Light-front Formalism Research Articles

Asymptotic properties of Hulthén model form factors on the light front

We use light-front dynamics to calculate the electromagnetic form-factor for the Hulthen model of the deuteron. For small momentum transfer Q^2 < 5 GeV^2 the relativistic effects are quite small. For Q^2 = 11 GeV^2 there is about a 13% discrepancy between the relativistic and non-relativistic approaches. For asymptotically large momentum transfer, however, the light-front form factor, log Q^2 /Q^4, markedly differs from the non-relativistic version, 1/Q^4. This behavior is also present for any wave function, such as those obtained from realistic potential models, which can be represented as a sum of Yukawa functions. Furthermore, the asymptotic behavior is in disagreement with the Drell-Yan-West relation. We investigate precisely how to determine the asymptotic behavior and confront the problem underlying troublesome form factors on the light front.

Light-Front Realization of Chiral Symmetry Breaking

We discuss a description of chiral symmetry breaking in the light-front (LF) formalism. Based on careful analyses of several models, we give clear answers to the following three fundamental questions: (i) What is the difference between the LF chiral transformation and the ordinary chiral transformation? (ii) How does a gap equation for the chiral condensate emerge? (iii) What is the consequence of the coexistence of a nonzero chiral condensate and the trivial Fock vacuum? The answer to Question (i) is given through a classical analysis of each model. Question (ii) is answered based on our recognition of the importance of characteristic constraints, such as the zero-mode and fermionic constraints. Question (iii) is intimately related to another important problem, reconciliation of the nonzero chiral condensate and the invariance of the vacuum under the LF chiral transformation. This and Question (iii) are understood in terms of the modified chiral transformation laws of the dependent variables. The characteristic ways in which the chiral symmetry breaking is realized are that the chiral charge is no longer conserved and that the transformation of the scalar and pseudoscalar fields is modified. We also discuss other outcomes, such as the light-cone wave function of the pseudoscalar meson in the Nambu-Jona-Lasinio model.

The Kalman-Tran-D'Souza model and the semileptonic decay rates of heavy baryons

We present an investigation of the inclusive semileptonic decay widths of the heavy baryons Λ Q , Σ Q and Ξ Q , ( q = b, c) performed within a relativistic constituent quark model, formulated on the light-front. In a way conceptually similar to the deep-inelastic scattering case, the H Q -baryon inclusive width is expressed as the integral of the free Q-quark partial width multiplied by a bound-state factor related to the Q-quark distribution function in the H Q . The non-perturbative meson structure is described through the quark-model wave functions, constructed via the Hamiltonian light-front formalism using as input the Kalman-Tran-D'Souza equal time wave functions. A link between spectroscopic quark models and the H Q decay physics is obtained in this way. It is shown that the bound-state effects and the Fermi motion of the b-quark remarkably reduce the decay rate with respect to the free-quark result. Our predictions for the BR(Λ c → X sl ν e ) and BR(Λ b → X cl ν e ) decays are in good agreement with existing data.

A field theoretic investigation of spin in QCD

Utilizing the kinematical boost in light-front formalism one can address the issue of relativistic spin operators in an arbitrary reference frame. In the gauge A + = 0, the interaction dependent transverse spin operators can be separated into three parts. In analogy with the helicity sum rule, we propose a transverse spin sum rule. We perform a one loop renormalization of the transverse spin operator and show that the counterterm needed is the same as the linear mass counterterm in the light-front QCD Hamiltonian.

Light-front aspects of chiral symmetry

Spontaneous chiral symmetry breaking and axial anomaly are studied in the light-front formulation. The existence of multiple vacua and a Nambu-Goldstone boson, both related to dynamical fermion zero modes, are demonstrated within a simple sigma model with fermions. The Weyl gauge formulation and a consistent gauge invariant point-splitting regularization, which includes the light front time, are crucial for obtaining the anomaly in the massive Schwinger model and QED(3+1).

SU(6) breaking effects in the nucleon elastic electromagnetic form factors

The effects of SU(6) breaking on the nucleon elastic form factors are investigated within the constituent quark model formulated on the light-front. It is shown that the kinematical SU(6) breaking caused by the Melosh rotations of the quark spins as well as the dynamical SU(6) breaking due to the mixed-symmetry component generated in the nucleon wave function by the spin-dependent terms of the quark-quark interaction, can affect both GEn(Q**2) and GMp(Q**2)/GMn(Q**2). The calculated GEn(Q**2) is found to be qualitatively consistent with existing data. while the calculations of GM(Q**2) based on the plus component of the current are found to be plagued by spurious effects related to the loss of the rotational covariance in the light-front formalism. These unwanted effects can be avoided by considering the transverse y-component of the current. In this way our light-front predictions are found to be consistent with the data on both GEn(Q**2) and GMp(Q**2)/GMn(Q**2). Finally, it is shown that a suppression of the ratio GEp(Q**2)/GMp(Q**2) with respect to the dipole-fit prediction can be expected in the constituent quark model provided the relativistic effects generated by the Melosh rotations of the constituent spins are taken into account.

Much ado about nothing: Vacuum and renormalization in the light-front framework

In the light-front (LF) formulation of quantum field theory, nontrivial vacuum structure can appear only in zero-modes. Integrating out zero-mode degrees of freedom leads to an effective LF Hamiltonian, which acts only on nonzero-modes and thus has a trivial vacuum, but is nevertheless equivalent to the Hamiltonian in normal coordinates (with nontrivial vacuum) since the nontrivial vacuum structure enters through the coefficients of the eff. LF Hamiltonian.

Dynamical chiral symmetry breaking on the light front: DLCQ approach

Dynamical chiral symmetry breaking in the DLCQ method is investigated in detail using a chiral Yukawa model closely related to the Nambu-Jona-Lasinio model. By classically solving three constraints characteristic of the light-front formalism, we show that the chiral transformation defined on the light front is equivalent to the usual one when bare mass is absent. A quantum analysis demonstrates that a nonperturbative mean-field solution to the ``zero-mode constraint'' for a scalar boson (sigma) can develop a nonzero condensate while a perturbative solution cannot. This description is due to our identification of the ``zero-mode constraint'' with the gap equation. The mean-field calculation clarifies unusual chiral transformation properties of fermionic field, which resolves a seemingly inconsistency between triviality of the null-plane chiral charge Q_5|0>=0 and nonzero condensate. We also calculate masses of scalar and pseudoscalar bosons for both symmetric and broken phases, and eventually derive the PCAC relation and nonconservation of Q_5 in the broken phase.

Connection between inclusive semileptonic decays of bound and free heavy quarks

A relativistic constituent quark model, formulated on the light front, is used to derive a new parton approximation for the inclusive semileptonic decay width of the B meson. A simple connection between the decay rate of a free heavy quark and the one of a heavy quark bound in a meson or in a baryon is established. The main features of the new approach are the treatment of the b quark as an on-mass-shell particle and the inclusion of the effects arising from the b quark transverse motion in the B meson. In a way conceptually similar to the deep-inelastic scattering case, the B meson inclusive width is expressed as the integral of the free b quark partial width multiplied by a bound-state factor related to the b-quark distribution function in the B meson. The nonperturbative meson structure is described through various quark-model wave functions, constructed via the Hamiltonian light front formalism, using as input both relativistic and nonrelativistic potential models. A link between spectroscopic quark models and B-meson decay physics is obtained in this way. Our predictions for the $\stackrel{\ensuremath{\rightarrow}}{B}{X}_{c}l{\ensuremath{\nu}}_{l}$ and $\stackrel{\ensuremath{\rightarrow}}{B}{X}_{u}l{\ensuremath{\nu}}_{l}$ decays are used to extract the CKM parameters $|{V}_{\mathrm{cb}}|$ and $|{V}_{\mathrm{ub}}|$ from available inclusive data. After averaging over the various quark models adopted and including leading-order perturbative QCD corrections, we obtain $|{V}_{\mathrm{cb}}|=(43.0\ifmmode\pm\else\textpm\fi{}{0.7}_{\mathrm{exp}}\ifmmode\pm\else\textpm\fi{}{1.8}_{\mathrm{th}})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ and $|{V}_{\mathrm{ub}}|=(3.83\ifmmode\pm\else\textpm\fi{}{0.48}_{\mathrm{exp}}\ifmmode\pm\else\textpm\fi{}{0.14}_{\mathrm{th}})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3},$ implying $|{V}_{\mathrm{ub}}{/V}_{\mathrm{cb}}|=0.089\ifmmode\pm\else\textpm\fi{}{0.011}_{\mathrm{exp}}\ifmmode\pm\else\textpm\fi{}{0.005}_{\mathrm{th}},$ in nice agreement with existing predictions.

Markov-Yukawa transversality on covariant light front: Pion form factor, gauge invariance and Lorentz completion

The Markov-Yukawa Transversality Principle (MYTP) on a 2-body Bethe-Salpeter kernel is formulated on a covariant Null Plane (NP) to reconstruct the 4D BS wave function for 2 fermion quarks in terms of 3D entities that satisfy a 3D BSE. This result is the light-front counterpart of a 3D-4D interlinkage for the 2-body BS wave functions found earlier by imposing MYTP covariantly in the instant frame (termed CIA) of the composite. This formulation yields a 3D BSE which is formally identical to its Instant form, thus fully preserving its spectral results, as well as covariance. Further, the reconstructed 4D vertex functions in the new formulation ensure that 4D quark-loops are now free from ill-defined time-like momentum integrations (which had plagued the earlier instant form vertex functions), while a simple prescription of `Lorentz completion' in the new description yields a manifestly Lorentz-invariant result. This is illustrated for the pion and kaon form factors with full QED gauge-invariance, showing a k −2 behaviour at large k 2, and `correct' slopes at small k 2. This method is compared with the Kadychevsky-Karmanov light-front formalism.

Covariant analysis of the light-front quark model

A manifestly covariant formalism is used as a guide to construct a covariant extension of the light-front quark model. Our analysis demonstrates in detail that covariance necessarily requires the inclusion of zero-mode contributions. The main goal of this paper is to use this technique in order to extend the standard light-front formalism such that all form factors that are necessary to represent the Lorentz structure of a hadronic matrix element can be calculated on the same footing. The form factors that have been calculated in the standard approach are reproduced, except for those that describe transitions that involve vector mesons. The covariant approach permits also the calculation of the scalar form factor for transitions between pseudoscalar mesons, and the form factor ${a}_{\ensuremath{-}}{(q}^{2})$ for transitions between pseudoscalar and vector mesons, which is not possible in the standard light-front formalism. The practical application of the covariant extension of the light-front quark model is successful only if the formulas for form factors are evaluated with standard light-front vertex functions. The latter violate the conditions for strict Lorentz covariance of the formalism. In order to explore the predictive power of this approach, we calculate various properties of pseudoscalar and vector mesons in the u-, d-, s-quark sector. We find good agreement with all available data for electroweak transitions.

Light-front QCD with Wilson fermions on a transverse lattice

In the light-front formulation of field theory, it is possible to write down a chirally invariant mass term. It thus appears as if one could solve the species doubling problem on a light-front quantized transverse lattice in a chirally invariant way. However, upon introducing link fields and after renormalizing, one finds exactly the same LF Hamiltonian as if one had started from the standard Wilson action in the first place. The (light-front) chirally invariant transverse lattice regularization is thus not chirally invariant in the conventional sense. As an application of the Wilson formulation for fermions on a $\perp$ lattice, we calculate spectrum, distribution functions and distribution amplitudes for mesons below $2 GeV$ in a truncated Fock space.

Infinite nuclear matter on the light front: Nucleon-nucleon correlations

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. We start with a hadronic meson-baryon Lagrangian that is consistent with chiral symmetry. This is used to obtain a light front version of a one-boson-exchange nucleon-nucleon potential (OBEP). The accuracy of our description of the nucleon-nucleon (NN) data is good, and similar to that of other relativistic OBEP models. We derive, within the light front formalism, the Hartree-Fock and Brueckner Hartree-Fock equations. Applying our light front OBEP, the nuclear matter saturation properties are reasonably well reproduced. We obtain a value of the compressibility, 180 MeV, that is smaller than that of alternative relativistic approaches to nuclear matter in which the compressibility usually comes out too large. Because the derivation starts from a meson-baryon Lagrangian, we are able to show that replacing the meson degrees of freedom by a NN interaction is a consistent approximation, and the formalism allows one to calculate corrections to this approximation in a well-organized manner. The simplicity of the vacuum in our light front approach is an important feature in allowing the derivations to proceed. The mesonic Fock space components of the nuclear wave function are obtained also, and aspects of the meson and nucleon plus-momentum distribution functions are computed. We find that there are about 0.05 excess pions per nucleon.

Light-front formalism in the quasipotential approach in quantum field theory

A review of the light-front formulation of the quasipotential approach in quantum field theory for bound-state and scattering problems is given.

Light front theory of nuclear matter

A relativistic light front formulation of nuclear dynamics is applied to infinite nuclear matter. A hadronic meson-baryon Lagrangian, consistent with chiral symmetry, leads to a nuclear eigenvalue problem which is solved, including nucleon-nucleon NN correlations, in the one-boson-exchange approximation for the NN potential. The nuclear matter saturation properties are reasonably well reproduced, with a compression modulus of 180 MeV. We find that there are ≈0.05 excess pions per nucleon.

Decoupling of zero modes and covariance in the light-front formulation of supersymmetric theories

We show under suitable assumptions that zero-modes decouple from the dynamics of non-zero modes in the light-front formulation of some supersymmetric field theories. The implications for Lorentz invariance are discussed.

Consistent perturbative light-front formulation of quantum electrodynamics

A new light-front formulation of Q.E.D. is developed, within the framework of standard perturbation theory, in which $x^+$ plays the role of the evolution parameter and the gauge choice is $A_+=0$ (light-front "temporal" gauge). It is shown that this formulation leads to the Mandelstam-Leibbrandt causal prescription for the non-covariant singularities in the photon propagator. Furthermore, it is proved that the dimensionally regularized one loop off-shell amplitudes exactly coincide with the correct ones, as computed within the standard approach using ordinary space-time coordinates.

Nucleon generalized polarizabilities within a relativistic constituent quark model

Nucleon generalized polarizabilities are investigated within a relativistic framework, defining such quantities through a Lorentz covariant multipole expansion of the amplitude for virtual Compton scattering. The key physical ingredients in the calculation of the nucleon polarizabilities are the Lorentz invariant reduced matrix elements of the electromagnetic transition current, which can be evaluated from off-energy-shell helicity amplitudes. The evolution of the proton paramagnetic polarizability, $\beta_{para}(q)$, as a function of the virtual-photon three-momentum transfer $ q,$ is explicitly evaluated within a relativistic constituent quark model by adopting transition form factors obtained in the light-front formalism. The discussion is focussed on the role played by the effects due to the relativistic approach and to the transition form factors, derived within different models.

Zero-mode contribution to the light-front Hamiltonian of Yukawa-type models

The light-front Hamiltonian for Yukawa-type models is determined without the framework of canonical light-front formalism. Special attention is paid to the contribution of zero modes. We find that zero modes lead to additional contributions in comparison with the naive canonical light-front Hamiltonian. The structure of such terms is discussed in detail.

Finiteness conditions for light-front Hamiltonians

In the context of simple models, it is shown that demanding finiteness for physical masses with respect to a longitudinal cutoff, can be used to fix the ambiguity in the renormalization of fermions masses in the Hamiltonian light-front formulation. Difficulties that arise in applications of finiteness conditions to discrete light-cone quantization are discussed.