pm\else\textpm\fi{}}$ bosons, we discuss vector anomalies occurring in the fermion loop that spoil the predictive power of the theory. While the previous analyses were limited to using essentially the manifestly covariant dimensional regulation method, we extend the analysis using both the manifestly covariant formulation and the light-front Hamiltonian formulation with several different regularization methods. We find that the zero-mode contribution to the helicity zero-to-zero amplitude for the ${W}^{\ifmmode\pm\else\textpm\fi{}}$ gauge bosons is crucial for the correct light-front (LF) calculations. Further, we confirm that the anomaly-free condition found in the analysis of the axial anomaly can also get rid of the vector anomaly in light-front dynamics (LFD) as well as in the manifestly covariant calculations. Our findings in this work may provide a bottom-up fitness test not only to the LF calculations but also to the theory itself, whether it is any extension of the Standard Model or an effective field theoretic model for composite systems.

Light-front field theory of quark matter at finite temperature in the Nambu–Jona-Lasinio model

We investigate relativistic quark matter at finite temperature and finite chemical potential. Special relativity is realized through the front form that allows for a Hamiltonian formulation of a statistical operator. We use a light-front formulation of a relativistic thermal field theory that includes a finite chemical potential. As an application we use the Nambu–Jona-Lasinio model to investigate the gap equation and chiral restoration. We compare our results to those of the instant form.

Electromagnetic form factors of pion and rho in the three forms of relativistic kinematics

The electromagnetic form factors of the π and the ρ are obtained using the three forms of relativistic kinematics, instant form, point form and (light) front form. Simple representations of the mass operator together with single quark currents are employed with all the forms. The Poincaré covariant current operators are generated by the dynamics from single-quark currents that are covariant under the kinematic subgroup. Front and instant forms allow to reproduce the available data for the pion form factor. On the other hand point form is not able to reproduce qualitatively the experimental data with reasonable values for the wave function parameters. For the ρ electromagnetic form factors, instant and front forms provide a consistent picture. The obtained results do not depend appreciably on the wave function used.

The Stability of the Relativistic Three-Body System and In-Medium Equations

We present a relativistic three-body equation to study the stability of the isolated three-body system and the correlations in a medium of finite temperatures and densities. Relativity is implemented utilizing the light-front form. Using a zero-range force we find the relativistic analog of the Thomas collapse and investigate the possibility that the nucleon exists as a Borromean system. Within a systematic Dyson equation approach we calculate the three-body Mott transition and the critical temperature of the color-superconducting phase.

Light front Hamiltonian formulation of QED and some tree level applications

In the light front formulation of quantum field gauge theories linear infrared singularities are present which must be addressed. In works by Zhang and Harindranath a prescription is given for the treatment of these singularities. They show that the application of this prescription leads to the cancellation of the linear infrared singularities in loop diagrams. In this work we do a second-order perturbative calculation and calculate the cross sections for e+e− → e+e− and give results for eγ → eγ, e+e− → μ+μ−, eμ → eμ applying the prescription to cancel the linear infrared singularity, whenever present. We show that the well-known expressions of the different cross sections for these processes are exactly reproduced.

Stability of Three-Body Bound States on the Light Front

We investigate the stability of the relativistic three-boson system with a zero range force in the light front form. In particular we study the dependence of the system on an invariant cut-off. We discuss the conditions for the relativistic Thomas collapse. Finally, we fix the parameters of the model introducing a scale.

Comparison of Relativistic Bound-State Calculations in Front-Form and Instant-Form Dynamics

Using the Wick-Cutkosky model and an extended version (massive exchange) of it, we have calculated the bound states in a quantum field theoretical approach. In the light-front formalism we have calculated the bound-state mass spectrum and wave functions. Using the Terent'ev transformation we can write down an approximation for the angular dependence of the wave function. After calculating the bound-state spectra we characterized all states found. Similarly, we have calculated the bound-state spectrum and wave functions in the instant-form formalism. We compare the spectra found in both forms of dynamics in the ladder approximation and show that in both forms of dynamics the O(4) symmetry is broken.

Gauge invariant reduction to the light front

The problem of constructing gauge invariant currents in terms of light-front bound-state wave functions is solved by utilizing the gauging of equations method. In particular, we show how to construct perturbative expansions of the electromagnetic current in the light-front formalism such that current conservation is satisfied at each order of the perturbation theory.

Consistent treatment of spin-1 mesons in the light-front quark model

We analyze the matrix element of the electroweak current between $q \qb$ vector meson states in the framework of a covariant extension of the light-front formalism. The light-front matrix element of a one-body current is naturally associated with zero modes, which affect some of the form factors that are necessary to represent the Lorentz structure of the light-front integral. The angular condition contains some information on zero modes, i.e., only if the effect of zero modes is accounted for correctly, is it satisfied. With plausible assumptions we derive from the angular condition several consistency conditions which can be used quite generally to determine the zero mode contribution of form factors. The correctness of this method is tested by the phenomenological success of the derived form factors. We compare the predictions of our formalism with those of the standard light-front approach and with available data. As examples we discuss the magnetic moment of the $\rho$, the coupling constant $g_{D^\ast D \pi}$, and the coupling constants of the pseudoscalar density, $g_\pi$ and $g_K$, which provide a phenomenological link between constituent and current quark masses.

Current in the light-front Bethe-Salpeter formalism. II. Applications

We pursue applications of the light-front reduction of current matrix elements in the Bethe-Salpeter formalism. The normalization of the reduced wave function is derived from the covariant framework and related to non-valence probabilities using familiar Fock space projection operators. Using a simple model, we obtain expressions for generalized parton distributions that are continuous. The non-vanishing of these distributions at the crossover between kinematic regimes (where the plus component of the struck quark's momentum is equal to the plus component of the momentum transfer) is tied to higher Fock components. Moreover continuity holds due to relations between Fock components at vanishing plus momentum. Lastly we apply the light-front reduction to time-like form factors and derive expressions for the generalized distribution amplitudes in this model.

Comparison among Hamiltonian light-front formalisms atq+=0andq+≠0:Spacelike elastic form factors of pseudoscalar and vector mesons

The electromagnetic elastic form factors of pseudoscalar and vector mesons are analyzed for space-like momentum transfers in terms of relativistic quark models based on the Hamiltonian light-front formalism elaborated in different reference frames (q+ 0 and q+ <> 0). As far as the one-body approximation for the electromagnetic current operator is concerned, it is shown that the predictions of the light-front approach at q+=0 should be preferred, particularly in case of light hadrons, because of: i) the relevant role played by the Z-graph at q+ <> 0, and ii) the appropriate elimination of spurious effects, related to the orientation of the null hyperplane where the light-front wave function is defined.

Light-front formulation of the standard model

Light-front (LF) quantization in the light-cone (LC) gauge is used to construct a renormalizable theory of the standard model. The framework derived earlier for QCD is extended to the Glashow-Weinberg-Salam (GWS) model of electroweak interaction theory. The Lorentz condition is automatically satisfied in LF-quantized QCD in the LC gauge for the free massless gauge field. In the GWS model, with the spontaneous symmetry breaking present, we find that the 't Hooft condition accompanies the LC gauge condition corresponding to the massive vector boson. The two transverse polarization vectors for the massive vector boson may be chosen to be the same as found in QCD. The nontransverse and linearly independent third polarization vector is found to be parallel to the gauge direction. The corresponding sum over polarizations in the standard model, indicated by ${K}_{\ensuremath{\mu}\ensuremath{\nu}}(k),$ has several simplifying properties similar to the polarization sum ${D}_{\ensuremath{\mu}\ensuremath{\nu}}(k)$ in QCD. The framework is unitary and ghost free (except for the ghosts at ${k}^{+}=0$ associated with the light-cone gauge prescription). The massive gauge field propagator has well-behaved asymptotic behavior. The interaction Hamiltonian of electroweak theory can be expressed in a form resembling that of covariant theory, plus additional instantaneous interactions which can be treated systematically. The LF formulation also provides a transparent discussion of the Goldstone boson (or electroweak) equivalence theorem, as the illustrations show.

Large-momentum convergence of Hamiltonian bound-state dynamics of effective fermions in quantum field theory

Contributions to the bound-state dynamics of fermions in local quantum field theory from the region of large relative momenta of the constituent particles, are studied and compared in two different approaches. The first approach is conventionally developed in terms of bare fermions, a Tamm-Dancoff truncation on the particle number, and a momentum-space cutoff that requires counterterms in the Fock-space Hamiltonian. The second approach to the same theory deals with bound states of effective fermions, the latter being derived from a suitable renormalization group procedure. An example of two-fermion bound states in Yukawa theory, quantized in the light-front form of dynamics, is discussed in detail. The large-momentum region leads to a buildup of overlapping divergences in the bare Tamm-Dancoff approach, while the effective two-fermion dynamics is little influenced by the large-momentum region. This is illustrated by numerical estimates of the large-momentum contributions for coupling constants on the order of between 0.01 and 1, which is relevant for quarks.

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 vertices; this implies that in the case of good amplitudes the Feynman triangle diagram and the one-body light-front result match exactly. For illustrative purposes our covariant light-front approach is applied to the evaluation of the $\ensuremath{\rho}$-meson elastic form factors.

Return of the EMC effect: Finite nuclei

A light front formalism for deep inelastic lepton scattering from finite nuclei is developed. In particular, the nucleon plus momentum distribution and a finite system analog of the Hugenholtz-van Hove theorem are presented. Using a relativistic mean field model, numerical results for the plus momentum distribution and ratio of bound to free nucleon structure functions for Oxygen, Calcium and Lead are given. We show that we can incorporate light front physics with excellent accuracy while using easily computed equal time wavefunctions. Assuming nucleon structure is not modified in-medium we find that the calculations are not consistent with the binding effect apparent in the data not only in the magnitude of the effect, but in the dependence on the number of nucleons.

Correlations in Hot and Dense Quark Matter

We present a relativistic three-body equation to investigate three-quark clusters in hot and dense quark matter. To derive such an equation we use the Dyson equation approach. The equation systematically includes the Pauli blocking factors as well as the self energy corrections of quarks. Special relativity is realized through the light front form. Presently we use a zero-range force and investigate the Mott transition.

Indispensability of residual gauge fields and extended hamiltonian formalism in light-front quantization of gauge fields

We consider introducing residual gauge degrees of freedom into the conventional formulation of the light-front quantization of gauge field theories. For that purpose we construct the canonical formulation of axial gauge fields of the type nμ Aμ = 0 in auxiliary coordinates: xμ = (xτ,xσ,x1,x2), where xτ = x0 sin φ + x3 cos φ and xσ = x0 cos φ − x3 sin φ. We then show that, irrespective of the quantization surface, and irrespective of the gauge fixing condition, residual gauge fields are indispensable in implementing the Mandelstam-Leibbrandt prescription and in regularizing the infrared divergences which are inherent in the canonical quantization of space-like axial gauge fields. With the residual gauge fields in place, we find that the infrared divergences are regulated with the Mandelstam-Leibbrandt prescription in the light-front formulation obtained as the limit φ→π/4 of the n2 = 0 case. In addition we show that, because an explicit quantization surface dependence does not appear in the n2 = 0 case, the light-front temporal gauge limit φ→π/4−0 agrees with the light-front spatial gauge limit φ→π/4+0 and that the perturbative Hamiltonian in the light-front formulation consists of physical degrees of freedom integrated over the hyperplane xl+ = (x0+x3)/√2 = constant and residual degrees of freedom integrated over the hyperplane xl− = (x0 − x3)/√2 = constant.

Three-quark clusters at finite temperatures and densities

We present a relativistic three-body equation to study correlations in a medium of finite temperatures and densities. This equation is derived within a systematic Dyson equation approach and includes the dominant medium effects due to Pauli blocking and self energy corrections. Relativity is implemented utilizing the light front form. The equation is solved for a zero-range force for parameters close to the confinement-deconfinement transition of QCD. We present correlations between two- and three-particle binding energies and calculate the three-body Mott transition.

INFINITE NUCLEAR MATTER ON THE LIGHT FRONT: A MODERN APPROACH TO BRUECKNER THEORY

Understanding an important class of experiments requires that light-front dynamics and the related light cone variables k+, k⊥ be used. If one uses k+=k0+k3 as a momentum variable the corresponding canonical spatial variable is x-=x0-x3 and the time variable is x0+x3. This is the light front (LF) approach of Dirac. A relativistic light front formulation of nuclear dynamics is developed and applied to treating infinite nuclear matter in a method which includes the correlations of pairs of nucleons. This is light front Brueckner theory.